ELEMENTS 

OF 

HEAT-POWER  ENGINEERING 


*  ELEMENTS 

OF 

HEAT- POWER    ENGINEERING 


BY 

C.  F.  HIRSHFELD,  M.M.E. 

Formerly  Professor  of  Power  Engineering,  Sibley  College, 
Cornell  University,  Ithaca,  N.  Y. 

AND 

WM.  N.  BARNARD,  M.E. 

Professor  of  Power  Engineering,  College  of  Engineering, 
Cornell  University,  Ithaca,  N.  Y. 


SECOND  EDITION,  REVISED 
TOTAL  ISSUE,  SEVENTEEN  THOUSAND 


NEW  YORK 

JOHN    WILEY   &    SONS,   INC. 
LONDON  :  CHAPMAN  &  HALL,  LIMITED 


COPYRIGHT,  1912,  1915 

BY 
C.  F.  HIRSHFELD 

AND 

W.  N.  BARNARD 


7 


BRAUNWORTH  ft  CO. 

7/24  COOK  MANUFACTURERS 

BROOKLYN,   N.  Y. 


PREFACE 


IN  preparing  this  textbook  the  Authors  have  attempted  to 
include  in  a  single  volume  not  only  the  elementary  thermo- 
dynamic  theory  of  gases  and  vapors  and  of  their  cycles,  but  also 
the  consideration  of  the  sources  of  heat,  the  methods  of  making 
it  available  for  useful  purposes,  its  utilization  in  the  various  types 
of  heat-driven  prime  movers  and  their  auxiliary  apparatus, 
together  with  a  discussion  of  the  fundamental  theory,  the  ideal 
and  actual  performance  and  the  practical  considerations  con- 
nected with  such  apparatus.  The  book  is  prepared  primarily  for 
the  use  of  students  in  Mechanical  Engineering  in  their  junior 
and  senior  years,  after  they  have  completed  college  courses  in 
physics,  chemistry,  analytical  and  applied  mechanics  and  empir- 
ical machine  design.  The  text  is  supposed  to  be  supplemented  by 
lectures,  lantern  slides,  a  study  of  trade  catalogues  and  collateral 
reading;  and,  as  it  is  prepared  primarily  for  students  who  will 
have  separate  courses  in  mechanical  laboratory  practice  and  in 
the  economic  problems  connected  with  heat-power  engineering, 
but  little  relating  to  these  branches  is  given. 

A  large  part  of  the  material  contained  in  the  following  pages 
has  been  used  during  the  last  four  years,  first  in  pamphlet 
and  later  in  book  form,  as  a  text  in  the  junior  and  senior  courses 
in  Sibley  College,  Cornell  University.  It  has  been  revised  from 
time  to  time  as  the  necessity  became  apparent,  and  now  the 
original  matter  has  been  practically  rewritten,  rearranged  and 
considerably  amplified  for  the  present  book. 

To  add  to  its  convenience  and  value  as  a  textbook  in  recita- 
tion courses,  all  sections  are  numbered,  the  sub-paragraphs  are 
lettered,  and  sample  problems  are  given  in  the  Appendix. 

Undoubtedly  errors  of  various  kinds  will  be  discovered,  and 
in  order  that  they  may  be  eliminated  it  is  hoped  that  they  will 
be  brought  to  the  attention  of  the  Authors,  who  will  also  welcome 
any  other  suggestions  for  the  improvement  of  the  book. 


iV  PREFACE 

The  Authors  express  grateful  acknowledgment  of  their  in- 
debtedness to  Professor  A.  W.  Smith,  Director  of  Sibley  College, 
for  many  helpful  suggestions  and  criticisms  during  the  inception 
and  progress  of  this  work,  and  to  Assistant  Professor  Ellenwood 
who  prepared  a  large  number  of  the  appended  problems. 

They  desire  to  extend  their  thanks  to  Professor  Lionel  S. 
Marks  and  to  Dr.  Harvey  N.  Davis,  and  their  publishers, 
Longmans,  Green  &  Co.,  for  permission  to  use  an  abstract  of 
their  steam  tables,  and  to  Professor  Cecil  H.  Peabody  and  John 
Wiley  and  Sons  for  permission  to  use  a  reduced  and  modified 
drawing  based  on  the  former's  temperature-entropy  chart. 
Thanks  are  also  due  the  following  members  of  the  Sibley  Col- 
lege instructing  staff  for  valuable  assistance:  Messrs.  H.  M. 
Parmley,  T.  C.  Ulbricht,  and  R.  Matthews;  and  to  F.  A.  Burr, 
formerly  Assistant  Professor  in  the  College. 

July  i,  1912. 


PREFACE   TO    SECOND   EDITION 


SINCE  the  appearance  of  the  First  Edition  of  this  book,  Pro- 
fessor Ellenwood  has  published  some  very  valuable  and  extensive 
steam  charts  which  have  a  much  wider  field  of  application  and 
greater  accuracy  than  have  any  of  the  Mollier  Charts  that  have 
appeared.  The  present  edition  includes  a  discussion  of  these 
important  new  charts  and  to  the  Appendix  has  been  added  a 
small  two  page  Ellenwood  chart  redrawn  from  the  original  ones, 
covering  twelve  pages.  The  other  changes  in  this  edition  consist 
of  a  number  of  minor  corrections  and  a  few  additions. 

The  authors  desire  to  express  to  Professor  Ellenwood  their 
appreciation  of  the  privilege  of  introducing  the  new  charts;  and 
they  desire  to  thank  him  and  also  Professor  Matthews  and 
Mr.  C.  H.  Berry  for  many  valuable  suggestions. 

August  i,  1915. 


CONTENTS. 


PAGE 


1.  INTRODUCTORY xv 

CHAPTER  I.  —  HEAT i 

2.  Heat  a  Form  of  Energy.     3.   Unit  of  Heat  Energy.     4.   Solar  Heat. 

5.   Heat  from  Mechanical  Energy.     6.   Heat  from  Electrical  Energy. 
7.   Heat  from  Chemical  Combination. 

CHAPTER  II.  —  ELEMENTARY  LAWS  OF  HEAT  ENERGY 6 

8.  Conservation  of  Energy.  9.  Ideal  Mechanisms.  10.  The  Second 
Law  of  Thermodynamics,  n.  Distribution  of  Associated  Heat 
Energy.  12.  Specific  Heat.  13.  Total  Associated  Heat. 

CHAPTER  III.  —  THE  HEAT-POWER  PLANT 16 

14.    General.     15.   The    Steam-power    Plant.      16.   The     Producer    Gas- 
power  Plant.     17.   Analogy.     18.   Further  Study. 

CHAPTER  IV.  —  THE  LAWS  OF  GASES 28 

19.  States  of  Aggregation  of  Substances.  20.  The  Ideal  Laws  of  Condi- 
tion of  Gases.  21.  The  Specific  Heats  of  Ideal  Gases.  22.  Constant- 
volume  Specific  Heat  of  Ideal  Gas.  23.  Constant-pressure  Specific 
Heat.  24.  The  Ratio  7.  25.  Table  of  Gas  Constants. 

CHAPTER  V.  —  EXPANSIONS  AND  COMPRESSIONS  OF  GASES 43 

26.  Volume  Changes.  27.  Isobaric  Changes  of  Gases.  28.  Isovolumic 
Changes  of  Gases.  29.  Isothermal  Changes  of  Gases.  30.  Adia- 
batic  Volume  Changes  of  Gases.  31.  General  Expression  for  Volume 
Changes.  32.  Construction  of  Lines  Representing  Volume  Changes. 

CHAPTER  VI.  —  REVERSIBILITY 59 

33.  Definition.  34.  Some  Reversible  Processes.  35.  Some  Irreversible 
Processes. 

CHAPTER  VII.  —  ENTROPY 65 

36.  Explanatory.  37.  Definition.  38.  Entropy  Changes  for  Reversible 
Processes  with  Ideal  Gases.  39.  Sign  of  Entropy  Changes  during 
Reversible  Processes.  40.  Reversible  Isobarics  of  Gases.  41.  Revers- 
ible Isovolumics  of  Gases.  42.  Reversible  Isothermals  of  Gases. 
43.  Reversible  Adiabatics  of  Gases.  44.  Irreversible  Adiabatic  Proc- 
esses of  Ideal  Gas,  and  the  Corresponding  Entropy  Changes.  45.  En- 
tropy Changes  Independent  of  Path.  46.  Temperature-entropy 
Diagrams. 

V 


VI  CONTENTS 

PAGB 

CHAPTER  VIII.  —  GAS  CYCLES 76 

47.  Definition  of  a  Cycle.  48.  Diagram  of  a  Cycle.  49.  The  Carnot 
Cycle  for  Gases.  50.  All  Reversible  Engines  Have  the  Same  Efficiency 
as  the  Carnot  Engine.  51.  Comparison  of  Carnot  Engine  and  Real 
Engine.  52.  T<£-Diagram  of  Carnot  Cycle.  53.  Criterion  of  Maxi- 
mum Efficiency.  54.  The  Constant-volume  Regenerative  or  Stirling 
Cycle.  55.  The  Constant-pressure  Regenerative,  or  Ericsson  Cycle. 

56.  Constant-volume  Heat-change,  Otto,  or  Beau  de  Rochas  Cycle. 

57.  Constant-pressure  Heat-addition,  Brayton,  or  Joule  Cycle.     58. 
Diesel  Cycle. 

CHAPTER  IX.  —  VAPORS 103 

59.  Vapors  and  Gases.  60.  Formation  of  Vapor.  61.  Heat  of  the  Liquid. 
62.  Latent  Heat  of  Vaporization.  63.  Total  Heat  per  Pound  of 
Vapor.  64.  Saturated  Vapor.  65.  Quality  66.  Superheated 
Vapor.  67.  Heat  per  Pound  of  Superheated  Vapor.  68.  Diagram  of 
Heat  Changes  during  Vaporization.  69.  Vapor  Tables.  70.  Satura- 
ation  Curve.  71.  Defining  Conditions  for  Saturated  Vapors. 
72.  Evaporation.  73.  Boiling.  74.  Temperature-entropy  Changes 
of  Vapors.  75.  Continuity  of  the  Liquid  and  Gaseous  States. 
76.  Van  der  Waals'  Equation  for  Real  Gases. 

CHAPTER  X.  —  PROPERTIES  or  STEAM 126 

77.  Steam  or  Water  Vapor.  78.  Sources  of  Data.  79.  Properties  of 
Dry  Saturated  Steam.  80.  Properties  of  Superheated  Steam. 
81.  Temperature-entropy  Chart  for  Water  and  Steam.  82.  Mollier 
Chart.  82A.  Ellenwood  Chart.  828.  External-work  Chart. 

CHAPTER  XI.  —  VOLUME  CHANGES  or  VAPORS 146 

83.  General.  84.  Constant-pressure  and  Isothermal  Volume  Changes  for 
Saturated  Vapors.  85.  Constant-pressure  Volume  Changes  of  Super- 
heated Vapors.  86.  Isothermal  Volume  Changes  of  Superheated 
Vapors.  87.  Adiabatic  Changes  of  Saturated  Vapors.  88.  Adiabatic 
Changes  of  Superheated  Vapors.  89.  Constant-volume  Changes  of 
Saturated  Vapors.  90.  Constant-volume  Changes  of  Superheated 
Vapors. 

CHAPTER  XII.  —  VAPOR  CYCLES 161 

91.  Carnot  Cycle  with  Dry  Saturated  Steam.  92.  The  Carnot  Cycle 
with  Any  Vapor.  93.  Clausius  Cycle  with  Dry  Saturated  Water 
Vapor.  94.  The  Clausius  Cycle  in  General.  95.  The  Rankine  Cycle. 
96.  The  Rankine  Cycle  in  General.  97.  Cycle  with  Rectangular  PV- 
diagram.  98.  The  Rectangular  PV-cycle  in  General. 

CHAPTER  XIII.  —  POWER,  EFFICIENCY,  AND  PERFORMANCE 180 

99.  Power.  100.  Distinction  between  Real  and  Ideal  Engines.  101.  The 
Indicator.  102.  The  Indicator  Diagram.  103.  Methods  of  Deter- 
mining the  Area  of  an  Indicator  Diagram.  104.  Delivered  Power. 
105.  Efficiencies.  106.  Engine  Performance. 


CONTENTS  Vii 

PAGE 

CHAPTER  XIV.  —  THE  THEORETICAL  STEAM  ENGINE 19<> 

107.  General.  108.  The  Carnot  Cycle  and  the  Steam  Engine.  109.  The 
Regenerative  Steam-engine  Cycle.  no.  The  Clausius  Cycle, 
in.  The  Rankine  Cycle.  112.  Clearance  and  Compression.  113. 
Cushion  Steam  and  Cylinder  Feed.  114.  Saturation  and  Quality 
Curves. 

CHAPTER  XV.  —  ACTION  OF  STEAM  IN  REAL  ENGINES 208 

115.  Cylinder  and  Thermal  Efficiencies  of  the  Steam  Engine.  116.  Act- 
ual Behavior  of  Steam  in  an  Engine  Cylinder.  117.  Diagrammatic 
Representation  of  the  Heat  Interchange  in  the  Cylinder.  118.  Deriv- 
ation of  a  T</>-diagram  from  a  PV-diagram.  119.  Hirn's  Analysis. 
1 20.  Experimental  Determination  of  the  Actual  Performance  of  Steam 
Engines.  121.  Steam  Calorimeters.  122.  Weight  of  Steam  Ac- 
counted for  by  the  Indicator  Diagram. 

CHAPTER  XVI.  —  METHODS  or  DECREASING  CYLINDER  CONDENSATION.  230 
123.  Condensation  and  Leakage.  124.  Size  and  Proportions  of  Cylinder. 
125.  Influence  of  Point  of  Cut-off.  126.  Compounding  of  Cylinders. 
127.  Gain  Due  to  Condensing  the  Exhaust  Steam.  128.  Effect  of 
Superheated  Steam.  129.  Use  of  Steam  Jackets.  130.  Reheating 
Receivers.  131.  Other  Methods  of  Reducing  Cylinder  Condensation. 

CHAPTER  XVII.  —  STEAM  ENGINES. 244 

132.    Steam-engine  Parts.     133.    Classification  and  Types  of  Steam  Engines. 

CHAPTER  XVIII.  —  STEAM-ENGINE  GOVERNORS 255 

134.  Governing.  135.  Governing  of  Steam  Engines.  136.  Governors. 
137.  Pendulum  Governors.  138.  Spring-balanced  Fly-ball  Governor. 
139.  Elementary  Shaft  Governors.  140.  Commercial  Types  of  Shaft 
Governors. 

CHAPTER  XIX.  —THE  VALVE  GEARS  OF  STEAM  ENGINES 271 

141.  Introduction.  142.  The  Engine  —  Definitions.  143.  The  Valve  — 
Definitions.  144.  Action  of  the  D-valve  and  Eccentric.  145.  Rela- 
tive Valve  and  Piston  Positions.  146.  Elliptical  Diagram.  147.  The 
Sweet  Diagram.  148.  Zeuner  Diagram.  149.  Bilgram  Diagram. 
150.  Distortion  Due  to  Angularity  of  the  Connecting  Rod.  151.  Valve 
Diagrams  Considering  "Angularity"  of  the  Connecting  Rod.  152. 
Valve  and  Port  Openings.  153.  Cushioning  the  Reciprocating  Parts. 
154.  Early  Valve  Opening.  155.  Limitations  of  the  Simple  Valve. 
156.  Special  Types  of  Single  Valves.  157.  Valve  Gears  for  High- 
speed Engines.  158.  General  Characteristics  of  Independent  Cut-off 
Gears.  159.  Independent  Cut-off  Valve  with  Stationary  Seat. 
160.  Riding  Cut-off  Valves.  161.  Gears  with  Oscillating  Valves. 
162.  Link  Gears.  163.  Radial  Valve  Gears.  164.  Poppet  Valves 
and  Their  Gears. 


Vlii  CONTENTS 

PAGE 

CHAPTER  XX.  —  CONVENTIONAL  INDICATOR  DIAGRAM 323 

165.  Conventional  Diagram  for  Simple  Engines.  166.  Diagrams  for  Mul- 
tiple-expansion Engines.  167.  Diagrams  of  Woolf  Type  of  Engine. 
168.  Diagrams  for  Engines  with  Infinite  Receivers  and  No  Clearance 
(General).  169.  Receiver  Pressures  in  Compound  Engines.  170. 
Cylinder  and  Expansion  Ratios  Used  in  Multiple-expansion  Engines. 
171.  The  Theoretical  Indicator  Diagrams  of  Multiple-expansion 
Engines  with  Clearance.  172.  Effects  of  Changing  the  Cut-offs  in  the 
Respective  Cylinders  of  Multiple-expansion  Engines.  173.  Theoreti- 
cal PV-diagrams  of  a  Tandem  Compound  Engine.  174.  Theoretical 
PV-diagrams  of  a  Cross  Compound  Engine.  175.  Theoretical  PV- 
diagrams  of  Multiple-expansion  Engines  (General  Case).  176.  The 
Actual  Combined  Indicator  Diagrams  of  Multiple-expansion  Engines. 
1 76 A.  Clayton's  Analysis  of  Expansion  Lines. 

CHAPTER  XXI.  —  PERFORMANCE  OF  STEAM  ENGINES 353 

177.   Steam  Consumption.     178.   Steam-engine  Performance  (Data). 

CHAPTER  XXII.  —  STEAM  TURBINES   359 

179.  introductory.  180  Thermodynamics  of  the  Ideal  Steam  Turbine. 
181.  Thermodynamics  of  Actual  Turbines.  182.  The  Dynamics  of 
Impulse  Steam  Turbines.  183.  De  Laval  Type  of  Single-Stage  Tur- 
bine. 184.  Pelton  Type  of  Steam  Turbine.  185.  Rateau  Type  of 
Steam  Turbine.  186.  Curtis  Type  of  Steam  Turbine.  187.  Veloc- 
ity Compounding  with  a  Single  Row  of  Rotating  Buckets.  188.  Re- 
action Turbines.  189.  Applications  of  the  Steam  Turbine.  190. 
Advantages  and  Disadvantages  of  the  Steam  Turbine.  191.  Steam 
Turbine  Performance. 

CHAPTER  XXIII.  —  EXTERNAL  COMBUSTION  GAS  ENGINES 397 

192.  Definition.  193.  The  Hot-Air  Engine.  194.  Rider  Hot-Air  En- 
gine. 195.  Ericsson  Hot-Air  Engine. 

CHAPTER  XXIV.  —  INTERNAL  COMBUSTION  ENGINES.       METHODS  OF 

OPERATION 403 

196.  Advantages  and  Types.  197.  Cylinder  Operations  of  Four-Stroke 
Otto  Cycle.  198.  The  Air  Card.  199.  Real  Indicator  Card  for 
Four-Stroke  Cycle.  200.  Losses  in  the  Four-Stroke-Cycle  Engine. 
aoi.  Requirements  for  High  Efficiency  of  Combustion.  202.  Indi- 
cated Work  and  Power  of  the  Four-Stroke-Cycle  Engine.  203.  The 
Two-Stroke-Cycle  Otto  Engine.  204.  The  Diesel  Engine.  205. 
Modifications  to  Suit  Different  Fuels.  206.  Compression  and  Maxi- 
mum Pressures. 

CHAPTER  XXV.  —  INTERNAL   COMBUSTION   ENGINES.         MECHANICAL 

FEATURES 420 

207.  Cylinder  Arrangement.  208.  Classification.  209.  Methods  of 
Producing  Combustible  Mixtures.  210.  Carburetors.  211.  Treat- 
ment of  Heavy  Oils.  212.  Methods  of  Governing  Internal-Comb  us- 


CONTENTS  ix 

tion  Engines.  213.  Gas  Valves,  Mixing  Valves,  etc.  214.  Methods 
of  Ignition.  215.  Hot-Tube  Ignition.  216.  Spontaneous  Ignition. 
217.  Electric  Ignition.  218.  Internal-Combustion  Engine  Valve 
Gear. 

CHAPTER  XXVI.  —  INTERNAL-COMBUSTION    ENGINES.          EFFICIENCY, 

PERFORMANCE  AND  POWER 443 

219.  Efficiencies  of  Otto  Four-Stroke-Cycle  Engine.  220.  Efficiencies  of 
Otto  Four-Stroke-Cycle  Engines.  221.  Heat  Balance  for  Gas  En- 
gines. 222.  Performance  of  Internal-Combustion  Engines. 

CHAPTER  XXVII.  —  FUELS 455 

223.  Fuels.  224.  Geology  of  Coal.  225.  Composition  of  Coal.  226. 
Coal  Analyses.  227.  Fuel  Values  of  Coals.  228.  Coke.  229. 
Wood.  230.  Municipal  and  Industrial  Waste.  231.  Natural  Oil  and 
Its  Products.  232.  Alcohol.  233.  Natural  Gas.  234.  Artificial 
Gases. 

CHAPTER  XXVIII.  —  COMBUSTION 472 

235.  Definitions.  236.  Combustion  of  Carbon.  237.  Weights  of  Oxy- 
gen and  Air  Necessary  for  Combustion  of  Carbon.  238.  Volumes  of 
Gases  Involved  in  Combustion  of  Carbon.  239.  Temperature  of 
Combustion.  240.  Combustion  of  Hydrogen.  241.  Hydrocarbons. 
242.  Combustion  of  Sulphur.  243.  Combustion  of  Mixture  of  Ele- 
ments. 244.  Fuel  Calorimeters  and  Heat  Value.  245.  Flue  Gas 
Analysis.  246.  Weight  of  Flue  Gases.  247.  Percentage  of  Excess 
Air.  248.  Stack  Losses. 

CHAPTER  XXIX. —  ACTUAL  COMBUSTION  OF  FUELS  —  FURNACES  AND 

STOKERS  —  OIL  BURNERS 503 

249.  Introductory.  250.  Air  Supply.  251.  Conditions  for  Complete 
and  Smokeless  Combustion.  252.  Value  of  Coal  as  Furnace  Fuel. 
253.  Burning  Powdered  Coal.  254.  Selection  and  Purchase  of  Coal. 
255.  Furnace  Operation.  256.  Grates  and  Furnaces.  257.  Auto- 
matic Mechanical  Stokers.  258.  Burning  Liquid  Fuel.  258A.  Burn- 
ing Gaseous  Fuels. 

CHAPTER  XXX.  —  BOILERS 533 

259.  Losses  Connected  with  Steam  Generation.  260.  Efficiencies  Con- 
nected with  Steam  Generation.  261.  Boiler  Heating  Surface  and 
Heat  Transmission.  262.  Boiler  Explosions.  263.  Selection  of 
Boilers.  264.  Classification  of  Boilers.  265.  Internally  Fired  Tu- 
bular Boilers.  266.  Externally  Fired  Tubular  Boilers.  267.  Water 
Tube  Boilers.  268.  Boiler  Accessories.  269.  Boiler  Performance. 
270.  Proportioning  the  Boiler  for  Power  Output. 

CHAPTER  XXXI.  —  SUPERHEATERS 5^5 

271.  Advantages  of  Superheating.  272.  Types  of  Superheaters.  273. 
Separately  Fired  Superheaters.  274.  Boiler  Draft  Superheaters. 
275.  Protection  of  Superheater.  276.  Superheater  Surface. 


X  CONTENTS 

CHAPTER  XXXII.  —  DRAFT  AND  DRAFT  APPARATUS 

277.  General  Principles.  278.  Amount  of  Pressure  Drop  Required. 
279.  Chimney  Draft.  280.  Artificial  Draft. 

CHAPTER  XXXIII.  —  GAS  PRODUCERS  AND  PRODUCER  GAS 590 

281.  Essentials  of  Producer-Gas  Apparatus.  282.  Simple  Theory  of  Pro- 
ducer Action.  283.  Efficiency,  Simple  Producer  Action.  284.  More 
Advanced  Theory  of  Producer  Action.  285.  Practical  Limitations. 
286.  Artificial  Cooling  of  Producers  (General).  287.  The  " Carbon 
Monoxide  "  Method  of  Temperature  Control.  288.  The  Water  Vapor 
Method  of  Temperature  Control.  289.  Effects  of  Hydrocarbons  \\. 
Fuels.  290.  Water  Bottom  and  Grate  Bottom  Producers.  291. 
Induced  Draft  and  Forced  Draft.  292.  Mechanical  Charging.  293, 
Cleaning  Apparatus.  294.  Producer  Gas  from  Oil. 

CHAPTER  XXXIV.  —  UTILIZATION  OF  WASTE  HEAT  —  FINANCIAL  CON- 
SIDERATIONS       619 

295.  General.  296.  Utilization  of  the  Heat  in  the  Flue  Gases.  297. 
Utilization  of  the  Heat  in  the  Exhaust  Steam.  298.  Heat  Transmis- 
sion. 299.  Financial  Considerations. 

CHAPTER  XXXV.  —  HEAT  TRANSFER 624 

300.  General.  301.  Heat  Conduction.  302.  Heat  Transfer  by  Convec- 
tion. 303.  Heat  Transfer  by  Radiation.  304.  Heat  Transfer  by 
Engineering  Apparatus.  305.  Effectiveness  of  Heat  Transmitting 
Surfaces.  306.  Cases  of  Heat  Transmission  through  Plates.  307. 
Case  I.  (T  =  Const.)  A  Hot  Substance  at  Constant  Temperature 
Surrenders  Heat  to  a  Cold  Fluid  which  Flows.  308.  Case  II.  (/  = 
Const.)  A  Substance  at  Constant  Temperature  (/)  Receives  Heat 
from  Another  Flowing  Substance  whose  Temperature  Decreases. 
309.  Case  III.  Parallel  Flow  in  the  Same  Direction.  310.  Case 
IV.  Counterflow.  311.  Case  V.  (T  =  const,  and  I  =  const.)  A 
Hot  Substance  Surrenders  Heat  at  Constant  Temperature  to  a  Cold 
Substance  whose  Temperature  is  Constant. 

CHAPTER  XXXVI.  —  APPARATUS  FOR  HEATING  FEED  WATER 651 

312.  Object  of  Heating  Feed  Water.  313.  Feed- Water  Heaters  in  Gen- 
eral. 314.  Open  Heaters.  315.  Closed  Heaters.  316.  Econo- 
mizers. 

CHAPTER  XXXVII.  —  CONDENSERS  AND  RELATED  APPARATUS 664 

317.  Advisability  of  Condensing.  318.  Condensers  in  General.  319. 
Contact  Condensers.  320.  Surface  Condensers.  321.  Air  Pumps. 
322.  Recovery  of  Condensing  Water. 

CHAPTER  XXXVIII.  —  WATER  PURIFICATION 685 

323.  Impurities  in  Natural  Waters.  324.  Troubles  from  Untreated  Feed 
Water.  325.  Methods  of  Treating  Feed  Waters. 


CONTENTS  XI 

PAGE 

CHAPTER  XXXIX.  —  POWER  PLANTS ; 690 

326.  General.  327.  Internal  Combustion  Engine  Plants.  328.  Steam 
Power  Plants. 

CHAPTER  XL.  —  CONTINUOUS  FLOW  OF  GASES  AND  VAPORS  THROUGH 

ORIFICES  AND  NOZZLES 698 

329.  Introductory.  330.  Flow  of  Saturated  Steam  in  the  Ideal  Case. 
331.  The  Ideal  Steam  Nozzle.  332.  Actual  Steam  Nozzles.  333. 
Empirical  Formulas  for  the  Flow  of  Steam  through  Orifices.  334. 
Flow  of  Steam  through  Pipes.  335.  Application  of  Steam  Nozzles. 
336.  Perfect  Flow  of  Ideal  Gases.  337.  Imperfect  Flow  of  Gases. 

CHAPTER  XLI.  —  COMPRESSED  AIR 716 

338.  Definitions.  339.  Elementary  Air  Compressor.  340.  Work  Done 
in  Compressor.  341.  The  Effect  of  Clearance.  342.  Real  Single 
Stage  Compressor  Diagram.  343.  Volumetric  Efficiency.  344. 
Cooling  During  Compression.  345.  Blowing  Engines.  346.  Tur- 
bine Compressors.  347.  Compressed  Air  Engines.  348.  Com- 
pressed Air  Engine  Cycles.  349.  Preheating. 

CHAPTER  XLII.  —  REFRIGERATION 734 

350.  Definition.  351.  Thermodynamics  of  Refrigeration.  352.  The  Air 
Refrigerating  Machine.  353.  Vapor  Compression  Process  of  Refrig- 
eration. 354.  Relative  Advantages  of  Different  Vapors.  355.  The 
Ammonia  Absorption  Process.  356.  Rating  of  Refrigerating  Ma- 
chines. 

PROBLEMS : 749 

APPENDIX 780 

TABLES..  xiii 


TABLES. 


TABLE  PAGE 

I.  —  Gas  Constants 40 

II.  —  Collected  P,  V,  T,  Formulas  for  Volume  Changes  of  Gases. .  58 

III.  —  Gas  Cycles 102 

IV.  —  Usual  Gage  Pressures 241 

V.  —  (i  -f  log*  r)  -T-  r 325 

VI.  —  Diagram  Factors 325 

VII.  —  Summary  of  Performances  of  Steam  Engines 355 

VIII.  —  Summaries  of  Efficiencies  of  Steam  Engines 358 

IX.  —  Steam  Consumptions  of  Steam  Engines . , 358 

X.  —  Steam-Turbine  Performance 395 

XI.  —  Common  Compression  Pressures 419 

XII.  —  Efficiencies  of  Otto  Four-Stroke  Cycle  Engines 443 

XIII. — Old  Classification  of  Coals J 457 

XIV.  —  Parr's  Classification  of  Coals  (Abbrev.) 458 

XV.  —  Ultimate  Analyses  of  Coals 460 

XVI.  —  Commercial  Sizes  of  Soft  Coal 465 

XVII.  —  Sizes  of  Anthracite  Coal 466 

XVIII.  —  Typical  Analyses  of  Natural  Gas 470 

XIX.  —  Combustion  Data 473 

XX.  —  Properties  of  Air 477 

XXI.  —  Flue  Gas  Constants 479 

XXII.  —  Flue  Gas  Constants 481 

XXIII.  —  Calorific  Values  of  Hydrocarbons 491 

XXIV.  —  Pressure  Drops  through  Boilers 578 

XXV.  —  Typical  Analyses  of  Producer  Gases 602 

XXVI.  —  Specific  Conductivity  of  Various  Materials 628 


xiii 


INTRODUCTORY. 


I.  The  advancement  of  the  human  race  has  been  largely  due 
to  the  fact  that  man  has  greater  ability  than  his  fellow  creatures 
to  utilize  nature's  resources.  At  first  he  was  driven  by  his  own 
weakness  to  seek  nature's  aid  for  protection,  and  he  thus  became 
familiar  with  her  simpler  laws.  This  knowledge  grew  steadily 
and  after  a  time  was  recorded.  Now  the  accumulated  informa- 
tion is  too  great  to  be  grasped  by  any  individual  or  group  and  it 
has  become  necessary  to  specialize.  One  group  of  specialists,  the 
scientists,  continue  to  delve  after  nature's  secrets  in  order  to  add 
to  the  store  of  human  knowledge;  another  group,  the  engineers, 
work  to  make  application  of  discovered  laws  to  meet  the  needs 
of  humanity. 

The  engineer  must  know  nature's  laws  and  must  be  familiar 
with  their  applications  in  order  that  he  may  be  able  to  aid  the 
race  in  the  development  and  improvement  of  its  life.  One  of  the 
most  important  of  his  problems  results  from  the  fact  that  man's 
body  cannot  supply  the  power  required  to  carry  out  the  con- 
ceptions of  his  mind.  To  solve  this  problem  the  engineer  draws 
on  nature's  store  of  energy. 

In  general,  the  energy  of  nature's  store  is  not  directly  available 
for-  human  uses ;  it  must  be  changed  in  kind  or  quality,  trans- 
mitted through  space,  and  made  available  at  times  of  demand. 
The  engineer  must  provide  means  for  effecting  these  results. 

One  of  the  best  examples  of  such  changes  is  furnished  by  the 
conversion  of  heat  energy  into  the  mechanical  form  by  means  of 
Heat  Engines.  Since  the  world  demands  enormous  supplies  of 
mechanical  energy,  this  sort  of  conversion  is  of  great  impor- 
tance, because  of  the  fact  that  immense  stores  of  easily  trans- 
portable fuel  are  distributed  over  the  earth  near  its  surface. 
This  fuel  has  latent  heat  energy,  which  may  be  easily  converted 
into  available  heat  energy  by  combustion.  It  is  then  the  duty 
of  the  heat  engine  to  convert  as  large  a  part  as  possible  of  this 

^  xv 


XVI  INTRODUCTORY 

available  heat  energy  into  the  more  desirable  form  of  mechanical 
energy. 

The  following  pages  are  devoted  to  a  consideration  of  trans- 
formations of  latent  heat  in  fuel  into  available  heat,  and  of  avail- 
able heat  into  mechanical  energy,  together  with  a  study  of  the 
devices  by  which  the  transformations  are  effected. 

The  theory  of  these  transformations  is  called  Thermodynamics, 
while  the  whole  subject,  theoretical  and  practical,  may  be  called 
Heat-Power  Engineering. 


HEAT-POWER    ENGINEERING. 


CHAPTER   I. 

HEAT. 

2.  Heat  a  Form  of  Energy.     It  has  been  shown  experimentally 
that  heat  can  be  produced  by  the  expenditure  of  other  forms 
of  energy,  and  that  other  forms  of  energy  can  be  produced 
by  the  expenditure  of  heat.     Therefore  the  conclusion  that  heat 
is  a  form  of  energy  is  justified. 

All  bodies  that  man  knows  possess  heat  energy,  "  associated 
heat";  whatever  the  material  or  state  of  a  body  may  be,  it  is 
possible  to  obtain  heat  energy  from  it.  It  is  not  known  how  this 
heat  energy  is  stored  in  matter,  but  it  is  certainly  possible,  and 
it  seems  probable,  that  it  is  in  some  way  associated  with  the 
motions  and  relative  positions  of  the  constituent  particles.  Be- 
yond this  it  is  not  necessary  to  generalize  here  in  the  present  state 
of  knowledge. 

3.  Unit   of   Heat   Energy.      The    unit   of   measurement   of 
energy  is  based  upon  some  effect  produced  by  the  kind  of  energy 
to  be  measured.     Under  certain  conditions  a  rise  in  temperature 
of  a  body  is  one  of  the  most  obvious  phenomena  connected  with 
an  increase  of  associated  heat;  and,  as  the  extent  of  this  effect 
may  be  measured,  it  is  used  as  the  basis  of  the  unit  of  heat 
energy. 

In  English-speaking  countries  the  unit  of  heat  energy  is 
known  as  the  British  Thermal  Unit  (B.t.u.)  and  is  defined  as 
follows : 

The  British  Thermal  Unit  is  the  quantity  of  heat  required  to 
raise  the  temperature  of  one  pound  of  pure  water  one  Fahrenheit 
degree. 

*    When  extreme  accuracy  is  desired  it  is  necessary  to  specify 
the  point  on  the  temperature  scale  at  which  the  one-degree  rise 


HEAT-POWER  ENGINEERING 


takes  place,  as  it  requires  slightly  different  amounts  of  heat  at 
different  temperatures.  This  temperature  is  usually  taken  either 
at  39.1°  F.,  at  which  water  has  maximum  density,  or  at  62°  F.* 

For  ordinary  engineering  purposes,  however,  it  is  customary 
and  sufficiently  accurate  to  consider  the  heat  corresponding  to 
one-degree  rise  as  constant  throughout  the  scale.  Hence  the 
definition  given  serves  for  the  engineer. 

What  has  been  termed  a  "  mean  B.t.u."  is  also  used.  It  is 
defined  as  Ti&th  of  the  heat  required  to  raise  the  temperature  of 
one  pound  of  pure  water  from  32°  to  212°  F.  The  difference 
between  this  mean  B.t.u.  and  the  one  defined  is  negligible  in 
most  engineering  computations. 

Sources  of  Heat. 

4.  Solar  Heat.  Heat  for  human  use  probably  all  conies, 
directly  or  indirectly,  from  the  sun.  This  heat  is  applied 
directly  to  produce  a  sufficiently  high  temperature  on  portions 
of  the  earth's  surface  to  render  plant  growth  and  animal  life 
possible. 

Heat  engines  have  been  built  which  convert  heat  derived 
directly  from  the  sun  into  mechanical  energy;  but,  because  their 
bulk  is  great  in  proportion  to  the  energy  transformed,  and  be- 
cause the  sun's  rays  are  not  always  available  when  needed, 
they  have  not  as  yet  been  commercially  successful. 

The  energy  of  the  sun's  rays  is  applied  indirectly  through  the 
agency  of  plant  growth  and  geologic  processes  to  produce  stores 
of  fuel  in  the  earth's  crust.  Heat  energy,  indirectly  from  the 
sun,  may  be  evolved  for  human  use  from  this  fuel. 

Also  the  sun's  rays  falling  upon  water  surfaces  cause  evapora- 
tion whereby  heat  is  converted  into  mechanical  energy.  This 
energy  lifts  the  water  vapor,  which  is  again  condensed  and  falls 
upon  the  earth's  surface  as  rain  or  snow.  The  resulting  water 
flowing  to  its  original  level  prepares  the  soil  for  plant  growth; 
it  irrigates  plants  and  turns  water  wheels  to  supply  mechanical 
energy. 

Heat  may  be  derived  from  mechanical  energy,  electrical  energy, 
or  from  the  chemical  combination  of  certain  elements.  In  most 
cases  the  ultimate  source  of  the  energy  is  probably  the  sun. 

*  The  value  59°  F.,  corresponding  to  the  scientist's  15°  C,  is  sometimes  used. 


HEAT  3 

5.  Heat  from  Mechanical  Energy.     Primitive  man  generated 
heat  to  kindle  fires  by  rubbing  two  sticks  together.      The  me- 
chanical  energy   due   to   the   muscular  effort   that   moves   the 
sticks  reappears  as  heat.     This  heat  is  derived  indirectly  from 
the  sun,  since  the  sun's  energy  makes  possible  animal  life  and 
therefore  muscular  effort. 

The  engineer  is  familiar  with  the  production  of  heat  by  machine 
friction.  This  again  is  a  case  of  conversion  of  mechanical 
energy  (indirectly  from  the  sun)  into  heat.  This  is  an  unde- 
sirable conversion,  since  mechanical  energy,  which  should  be 
available  for  useful  purposes,  becomes  useless  heat.  The  same 
change  occurs  when  a  machine  is  retarded  or  stopped  by  a  fric- 
tion brake.  This  is  a  useful  change,  however,  since  mechanical 
energy,  which  cannot  be  used  and  which  may  become  dangerous, 
is.  dissipated  as  heat  and  rendered  harmless. 

In  general,  heat  for  human  use  is  not  derived  from  mechanical 
energy  because  it  may  be  obtained  in  other  ways  more  con- 
veniently and  at  less  cost. 

6.  Heat  from   Electrical   Energy.     The   conversion   of  elec- 
trical energy  into  heat  is  illustrated  by  every  electric  conductor 
that  carries  a  current;  for,  though  the  reason  is  unknown,  heat 
results   whenever    an    electric    current    flows.     This    is    known 
to  the  electrician  as  the  /2^?-loss.     It  is  always  a  loss  if  the 
delivery  of  maximum  electrical  energy  is  the  object  of  the  flow; 
but  it  would  not  be  a  loss  if  heat  were  the  object,  as  in  electric 
furnaces  and  stoves.     Except  for  special  service  electrical  energy 
is  too  expensive  a  source  of  heat. 

7.  Heat    from    Chemical    Combination.     There    is    almost 
always  a  liberation  of  heat  when  substances  combine  chemically. 
In  general,  the  more  violent  the  reaction  and  the  more  stable  the 
compound  formed,  the  greater  the  amount  of  heat  liberated. 
There  are  a  few  combinations  which  are  accompanied  by  heat 
absorption;    but    the    compounds    formed    are    generally    quite 
unstable  at  ordinary  pressures  and  temperatures  and  the  heat 
absorbed  is  usually  quite  small. 

The  physical  chemist  briefly  explains  the  phenomenon  of  heat 
evolution  during  chemical  combination  by  saying  that  chemical 
energy  is  converted  into  heat  energy.  It  is  well,  however,  to 


4  HEAT-POWER  ENGINEERING 

understand  his  more  exact  expression,  which  is  at  times  useful 
to  the  engineer. 

In  every  chemical  system,  or  group  of  systems,  there  is  a  cer- 
tain total  amount  of  "  intrinsic  "  energy.  This  amount  depends 
upon  the  kind  of  system  and  upon  the  physical  condition.  If 
several  such  systems  react  to  form  new  systems,  the  latter  may 
have  a  different  total  quantity  of  intrinsic  energy  from  the  former. 
If  the  intrinsic  energy  of  the  new  system  is  less  than  that  of  the 
other,  energy  must  have  been  liberated;  if  greater,  energy  must 
have  been  absorbed.  Energy  thus  liberated  may  appear  in  one 
or  all  of  its  forms;  but  the  largest  part  of  it  usually  appears  as 
heat. 

Thus  to  supply  heat  by  chemical  combination  it  is  necessary 
to  utilize  systems  that  can  react  to  form  new  systems  with  less 
total  intrinsic  energy. 

To  illustrate,  consider  the  production  of  heat  by  the  combina- 
tion of  carbon  and  oxygen  to  form  carbon  dioxide.  The  total 
intrinsic  energy  of  the  system  of  carbon  molecules  and  of  the 
system  of  oxygen  molecules  is  greater  than  the  intrinsic  energy 
of  the  resulting  system  of  carbon-dioxide  molecules.  This  dif- 
ference is  the  source  of  most  of  the  heat  energy  used  by  the 
engineer. 

It  is  convenient  when  dealing  with  these  changes  to  refer  to 
gaseous  materials  as  standards,  since  the  laws  of  gases  are  sim- 
plest. If  a  unit  weight  of  gaseous  carbon  could  be  combined  with 
gaseous  oxygen  at  some  standard  temperature  and  pressure  to 
form  gaseous  carbon  dioxide,  a  certain  amount  of  energy  would 
be  liberated.  If  some  or  all  of  this  energy  appeared  as  heat,  and 
if  the  reacting  substances  were  insulated  so  that  no  heat  could 
leave  the  system,  the  resulting  carbon  dioxide  would  be  raised 
to  a  high  temperature  and  possibly  to  a  high  pressure.  Then  if 
heat  were  withdrawn  until  the  original  temperature  and  pressure 
were  reached,  the  heat  removed  might  be  called  the  standard 
heat  quantity  due  to  this  reaction.  Gaseous  carbon,  however, 
cannot  be  used  in  these  operations,  only  the  solid  forms  being 
available.  Experience  and  experiment  show  that  to  change  a 
solid  to  a  liquid  or  a  gas  requires  an  expenditure  of  heat.  In 
the  chemical  combination  just  referred  to,  heat  is  absorbed  to 
change  solid  carbon  to  gaseous  carbon,  so  that  the  heat  liberated 
is  less  than  if  gaseous  carbon  bad  been  used;  that  is,  the  heat 


HEAT  5 

liberated  is  less  than  that  which  has  been  called  the  standard 
quantity.  Similarly,  if  the  product  of  the  reaction  were  liquid 
or  solid  at  ordinary  temperatures,  instead  of  a  gas,  the  heat 
withdrawn  to  condense  to  the  liquid  or  solid  form  would  be  added 
to  the  standard  quantity. 

There  will  be  further  discussion  of  these  phenomena  under  the 
head  of  combustion.  They  are  mentioned  here  to  indicate  the 
nature  of  the  engineer's  problem  of  heat  generation. 


CHAPTER  H. 

ELEMENTARY  LAWS  OF  HEAT  ENERGY. 

8.  Conservation  of  Energy,  (a)  It  seems  to  be  one  of  nature's 
great  universal  laws  that  energy  cannot  be  created  or  destroyed. 
Experience  and  experiment  have  tended  to  establish  this  law, 
and  now  there  is  no  reason  to  doubt  that  it  holds  throughout 
the  universe.  This  Law  of  Conservation  of  Energy  may  be 
stated  as  follows:  Energy  cannot  be  created  or  destroyed;  but  all 
forms  of  energy  are  mutually  interconvertible. 

Unfortunately,  the  engineer  has  adopted  no  unit  for  the  meas- 
urement of  quantities  of  energy  that  is  common  to  all  its  forms. 
Each  kind  of  energy  is  measured  in  its  own  unit  of  quantity, 
and  each  unit  was  originally  fixed  independently,  because  of 
convenience  of  measurement.  The  necessity  for  conversion  of 
units  of  one  form  of  energy  into  the  units  of  another  form  was 
disregarded ;  as  a  result  the  constant  for  conversion  is  sometimes 
inconvenient  for  use.  Thus,  for  example,  the  unit  of  mechanical 
energy,  the  foot-pound,  is  about  7}s  of  the  unit  of  heat,  the 
British  thermal  unit;  while  the  unit  of  electrical  energy,  the 
joule,  is  equal  to  0.7373  foot-pounds. 

The  engineer  who  deals  with  heat  engines  is  chiefly  concerned 
with  the  intercon version  of  units  of  heat  and  units  of  mechanical 
energy;  he  must  constantly  use  the  corresponding  conversion 
factor.  The  determination  of  this  factor  requires  very  accurate 
experimentation  with  very  delicate  apparatus,  and  the  most  care- 
ful determinations  yet  made  leave  some  uncertainty  as  to  the 
exact  value.  Pending  more  exact  knowledge,  engineers  com- 
monly use  the  value  778. 

(b)  The  Law  of  Conservation  of  Energy,  when  limited  to 
heat  and  mechanical  energy,  is  called  the  First  Law  of  Thermo- 
dynamics, and  it  may  be  stated  thus: 

Heat  and  mechanical  energy  are  indestructible  and  interconvertible. 
The  relation  of  units  is 

1  B.t.u.  =  778  foot-pounds. 


ELEMENTARY   LAWS  OF   HEAT  ENERGY  7 

In  heat  engines  all  of  the  energy  supplied  as  heat  does  not 
appear  as  mechanical  energy.  This  is  not  because  heat  energy 
is  destroyed,  but  because  part  of  it  escapes  conversion  and  leaves 
the  engine  still  in  the  form  of  heat.  However,  each  B.t.u.  that 
is  converted  is  transformed  into  778  foot-pounds  of  work. 

(c)  In  order  to  do  mechanical  work  there  must  be  motion,  and 
in  all  real  cases  the  motion  meets  with  resistance  of  some  form. 
Anything  that  resists  motion  takes  away  energy;  thus,  friction 
might  take  away  heat;  a  belt  might  take  away  mechanical  energy; 
a  metallic  circuit  might  take  away  electrical  energy;  if  the 
motion  produces  sound,  energy  is  taken  away  as  sound  waves  in 
the  air.  If  any  energy  whatever  were  taken  away,  that  is,  if  there 
were  any  resistance,  and  the  machine  continued  in  motion  without 
continued  energy  supply,  it  would  have  to  give  out  energy  that 
it  did  not  receive. 

It  is,  of  course,  impossible  to  conceive  of,  or  build,  a  machine 
which  will  create  energy.  Such  a  machine  would  give  one 
type  of  "  perpetual  motion."  To  distinguish  this  type,  in 
which  energy  is  created,  from  the  others  to  be  considered  later, 
it  will  be  called  Perpetual  Motion  of  the  First  Type. 

It  follows  directly,  from  the  law  of  conservation  of  energy, 
that  Perpetual  Motion  of  the  First  Type  is  impossible.  It  is 
also  apparent  that  the  First  Law  of  Thermodynamics  is  a  special 
case  falling  under  this  broad  general  statement. 

9.  Ideal  Mechanisms.  In  the  discussion  of  some  engineering 
problems  it  is  customary  to  assume  ideal  mechanisms  for  pur- 
poses of  comparison.  There  are  three  types  of  Perpetual  Motion 
used  in  discussing  these.  The  first  has  just  been  considered; 
that  commonly  termed  the  "  Second  Type"  will  be  more  easily 
understood  later  in  the  discussion.  The  Third  Type  of  Per- 
petual Motion  is  that  most  commonly  assumed  for  purposes  of 
analysis  of  mechanical  problems.  It  is  the  ideal  perpetual 
motion  of  a  frictionless  machine,  which,  once  started,  would 
continue  in  motion  forever  unless  stopped  by  some  external 
resistance  or  force. 

As  a  matter  of  fact,  no  real  machine  can  be  frictionless,  and 
therefore  no  real  machine  could  continue  in  motion  indefinitely; 
but  the  friction  losses  in  machines  can  be  reduced  to  almost 
negligible  values,  and  for  the  purpose  of  analysis  this  may  be 


8 


HEAT-POWER  ENGINEERING 


assumed  to  be  carried  to  the  limit,  giving  perpetual  motion  of 
the  third  type  as  an  ideal  possibility. 

10.  The  Second  Law  of  Thermodynamics,  (a)  It  is  a  matter 
of  common  observation  that  in  a  steam  engine,  for  instance,  the 
steam  exhausted  still  contains  a  considerable  quantity  of  heat, 
and  that  its  temperature  is  lower  than  that  of  the  steam  supplied 
to  the  engine. 

This  phenomenon  of  receiving  heat  at  a  high  temperature 
and  rejecting  some  of  it  at  a  lower  temperature  is  characteristic 

of  every  real  engine,  and  will 
be  shown  later  to  be  charac- 
teristic of  every  ideal  engine, 
no  matter  how  perfect.  The 
operation  of  all  such  engines  is 
pictured  graphically  in  Fig.  i. 
Heat  energy  at  the  high  tem- 
perature TI  flows  from  reser- 
voir /  into  the  engine.  There 
part  of  it  is  converted  into  the 
stream  of  mechanical  energy 
(shown  flowing  out  to  the 
right),  while  the  rest  passes 


Fig.  i  —  Diagrammatic  Representation 
of  a  Heat  Engine. 


completely  through  the  engine 
and  emerges,  still  in  the  form 
of  heat,  but  at  the  lower  tem- 
perature 7*2  of  heat  receiver  //,  which  absorbs  it. 

Calling  the  heat  supplied  in  a  given  time  Qi,  the  mechanical 
energy  leaving  W,  and  the  heat  leaving  Q2j  it  follows  from  the 
conservation  of  energy  that 

^  +  <22  =  <2i. 
This  rearranged  gives 

W  =  Qi-  ft, 

from  which  it  immediately  appears  that  the  smaller  Q2  is  the 
greater  will  be  the  work  resulting  from  the  use  of  a  given  quantity 
of  heat  <2i. 

(b;  Experience  has  shown  that  no  device  can  even  be  imagined 
which,  under  existing  circumstances,  could  continuously  convert 
into  mechanical  form  all  of  the  heat  energy  supplied  it.  All 
machines  so  far  devised,  actual  or  ideal,  can  continuously  convert 


ELEMENTARY  LAWS  OF  HEAT  ENERGY  9 

only  part  of  the  heat  supplied  them  and  must  reject  the  remainder 
at  a  lower  temperature  than  that  at  which  it  was  received.  This 
is  summed  up  in  the  so-called  Second  Law  of  Thermodynamics 
as  follows: 

No  machine,  actual  or  ideal,  can  both  completely  and  continu- 
ously transform  heat  into  mechanical  energy* 

(c)  If  such  complete  transformation  could  be  effected^  it  would 
give  what  is  called  Perpetual  Motion  of  the  Second  Type. 

So  long  as  heat  must  be  exhausted  at  a  lower  temperature 
the  possibility  of  obtaining  mechanical  energy  from  heat  ceases 
as  soon  as  the  temperature  of  all  the  heat  in  the  universe  has 
been  dropped  to  the  lowest  attainable  value. 

If  this  necessity  of  exhausting  heat  at  a  lower  temperature 
were  removed,  it  would  be  possible  to  continue  the  conversion 
of  heat  into  mechanical  energy  after  all  means  of  obtaining  a 
temperature  difference  had  been  used  up,  that  is,  after  all  heat 
had  been  reduced  to  the  lowest  attainable  temperature. 

As  all  mechanical  energy  eventually  passes  back  into  heat 
energy  (generally  at  low  temperature)  through  friction  and 
allied  phenomena,  there  would  be  no  danger  of  the  supply  of 
heat  giving  out.  The  cycle  would  then  be  an  endless  one,  con- 
sisting of  the  transformation  of  heat  into  mechanical  energy, 
the  retrogression  from  this  form  of  energy  to  heat,  the  conversion 
to  mechanical  form  again,  and  so  on  ad  infinitum. 

This  would  then  be  equivalent  to  a  sort  of  perpetual  motion 
which  is  distinguished  from  the  other  two  types  by  calling  it,  as 
above,  Perpetual  Motion  of  the  Second  Type.  Hence  the  Second 
Law  of  Thermodynamics  may  also  be  stated  thus : 

Perpetual  Motion  of  the  Second  Type  is  impossible. 

This  Second  Type  of  Perpetual  Motion,  like  the  First  Type,  is 
impossible  even  in  imagination,  whereas  the  Third  Type,  though 
impossible  of  realization,  is  an  ideal  limit  of  possibilities. 

ii.  Distribution  of  Associated  Heat  Energy,  (a)  Common  ex- 
perience shows  that  the  quantity  of  heat  associated  with  any  por- 
tion of  matter  may  be  changed  and  that  the  transformation  is 
accompanied  by  other  definite  phenomena  such  as  change  of 

*  There  are  almost  as  many  statements  of  the  Second  Law  as  there  are  authors 
of  books  on  thermodynamics.  It  is  believed  that  the  statement  as  here  given  is  the 
most  satisfactory  for  the  purposes  of  this  book. 


10  HEAT-POWER   ENGINEERING 

pressure,  or  of  volume,  or  of  temperature,  or  of  physical  state, 
chemical  change  may  also  occur  and  other  forms  of  energy  may 
appear  or  disappear. 

Despite  these  varied  possibilities  a  very  simple  and  definite 
generalization  may  be  made.  This  at  least  serves  the  purpose 
of  establishing  a  viewpoint  and  aids  in  analysis. 

Consider,  for  example,  a  single  chemical  substance,  which 
may  be  an  element  or  a  compound,  and  which  is  assumed  not 
to  be  set  in  motion  as  a  whole,  nor  to  be  altered  chemically,  nor  to 
lose  energy  by  any  form  of  radiation.  In  such  a  substance  there 
can  be  only  three  results  from  adding  heat,  and  there  are  only 
three  sources  from  which  heat  can  be  abstracted. 

1.  Heat  addition  may  be  accompanied  by  rise  in  temperature. 
In  this  case  that  part  of  the  heat  which  is  used  in  causing  the 
temperature  change  may  be  conceived  as  effecting  an  increase 
in  the  motion  of  the  constituent  particles.     Heat  thus  used  is 
known  as  Sensible  Heat  and  its  addition  increases  the  substance's 
store  of  sensible  heat.     Conversely,  the  abstraction  of  heat  may 
be  accompanied  by  a  fall  in  temperature   (probably  decrease 
of  internal  motion),  and  the  source  of  part  of  the  abstracted  heat 
is  the  store  of  sensible  heat  of  the  substance. 

2.  Heat  addition  may  be  accompanied  by  a  variation  of  the 
internal  structure  of  the  substance,  and  this  may  be  imagined  as 
a  molecular  rearrangement.     The  part  of  the  heat  which  is  used  in 
causing  this  change  is  called  Internal  Latent  Heat.     Conversely, 
the  abstraction  of  heat  may  cause  the  reverse  change. 

3.  In  i  and  2  when  heat  is  added  the  size  of  the  substance  may 
change;  there  would  then  be  a  positive  or  negative  displacement  of 
surrounding  media,  against  resistance,  and  part  of  the  heat  added 
supplies  the  necessary  mechanical  energy  for  this  displacement. 
The  heat  thus  transformed  is  sometimes  called  External  Latent 
Heat.     Conversely,  when  heat  is  abstracted  in  I  and  2  the  sur- 
rounding media  may  return  and  the  equivalent  of  the  external 
latent  heat  be  abstracted  as  heat. 

(b)  Heat  energy  added  may  then  be  imagined  to  produce 
results  as  follows: 

In  i,  part  of  the  added  heat  may  increase  the  kinetic  energy  of 
the  molecules. 

In  2,  part  of  the  added  heat  may  overcome  the  resistance  to  re- 
arrangement of  the  molecules. 


ELEMENTARY  LAWS  OF  HEAT  ENERGY  n 

In  3,  part  of  the  added  heat  may  overcome  the  resistance  of 
surrounding  media  to  displacement. 

In  all  cases  the  added  heat  becomes  stored  energy;  for  if  the 
phenomena  are  reversed  (conduction  and  radiation  loss  being 
prevented)  the  substance  will  return  to  its  original  dimensions, 
state,  and  temperature,  and  the  energy  previously  given  to  the 
substance  to  accomplish  these  results  will  be  returned  as  heat. 
Since  the  sensible  heat  and  the  internal  latent  heat  are  stored 
within  the  substance  itself,  and  since  the  external  latent  heat  is 
stored  in  external  media,  it  is  common  to  call  the  sum  of  the  first 
two  the  Change  of  Intrinsic  Heat  Energy  and  the  third  the  Change 
of  External  Heat  Energy. 

(c)  The  following  symbols  will  be  used  to  designate,  in  thermal 
units,  the  various  quantities  concerned  in  changes  of  associated 
heat  energy  in  substances : 

AQ  =  the  total  quantity  of  heat  added  to  or  taken  from  the 

substance. 
AS  =  the  part  of  AQ  associated  with  temperature  change; 

this  equals  the  change  of  sensible  heat. 
A/  =  the  part  of  AQ  associated  with  internal  rearrangement; 

this  equals  the  change  of  internal  latent  heat. 
AE  =  the   part  of   A(?  associated   with   the  displacement  of 

external  media;  this  equals  the  change  of  external 

latent  heat. 

From  the  foregoing  discussion  it  follows  that: 

AQ  =  AS  +  A/  +  AE, (i) 

for  the  three  symbols  on  the  right  of  the  equation  represent  the 
only  destinations  possible  for  added  heat,  and  the  only  possible 
sources  of  abstracted  heat. 

Thus  the  change  of  intrinsic  heat  energy  =  AS  +  A/,  the 
change  of  external  heat  energy  =  AE  and  the  change  of  total 
associated  heat  energy  =  A<2  =  AS  +  A/  +  AE. 

It  is  in  general  possible  for  any  or  all  of  the  three  terms  on 
the  right  of  the  last  equation  to  be  either  positive  or  negative  or 
equal  to  zero.  Hence  it  is  necessary,  within  the  conditions  set 
at  the  beginning,  to  consider  the  equation  as  perfectly  general, 
and  to  interpret  it  for  the  conditions  of  each  case. 

(d)  As  an  illustration  of  the  foregoing  statements,  consider 
the  transformations  that   occur  and  the  heat   that  is  utilized 


12 


HEAT-POWER  ENGINEERING 


Fig.  2. 


in  generating  steam  from 'cold  water.  In  the  cylinder,  above 
burner  a  in  Fig.  2,  let  there  be  cold  water,  say  at  room  temper- 
ature, below  the  piston.  Let  the 
temperature  be  raised  by  the  ex- 
ternal application  of  heat. 

Common  experience  shows  that 
this  rise  of  temperature  will  be 
accompanied  by  a  slight  increase 
of  volume,  and  refined  experi- 
ment leads  to  the  belief  that  it 
will  also  be  accompanied  by  cer- 
tain intramolecular  changes.  Be- 
cause of  the  volume  increase  some 
of  the  heat  supplied  in  raising 
the  temperature  must  be  used  in 
doing  the  external  work  of  lift- 
ing  the  weight  W  and  the  piston 
against  the  action  of  gravity,  and 
of  moving  the  piston  against  the  atmospheric  pressure  on  its 
upper  side.  This  part  of  the  total  heat  supply  may  be  called" 
AE.  Because  of  the  intramolecular  work  and  because  the  mole- 
cules must  be  separated  against  any  interattractions,  as  the  vol- 
ume increases,  some  of  the  heat  applied  during  the  temperature 
increase  must  be  used  for  doing  internal  work  and  may  be  desig- 
nated by  A/.  The  part  of  the  heat  supplied  and  not  accounted 
for  by  the  sum  of  AE  and  A/  must  be  that  used  in  what  is  rec- 
ognized as  a  rise  of  temperature  and  may  therefore  be  designated 
by  AS,  the  sensible  heat. 

Then  the  total  heat  (AQ)  supplied  during  the  temperature 
rise  is  A0  =  AS  +  A/  +  AE. 

It  so  happens,  however,  that  in  this  case,  in  which  water  is 
heated,  the  numerical  values  of  A/  and  AE  are  so  very  small,  as 
compared  with  that  of  AS,  that  for  engineering  purposes  they 
may  be  neglected  without  serious  error  and  A<2  may  be  taken  as 
equal  to  AS,  as  illustrated  at  a  in  Fig.  2. 

(e)  Suppose,  now,  that  the  temperature  of  the  water  in  the 
cylinder  has  been  raised  to  that  at  which  steam  is  formed.  Then 
continued  addition  of  heat  will  not  further  raise  the  temperature, 
but  it  will  cause  the  formation  of  steam  (at  constant  tempera- 
ture and  constant  pressure),  with  a  very  great  increase  of  volume, 


ELEMENTARY  LAWS  OF  HEAT  ENERGY  13 

and  its  accompanying  separation  of  molecules.  There  will  also 
probably  be  certain  intramolecular  changes. 

As  there  is  no  temperature  change  during  the  process  of 
vaporization,  no  part  of  the  heat  (AQ)  supplied  can  be  used  to 
change  the  sensible  heat,  that  is,  as  AS. 

The  enormous  increase  of  volume  during  vaporization,  with 
the  consequent  raising  of  the  piston  against  the  resistance 
offered  by  the  weight  of  the  piston,  the  superincumbent  at- 
mosphere, and  the  weight  W,  involves  the  doing  of  external 
work,  and  some  of  the  heat  supplied  during  the  process  must  be 
used  for  that  purpose.  This  heat,  which  may  be  designated  by 
AE,  is  known  as  the  external  latent  heat  of  vaporization  and  is 
stored  as  potential  energy  in  the  mechanical  parts  of  the  system, 
not  in  the  steam  itself. 

The  intramolecular  and  the  intermolecular  work  consume  the 
rest  of  the  heat  supplied,  and  the  part  used  for  such  purposes  is 
called  the  internal  latent  heat  of  vaporization.  According  to 
/the  symbols  adopted  it  would  be  designated  by  A/. 

Thus  the  heat  supplied  during  vaporization  is 

A<2  =  A/  +  AE, 

and  this  is  shown  at  b  in  Fig.  2. 

Considering  the  whole  process  of  heating  the  water  and  vaporiz- 
ing 

A<2  =  ASZ  +  A/*  +  AS/  +  A/v 


in  which  the  subscript  /  indicates  heat  added  to  the  liquid  while 
raising  the  temperature  and  subscript  v  refers  to  the  heat  added 
during  vaporization.  On  the  assumption  that  A/j  and  AE* 
are  negligible, 

A<2  =  AS*  +  A/,  +  AEV. 

While  water  has  been  used  as  an  example,  all  liquids  present 
sikiilar  phenomena  during  heating  and  vaporization.  Liquid 
ammonia,  liquid  sulphur  dioxide,  liquid  carbon  dioxide,  or  any 
one  of  a  number  of  other  materials,  might  have  been  used  as  an 
illustration. 

Other  examples  of  processes  showing  the  different  utilizations 
of  heat  might  be  cited,  but  it  is  believed  that,  for  present  pur- 
poses, the  one  given  above  sufficiently  illustrates  the  ideas  and 
the  meanings  of  the  symbols  used. 


14  HEAT-POWER  ENGINEERING 

12.  Specific  Heat,  (a)  As  just  indicated,  the  change  of  tem- 
perature, with  corresponding  change  of  sensible  heat,  may  be 
accompanied  by  two  other  changes,  and  it  is  clear  that  the  change 
in  associated  heat  energy  is  dependent  upon  all  three  factors. 
This  must  be  taken  into  account  in  considering  specific  heat, 
which  may  be  denned  thus: 

The  specific  heat  of  a  substance  is  the  heat  added  to,  or  abstracted 
from,  a  unit  weight  of  that  substance  when  its  temperature  is  changed 
one  degree. 

The  quantity  of  heat  thus  defined  may  be  used  in  any  one  or 
all  of  three  ways:  (i)  to  raise  temperature,  (2)  to  do  internal 
work,  (3)  to  do  external  work.  The  quantity  of  heat  required 
simply  to  raise  the  temperature  would  obviously  be  less  than  the 
quantity  required  to  raise  the  temperature  and  also  to  do  work, 
external  or  internal.  Hence  for  every  substance  there  must 
be  several  specific  heats,  the  values  of  which  depend  upon  the 
use  made  of  the  heat. 

But  by  whatever  method  the  heat  is  applied  and  whatever  the 
use  made  of  it  during  its  addition  to  a  substance,  if  the  method  is 
the  same  throughout,  the  specific  heat,  C,  by  definition  must  be 


in  which 

A<?  =  heat  added. 

W  =  weight  of  substance  receiving  heat. 
TI  =  temperature  before  A<2  is  added. 
T2  =  temperature  after  AQ  is  added. 

(b)  If  the  specific  heat  is  not  constant,  with  any  method  of  heat 
application,  the  value  of  C  from  Eq.  (2)  is  an  average  value  for 
the  temperature  range  and  is  called  a  Mean  Specific  Heat.* 

Hereafter  mean  specific  heats  will  be  denoted  by  putting  a 
vinculum  over  the  symbol,  and,  where  essential,  the  temperature 
range  will  be  indicated  by  subscripts;  thus,  C75-i8o  should  be  read 
as  the  mean  specific  heat  between  75°  and  180°. 

If  the  specific  heat  is  constant  the  heat  added  during  the  tem- 
perature change  from  7\  to  T2  is 


rj   ......     (3) 

*  The  mean  specific  heat  is  thus  useless  for  purposes  of  exact  calculation  unless 
the  temperature  range  over  which  it  is  the  average  is  known  and  unless  it  is  used 
in  calculations  involving  that  same  temperature  range. 


ELEMENTARY  LAWS  OF  HEAT  ENERGY  15 

If  the  specific  heat  is  variable 

A<2=  CWWt-Td (4a) 

or  =  W  i    *  CdT,  (4b) 

JTI 

in  which  C  represents  the  successive,  or  instantaneous,  values 
of  the  variable  specific  heat  as  the  temperature  changes  from 
Ti  to  T2. 

(c)  It  is  conceivable  that  the  temperature  of  a  substance  may 
be  raised  in  such  manner  that  no  internal  or  external  work  is 
done,  and  the  heat  would  then  be  applied  only  to  raising  tem- 
perature, and  would  be  a  true  specific  heat.  Such  true  specific 
heats,  it  will  be  found  later,  are  sometimes  closely  approximated 
in  the  case  of  gases. 

13.  Total  Associated  Heat.  It  is  impossible  at  present  to 
determine  the  total  quantity  of  heat  energy  associated  with  a 
substance  under  given  conditions,  because  no  means  are  available 
for  complete  heat  removal. 

To  compare  associated  heats  of  substances  at  different  tempera- 
tures, a  convenient  value  for  TI  is  assumed  as  a  datum  and 
calculations  are  confined  to  the  region  above  it.  This  method 
gives  relative  and  not  absolute  results,  but  serves  for  engineering 
purposes.  The  value  of  TI  is  usually  32°  F.,  when  such  a  choice 
is  possible. 


CHAPTER   III. 

THE  HEAT-POWER  PLANT. 

14.  General.     It  has  already  been  stated  that  the  heat-power 
engineer  has  to  do  largely  with  the  conversion  of  the  latent 
heat  in  fuels  into  available  mechanical  energy.     This  transfor- 
mation is  effected  by  means  of  various  pieces  of  apparatus, 
used  singly  in  some  cases  and  in  series  in  others.     All  of  the 
apparatus  necessary  in  any  individual  case  may  be  called  a 
"  Power  Plant." 

That  part  of  the  power  plant  which  receives  heat  energy  and 
delivers  mechanical  energy,  i.e.  the  "engine,"  is  often  called  a 
"Prime  Mover."  < 

Examples  of  heat-power  plants  are  familiar  to  all.  They  may 
contain  Steam  Engines  and  Boilers,  with  certain  auxiliary 
apparatus  necessary  for  the  satisfactory  operation  of  these  two 
principal  pieces;  they  may  contain  Gas  Producers  and  Gas 
Engines,  with  suitable  "  auxiliaries;"  or  they  may  contain  an 
engine  only,  as  in  the  case  of  a  gasoline-engine  or  an  oil-engine 
power  plant. 

No  matter  what  the  type  of  plant,  a  certain  general  method  of 
operation  is  common  to  all.  This  is  illustrated  in  Fig.  i.  Heat, 
from  some  kind  of  fuel,  is  continually  flowing  in,  forming  a 
"  stream  of  energy."  This  energy  leaves  the  system  in  a  number 
of  different  ways,  divisible  broadly  into  waste  (or  lost)  energy 
and  useful  energy.  In  all  plants,  including  those  theoretically 
perfect,  there  must  always  be  a  loss;  thus  the  energy  flowing  out 
in  useful  form  must  always  be  only  a  fraction  of  that  flowing  in. 
This  will  be  illustrated  by  the  description  of  the  operation  of 
the  Steam-Power  Plant,  in  Section  15,  and  of  the  Producer  Gas- 
Power  Plant,  in  Section  16. 

15.  The  Steam-Power  Plant,      (a)  This  type,  which  is  the 
oldest  and  is  the  most  used  of  all  forms  of  heat-power  plant, 
may  be  said  to  consist  of  four  essential  parts,  —  the  "Steam 

L6 


THE  HEAT-POWER  PLANT  17 

Boiler,"  including  the  "furnace,"  the  "Steam  Engine,"  the 
"  Condenser,"  and  the  "  Boiler  Feed-Water  Pump."  It  is 
shown  in  one  of  its  many  forms  in  Fig.  3,  with  these  four  parts 
named.  The  method  of  operation  is  as  follows. 

(b)  Fuel  is  burned  on  the  "grate  "  in  the  furnace  under  the 
boiler.     The  combustion  of  this  fuel  liberates  a  large  amount  of 
heat  energy,  which  is  partly  absorbed  by  the  products  of  com- 
bustion, partly  radiated  to  the  water  through  the  "  heating  sur- 
faces "  of  the  boiler  tubes  and  shell,  and  partly  radiated  through 
the  furnace  walls  to  the  surrounding  air.     This  latter  type  of 
radiation  represents  a  loss,  which  can  never  be  prevented,  as  the 
furnace  walls  cannot  be  made  nonconducting. 

The  furnace  may  be  regarded  as  the  part  of  the  boiler  apparatus 
which  converts  the  heat  energy,  latent  in  the  fuel,  into  available 
heat  energy.  It  will  be  found  that  there  are  certain  losses  in 
this  conversion  which  can  never  be  entirely  prevented  in  any 
real  case.  They  may  be  summarized  as  follows: 

(1)  Some  of  the  fuel  falls  through  the  grate  and  is  not  burned. 

(2)  The   ashes   and   refuse    drop    through    the   grate   with   a 
higher  temperature  than  that  at  which  they  were  put  into  the 
furnace. 

(3)  Some  of  the  more  volatile  parts  of  the  fuel  pass  off  with 
the  products  of  combustion  and  are  not  burned. 

(4)  In  order  to  insure  the  complete  combustion  of  the  fuel, 
a  larger  amount  of  air  must  be  supplied  the  furnace  than  is 
theoretically  necessary.     This  mixes  with  the  products  of  com- 
bustion proper  and   represents  just  so  much   more  gas  to  be 
heated  by  the  energy  liberated  by  combustion.     As  a  result  the 
temperature  attained  by  these  gases  is  proportionately  lower  and, 
as  will  be  discovered  later,  the  subsequent  utilization  of  the  heat 
is  made  more  difficult. 

(c)  During  the  operation  of  the  furnace  a  stream  of  radiant 
heat  energy  from  the  incandescent  fire  passes  through  the  heat- 
ing surfaces  to  the  water  and  steam,  and  there  is  also  a  stream  of 
hot  gas  which,  as  it  passes  over  these  surfaces,  gives  up  heat  to 
the  fluids  within.     In  this  part  of  the  process  there  will  always 
be  three  losses: 

(i)  Part  of  the  heat  carried  by  the  products  of  combustion 
will  pass  out  through  the  external  walls  of  the  "  boiler  setting," 
instead  of  into  the  heating  surfaces. 


i8 


HEAT-POWER  ENGINEERING 


THE  HEAT-POWER  PLANT  19 

(2)  The  gases  can  in  theory  pass  heat  into  the  heating  surfaces 
so  long  as  their  temperature  is  higher  than  that  of  the  water  and 
steam.     In  the  ideal  boiler  these  gases  would  be  cooled  to  the 
temperature  of  the  water  and  steam,  but  in  practice,  for  vari- 
ous reasons,  they  leave  .the  apparatus  when  there  is  still  a  dif- 
ference  of   temperature   of   from   200°  F.   to  500°   F.  or  even 
more. 

(3)  The  temperatures  of  the  fuel  and  air  entering  the  furnace 
of  course  approximate   that  of  the  room,  and  the  products  of 
combustion  are  heated  from  that  value  (about  60°  F.)  to  the 
high    temperature   with   which    they   leave   the   furnace.     The 
temperature  of  the  water  and  steam  within  the  boiler  is  always 
from  about  200°  to  400°  F.,  or  more,  higher  than  room  tem- 
perature; thus,  even  if  the  gases  were  cooled  the  theoretically 
maximum  amount,  they  would  still  carry  off  considerably  more 
heat  than  they  would  if  cooled  to  atmospheric  temperature. 

Despite  all  the  losses  so  far  enumerated,  a  considerable  pro- 
portion (from  50  to  80  per  cent)  of  the  original  heat  energy  of 
the  fuel  is  passed  through  the  heating  surface  and  is  used  in 
raising  the  temperature  of  the  water  and  in  generating  steam. 
This  heat  is  stored  in  the  steam. 

(d)  As  was  explained  in  Section  n  (d),  under  the  conditions 
governing  the  generation  of  steam  in  a  steam  boiler,  the  liquid 
must  first  be  raised  to  a  definite  temperature,  dependent  on  the 
pressure,  before  it  can  be  vaporized.  To  raise  the  water  to  this 
temperature  a  certain  amount  of  heat  must  be  added  to  it;  and, 
the  lower  the  temperature  at  which  the  water  enters  the  boiler 
and  the  higher  the  temperature  of  the  steam,  the  greater  will 
be  the  quantity  of  heat  needed. 

After  the  absorption  of  this  amount  of  heat  a  still .  larger 
quantity,  known  as  the  "  latent  heat  of  vaporization,"  must  be 
supplied  to  convert  the  hot  water  into  steam  at  the  same  tem- 
perature. 

The  total  heat  supplied  can  be  subsequently  abstracted,  as 
heat,  by  condensing  and  cooling  and  thus  obtaining  the  same 
water  at  the  original  temperature,  or  part  of  it  can  be  obtained 
in  the  form  oL useful  mechanical  energy  by  certain  transforma- 
tions which  may  be  made  to  take  place  in  the  steam-engine 
cylinder.  For  our  present  purposes  this  latter  is  the  more 
important  of  the  two  possibilities. 


20  HEAT-POWER  ENGINEERING 

(e)  The  steam  is  led  to  the  cylinder  of  the  steam  engine  by 
the  "  steam   pipe  "   shown  in  Fig.  3-     In  the  cylinder  a  part 
of  the  heat  in  the  steam  is  converted  into  mechanical  energy  by 
the  action  of  the  steam  on  the  piston,  part  is  wasted  by  "  cylinder 
losses,"  which  will  be  considered  in  a  later  chapter,  and  the 
remainder  is  still  in  the  steam  when  this  is  discharged  from  the 
cylinder.     Only  from  5  to  22  per  cent  of  the  heat  available  in 
the  steam  is  converted  into  useful  energy  in  the  cylinder,  and, 
because  of  friction  of  engine  parts  and  work  done  in  driving  the 
pumps,  not  all  of  this  is  delivered  by  the  engine  to  the  belt  or 
other  power  consumer. 

The  exhaust  steam,  still  retaining  the  greater  part  of  the  heat 
that  was  furnished  by  the  fuel,  is  conducted  to  the  "  surface 
condenser"  (see  Fig.  3),  where  it  is  condensed  on  the  outer 
surfaces  of  the  condenser  tubes,  through  which  the  "  condensing 
water  "  is  circulated.  The  heat  which  the  condensing  water 
absorbs  in  liquefying  the  steam  is  the  "  latent  heat  of  vapori- 
zation," and  this  is  large  in  amount.  In  the  plant  shown  this 
heat  is  not  further  utilized  and  hence  represents  a  considerable 
loss. 

The  water  resulting  from  the  condensation  of  the  steam,  known 
as  the  "  condensed  steam  "  or  "  condensate,"  is  transferred 
from  the  condenser,  in  which  the  pressure  is  below  that  of  the 
atmosphere,  to  the  "  hot  well  "  by  the  "  vacuum  pump,"  which 
also  removes  any  air  which  may  accumulate  in  the  condenser. 
The  "  feed -water  pump  "  takes  this  water  from  the  hot  well, 
with  whatever  heat  it  contains,  raises  its  pressure  to  that  of  the 
steam,  and  returns  it  to  the  boiler,  where  it  is  reconverted  into 
steam  and  started  again  on  the  round  just  described. 

(f)  Such  a  combination  of  processes,  which  periodically  brings 
the  material  back  to  starting  conditions,  is  known  as  a  "  cycle," 
or,  more  properly,  as  a  "  closed  cycle." 

The  characteristic  of  the  cycle  above  outlined  is  the  fact  that 
the  water  (or,  speaking  more  generally,  the  "working  sub- 
stance ")  is  not  lost  or  used  up  or  permanently  altered  in  any 
way.  It  serves  simply  as  a  carrier  and  transformer  of  heat 
energy,  receiving  it  from  the  boiler  furnace,  giving  up  some  of 
it  as  mechanical  energy  to  the  piston,  rejecting  the  remainder 
to  the  condenser,  and  then  returning  to  the  boiler  to  start  the 
cycle  once  more. 


THE   HEAT-POWER  PLANT  21 

This  is,  in  theory  at  least,  characteristic  of  all  processes  by 
means  of  which  heat  is  converted  into  work.  In  practice  it  is 
sometimes  found  to  be  simpler  or  more  desirable  to  throw  away 
the  working  substance  after  it  has  been  used  in  the  engine  and 
to  continue  to  supply  new  quantities  for  the  reception  of  heat 
at  high  temperature.  In  steam-power  plants,  for  instance,  the 
condensate  is  often  abandoned,  and  the  boilers  are  then  supplied 
with  corresponding  quantities  of  water  from  some  other  sources, 
such  as  wells  or  streams. 

Theoretically,  however,  it  is  immaterial  whether  one  pound  of 
water  is  used  time  after  time,  or  whether  new  is  substituted  for 
old,  pound  for  pound,  at  some  point  in  the  process,  provided  only 
that  the  substitute  have  the  same  volume,  pressure,  temperature, 
and  heat  conditions  as  that  which  it  replaces. 

In  the  lower  part  of  Fig.  3  is  a  "  heat-flow  diagram."  This 
shows  the  stream  of  heat  energy  flowing  from  the  boiler  to  the 
engine.  Its  width  shows  the  relative  amount  of  heat  remaining 
available  for  doing  external  work,  and  the  offshoots  show  the 
losses  that  occur  at  different  stages  of  the  process. 

(g)  Returning  to  the  engine,  the  action  of  the  steam  within  the 
cylinder  will  now  be  considered  in  a  very  elementary  manner,  in 
order  to  bring  out  certain  conceptions  which  will  be  useful  in 
the  discussions  of  the  following  chapters.  This  action  of  the 
steam  will  be  considered  in  detail  later. 

The  steam,  upon  its  arrival  at  the  engine  (which,  for  sim- 
plicity, will  be  considered  "  single-acting  "),  is  admitted  by  the 
"  admission  valve  "  to  one  end  of  the  cylinder,  where  it  acts  on 
the  piston,  causing  it  to  move  and  deliver  mechanical  energy. 
The  valve  may  remain  open  during  the  entire  stroke  of  the  piston, 
or  it  may  close  before  the  stroke  ends,  which  is  the  usual  practice. 

If  the  different  positions  of  the  piston  in  its  stroke  are  plotted 
as  abscissas  and  the  corresponding  pressures  acting  on  the 
piston  face  are  erected  as  ordinates,  there  will  be  obtained  a 
line  like  ab,  in  Fig.  4,  which  line  is  a  graphical  representation  . 
of  pressures  occurring  within  the  cylinder  during  the  admission 
of  the  steam.  The  work  done  on  the  piston  in  moving  it  from 
position  I  to  2  can  be  computed  if  the  constant  pressure  acting 
on  the  piston  and  the  distance  traversed  are  known. 

If  the  admission  valve  be  assumed  to  close  (at  2)  when  the  dis- 
tance moved  is  less  than  the  stroke,  the  expansion  of  the  steam 


22  HEAT-POWER  ENGINEERING 

thus  entrapped  will  continue  to  drive  the  piston  until  the  end  of 
the  stroke  is  reached.  It  will  be  discovered  in  later  chapters  that 
this  expansion  is  accompanied  by  a  drop  in  the  pressure  and  in 
the  temperature  of  the  steam.  The  way  the  pressure  drops 
during  the  expansion  is  shown  by  the  curve  be  in  Fig.  4.  The 
work  done  while  the  piston  is  moving 
from  position  2  to  3  can  be  computed 
when  the  average  pressure  acting  on 
the  piston  and  the  distance  traveled  are 
known.  The  average  pressure  is  pro- 
\d  portional  to  the  mean  ordinate  of  the 
curve  be.  The  method  of  determining 


piston  Positions  it  will  be  given  later.  At  present  it  is 

Fjg  4  sufficient  to  know  that  work  is  done 

'during  this  expansion. 

When  the  piston  arrives  at  the  end  of  its  stroke  the  "  exhaust 
valve  "  opens  communication  between  the  interior  of  the  cylinder 
and  the  condenser,  in  which  a  comparatively  low  temperature 
and  pressure  are  maintained,  and  some  of  the  steam  at  once 
rushes  from  the  cylinder  to  the  condenser,  where  it  is  liquefied 
and  discharged  to  the  hot  well  in  the  manner  already  discussed. 
This  process  is  shown  by  the  line  cd  in  Fig.  4,  the  pressure  within 
the  cylinder  decreasing  to  the  value  prevailing  within  the  con- 
denser. 

If,  now,  the  piston  is  driven  back  to  the  beginning  of  the 
stroke,  it  will  force  all  the  steam  from  the  cylinder  into  the 
condenser,  where  it  will  be  liquefied  as  fast  as  it  enters.  In 
moving  from  position  3  to  I,  in  Fig.  4,  the  piston  will  have  swept 
through  the  entire  stroke  against  a  constant  resisting  pressure 
equal  to  the  "  back  pressure  "  or  "  condenser  pressure."  This 
operation  is  represented  by  the  line  de  in  Fig.  4.  In  forcing 
the  steam  from  the  cylinder,  the  piston  does  work  which  can  be 
computed  if  the  mean  resisting  pressure,  as  shown  by  the  ordi- 
nate of  de,  and  the  stroke  are  known. 

Obviously,  no  work  is  done  on  or  by  the  piston  during  the 
process  represented  by  cd,  as  it  is  not  accompanied  by  motion  of 
the  piston.  Similarly,  if  the  piston  is  stationary  at  the  beginning 
of  its  stroke  while  the  pressure  is  raised  by  the  entering  steam 
fiom  the  value  shown  at  e  to  that  at  a,  no  work  is  done  during 
that  process. 


THE  HEAT-POWER  PLANT  23 

The  total  work  done  during  the  two  strokes  is  the  difference 
between  the  work  done  on  the  piston  during  processes  represented 
by  lines  ab  and  be  and  that  done  on  the  steam  by  the  piston  during 
process  de. 

The  processes  through  which  the  steam  has  been  carried  in  the 
cylinder  (as  shown  in  diagram,  Fig.  4)  are  idealized  versions  of 
what  occurs  in  actual  engines,  and  it  is  seen  that  even  in  this 
ideal  case  only  a  small  part  (theoretically,  from  10  to  30  per  cent) 
of  the  heat  in  the  steam  could  be  actually  converted  into  work, 
the  rest  remaining  in  the  steam  exhausted.  In  the  actual  case  a 
still  larger  amount  of  the  heat  is  wasted  in  the  cylinder  and  a 
proportionately  less  amount  of  heat  is  delivered  as  mechanical 
energy  to  the  piston.  These  losses  occurring  within  the  cylinder 
are  quite  large  and  may  be  called  "  cylinder  losses." 

Not  all  the  mechanical  energy  that  is  available  at  the  piston 
is  delivered  by  the  engine  (by  belt  or  other  means)  for  doing 
useful  work,  for  some  of  this  energy  is  used  in  overcoming  the 
friction  of  the  engine  itself. 

The  relative  amounts  of  energy  available  for  doing  work  and 
the  losses  occurring  at  the  different  stages  are  shown  in  amount 
by  the  width  of  the  energy  stream  in  the  lower  part  of  Fig.  3. 

(h)  In  imagination  at  least,  it  may  be  considered  that  the 
same  operations  that  have  been  described  for  the  power  plant  as 
a  whole  can  be  performed  entirely  within  the  engine  cylinder 
alone.  Thus  the  water  (or  working  substance),  constant  in 
amount,  can  be  considered  as  always  remaining  within  the  cyl- 
inder, and  can  be  imagined  first  as  being  there  heated  and  vapor- 
ized (corresponding  to  lines  ea  and  ab  in  Fig.  4),  then  as  steam 
acting  on  the  piston  during  the  expansion  (corresponding  to 
line  be  in  Fig.  4),  and  finally  as  being  condensed  and  returned 
to  its  original  condition  (according  to  lines  cd  and  de)  by  the 
abstraction  of  heat  by  some  process  equivalent  to  that  per- 
formed by  the  condenser. 

As  all  these  processes  are  imagined  to  be  performed  with  the 
same  working  substance,  and  as  this  is  always  returned  to  its 
original  condition,  the  operations  within  the  cylinder  may  be  said 
to  constitute  a  cycle,  which  may  be  called  "  the  engine  cycle  " 
to  distinguish  it  from  the  cycle  of  the  power  plant  as  a  whole. 
(i)  It  should  be  noted  that,  in  obtaining  mechanical  energy 
from  heat  by  means  of  the  engine,  the  working  substance  supplies 


24  HEAT-POWER  ENGINEERING 

heat  energy  to  the  engine  at  a  high  temperature  (that  is,  it  fur- 
nishes what  may  be  called  "  high-temperature  heat"),  and  that 
upon  leaving  the  cylinder  the  working  substance  still  retains 
some  of  the  heat  but  at  a  lower  temperature  (that  is,  it  retains 
what  may  be  called  "  low-temperature  heat  ").  This  will  be 
found  to  be  characteristic  of  every  process  by  which  heat  is  con- 
verted into  mechanical  energy.  Evidently,  the  more  heat  con- 
verted into  mechanical  energy  and  the  less  rejected  at  low 
temperature,  the  more  efficient  is  the  engine.  But  even  in  the 
ideal  case  it  will  be  found  that  some  heat  must  be  rejected, 
which  is  in  accordance  with  the  statement  of  the  Second  Law  of 
Thermodynamics  and  is  shown  diagrammatically  in  Fig.  i. 

16.  The  Producer  Gas-Power  Plant.  The  principal  parts  of 
this  plant  are  represented  in  Fig.  5.  The  fuel  enters  the  gas 
producer,  carrying  with  it  its  store  of  heat.  In  the  producer 
the  combustible  part  of  this  fuel  is  gasified  at  the  expense  of 
some  of 'its  heat,  while  in  theory  the  rest  of  its  heat  is  stored  in 
the  combustible  gas  formed.  The  gas,  carrying  this  part  of  the 
heat  with  it,  enters  the  engine  cylinder,  mixes  with  air,  and  is 
ignited.  The  resulting  inflammation  raises  the  temperature  and 
pressure  of  the  products  of  combustion  to  high  values.  These 
gases  then  do  work  on  the  piston  at  the  expense  of  this  high- 
temperature  heat  and  sustain  a  corresponding  drop  in  tem- 
perature. They  are  finally  rejected,  carrying  with  them  a  certain 
part  of  the  original  heat  content,  now  existing  at  a  lower  tem- 
perature. 

Theoretically,  it  would  be  possible  to  remove  this  low-tem- 
perature heat  in  an  apparatus  corresponding  to  a  condenser, 
return  the  same  mass  of  working  substance  to  its  original  chemical 
composition,  and  start  the  cycle  over  again.  Practically,  how- 
ever, it  is  found  much  simpler  to  throw  the  burned  gases  away 
each  time  and  to  start  again  with  fresh  working  substance. 

For  this  reason  the  atmosphere  is  commonly  used  in  place  of 
a  condenser.  It  possesses  the  necessary  characteristic  of  low 
temperature,  as  compared  with  the  highest  attained  in  the  opera- 
tion of  the  engine,  and  has  ability  to  absorb  all  the  heat  rejected 
by  the  engine.  It  possesses  the  further  convenient  characteristic 
of  being  able  to  absorb  the  working  substance  as  fast  as  it  is 
rejected  by  the  engine. 


THE  HEAT-POWER  PLANT 


26  HEAT-POWER  ENGINEERING 

Although  the  series  of  operations  that  was  outlined  in  con- 
nection with  the  steam-power  plant  is  not  quite  so  evident 
in  this  case,  analysis  will  show  that,  in  theory  at  least,  the 
working  substance  could  be  used  over  and  over  again,  serv- 
ing only  to  receive  high-temperature  heat,  to  transform  some 
of  it  into  mechanical  energy,  and  to  reject  the  rest  at  a  low 
temperature. 

17.  Analogy.     The  operation  of  heat  engines  has  often  been 
compared  to  the  operation  of  water  wheels,  and  there  is  much 
that  is  similar. 

A  water  wheel  develops  mechanical  energy  by  receiving  water 
under  a  high  head,  absorbing  some  of  its  energy,  and  then  re- 
jecting the  fluid  under  a  low  head. 

A  heat  engine,  in  developing  mechanical  energy,  receives  heat 
energy  at  a  high  temperature  (head),  absorbs  some  of  it,  which 
is  converted  into  mechanical  energy,  and  then  rejects  the  rest 
at  a  low  temperature  (head). 

This  analogy  between  "  heat  sliding  down  a  temperature 
hill,"  as  it  is  sometimes  stated,  and  "  water  sliding  down  a 
grade,"  is  very  useful,  but  should  not  be  carried  too  far. 

One  point  of  resemblance  is,  however,  worthy  of  special  note: 
The  water  wheel  never  removes  all  of  the  energy  of  the  water; 
there  is  always  a  certain  discharge  loss,  or  a  certain  amount  of 
energy  rejected.  In  the  same  way  the  heat  engine  never  removes 
all  of  the  heat  energy  from  the  working  substance;  there  is 
always  a  certain  discharge  loss,  or  a  certain  amount  of  energy 
rejected  (Second  Law  of  Thermodynamics). 

1 8.  Further  Study.     A  number  of  theoretical  considerations 
must  be  studied  in  detail  before  this  subject  of  conversion  of 
heat  energy  into  mechanical  form  can  be  discussed  more  thor- 
oughly.    It  is   necessary   to   learn   some   of   the   physical   and 
chemical  properties  of  the  common  working  substances,  some 
of  the  different  kinds  of  changes  they  can  be  made  to  undergo 
for  the  doing  of  work,  and  to  develop  certain  theoretical  cycles 
of  operation  upon  which  the  real  cycles  are  based. 

This  is  done  in  the  immediately  succeeding  chapters.  Gases 
are  considered  first  because  their  laws  permit  of  simpler  forms 
of  expression  and  are  more  easily  understood  than  are  those  of 


THE  HEAT-POWER  PLANT  27 

vapors,  which  are  the  only  other  working  substances  commonly 
used. 

In  later  chapters  the  real  cycles,  the  engines,  and  their  auxil- 
iaries, the  power  plants,  and  the  commercial  and  operating  con- 
siderations connected  therewith,  will  be  taken  up  again. 


CHAPTER   IV. 

THE  LAWS   OF  GASES. 

19.  States  of  Aggregation  of  Substances,  (a)  Almost  every 
substance  known  has,  under  proper  temperature  and  pressure 
conditions,  been  made  to  exist  in  three  physical  states,  or  condi- 
tions of  aggregation,  —  namely,  as  a  solid,  as  a  liquid,  and  as  a  gas; 
and  it  is  probable  that  this  can  be  done  for  all  matter  with  proper 
regulation  of  temperature  and  pressure. 

The  higher  the  temperature  and  the  lower  the  pressure,  the 
greater  the  tendency  to  exist  in  the  more  rarefied  condition  of 
aggregation  —  that  is,  as  a  gas;  while  the  lower  the  temperature 
and  the  higher  the  pressure,  the  greater  the  tendency  toward  the 
solid  form.  The  values  of  the  limiting  conditions,  —  namely,  tem- 
perature and  pressure,  —  which  will  determine  any  of  the  three 
states,  vary  widely  with  the  different  substances,  and  under 
ordinary  atmospheric  conditions  some  of  the  materials  in  the 
universe  are  known  as  solids,  others  as  liquids,  and  still  others 
as  gases. 

The  various  substances  obey  certain  laws,  differing  for  different 
states,  and  with  constants  that  vary  with  the  substance.  The 
laws  that  govern  matter  in  the  gaseous  state  are  the  simplest 
and  at  present  are  best  known.  These  laws  will  now  be  de- 
veloped and  will  be  more  fully  discussed  in  Chapter  IX. 

(b)  The  laws  of  gases  may  be  divided  into  two  groups,  - 
Ideal  Laws  and  Actual  Laws. 

The  ideal  laws  or  laws  of  ideal  gases  are  not  absolutely  true 
for  any  real  gases,  but  hold,  with  sufficiently  close  approximation 
for  engineering  purposes,  for  all  gases  which  are  far  removed 
from  liquefaction,  like  hydrogen,  nitrogen,  oxygen,  and,  to  a 
certain  extent,  carbon  dioxide. 

The  actual  laws  of  gases  are  the  ideal  laws  modified  so  as  to 
conform  as  accurately  as  possible  to  the  behavior  of  real  gases, 
and  they  generally  take  account  of  different  theories  of  the 

28 


THE  LAWS  OF  GASES  29 

actual  composition  of  gases.     They  are  seldom  used  by  engineers 
and  their  consideration  is  left  for  another  chapter. 

In  general,  the  variation  from  the  ideal  laws  becomes  less  as 
the  real  gases  are  further  removed  from  the  conditions  of  lique- 
faction, or  as  the  molecules  become  more  widely  separated  and 
the  effect  of  intermolecular  forces  becomes  less.  From  this  it 
is  concluded  that  the  hypothetical  ideal  gas  must  be  imagined 
devoid  of  such  intermolecular  forces. 

20.  The  Ideal  Laws  of  Condition  of  Gases.    These  laws  are, 

1.  The  Law  of  Boyle  or  of  Marriotte,  and 

2.  The  Law  of  Charles  or  of  Gay  Lussac. 

i.  Boyle's  Law. 

This  law,  which  deals  with  variations  of  pressure  and  volume 
at  constant  temperature,  is: 

When  the  temperature  of  a  given  weight  of  gas  is  maintained 
constant  the  volume  and  pressure  vary  inversely.  Mathematically 
expressed,  it  becomes 

£-£,.  • ....  •  ...  (5) 

V2          JT\ 

or 

ViPj.  =  F2P2  =  F3P3    .    •    =  VnPn  =  Constant,      .     (6) 

in  which 

Vi,  V2,  etc.  =  the  volumes  occupied  by  a  given  weight  of  a 
particular  gas  at  constant  temperature  but 
different  pressures,  and 

PI,  P2,  etc.  =  the  corresponding  pressures  exerted  by  the 
gas,  or  to  which  the  gas  is  subjected. 

2.   Charles*  Law. 

(a)  This  law,  which  deals  with  volume  or  with  pressure 
changes  accompanying  temperature  variations  may  be  con- 
veniently divided  into  two  statements  : 

(i)  When  the  pressure  of  a  given  weight  of  gas  is  maintained 
constant  the  volume  increases  ?|^*  of  its  value  at  32°  F.  for  every 
Fahrenheit  degree  rise  of  temperature  and  decreases  the  same  amount 
for  every  degree  decrease  of  temperature. 

*  The  exact  value  is  not  T|?,  but  this  is  probably  the  nearest  simple  fraction 
and  is  close  enough  for  engineering  purposes. 


£0  HEAT-POWER  ENGINEERING 

(2)  When  the  volume  of  a  given  weight  of  gas  is  maintained 
constant  the  pressure  increases  ,4*  of  its  value  at  32°  F.  for  every 
Fahrenheit  degree  increase  in  temperature  and  decreases  the  same 
amount  for  every  degree  decrease  in  temperature. 

(b)  Given  a  unit  volume  of  gas  at  32°  F.  with  pressure  main- 
tained constant,  then  increasing  the  temperature  i°  F.  would 
cause  the  volume  to  become  ,4*  larger,  while  a  decrease  of  i°  F. 
would  result  in  a  volume  ^  smaller;  a  2°  change  in  temperature 
would  cause  the  volume  to  alter  ?f  „  and  so  on.  Writing  tem- 
peratures and  corresponding  volumes  for  this  case  side  by  side, 
and  beginning  with  a  temperature  of  (492  +  32)  degrees,  gives: 

Temperatures,  Fahr.  Volumes 

524°  (=32  +  492).     •     i  +(492  X*W  =ttf  =  2 


33°  .     •     ...    '  >     '  +  (     IX  ***> 

32°   .     .     -.    V    .     .".!+(     o  X  dnr)  =  III  = 

31°   .......     I  -  (     I  X  ,4*)  =  f  f  4 


-  (  32  x  ,4*)  =  in 


-  460°  (=  32  -  492)  .    .    i  -  (492  X  ,4*)  =  rfy  =  o. 

If  these  volumes  are  plotted  as  abscissas  with  tempera- 
tures in  degrees  Fahr.  as  ordinates,  the  points  will  be  found 
to  lie  on  a  straight  line  which  intersects  the  temperature  axis 
at  -  460°. 

If  the  law  holds  consistently  the  volume  will  be  reduced  to 
zero  at  —  460°  F.  Similarly  with  constant  volume  the  pressure 
must  become  zero  at  —  460°  F.  This  point  of  the  temperature 
scale  is  called  the  Absolute  Zero  of  temperature,  and  tempera- 
tures measured  from  it  are  known  as  Absolute  Temperatures. 
Since  this  point  is  460  Fahrenheit  degrees  below  Fahrenheit  zero, 
the  absolute  temperature,  T,  corresponding  to  any  Fahrenheit 
temperature,  t,  can  be  found  by  adding  460  to  the  latter;  that  is, 

T  =  460  +  /  ........     (7) 


THE  LAWS  OF  GASES  31 

(c)  The  conception  of  absolute  temperature  makes  possible  a 
very   simple   mathematical   statement   of   Charles'   law.     This 
should  be  evident  from  the  foregoing  table. 

Thus,  the  two  parts  of  the  law  are: 

(1)  With  pressure  constant     — ?  =  -=i, (8) 

K2  ll 

and 

(2)  With  volume  constant        §«5 (9) 

-ri       ^2 

(d)  The  apparent  anomaly  of  zero  volume  at  absolute  zero 
temperature  results  from  assuming  the  law  to  hold  continuously 
to  the  lowest  temperatures.     It  should  be  remembered  that  this 
is  a  law  for  an  ideal  substance  only,  and  does  not  represent  the 
behavior  of  any  material  actually  existing.     Therefore  there  is  no 
a  priori  reason  for  doubting  the  result.     A  possible  explanation 
of  this  matter  will  be  given  in  Section  76  (e).     Despite  its  appar- 
ently ridiculous  meaning  at  low  temperatures,  the  law  holds  with 
sufficient  accuracy  for  most  gases  at  the  temperatures  used  in 
ordinary  engineering. 

3.   Combination  of  the  Laws  of  Boyle  and  Charles. 

(a)  Since  it  is  seldom  true  in  actual  practice  that  one  of  the 
three  possible  variables,  P,  V,  and  T,  remains  constant  while  the 
other  two  change,  it  is  convenient  to  combine  Boyle's  law  with 
that  of  Charles  so  as  to  obtain  an  expression  giving  the  relation 
among  all  three  variables.     The  resulting  expression  is  known  as 
the  Law  of  Condition  of  Ideal  Gases,  or,  more  simply,  as  the  Law 
of  Ideal  Gases. 

(b)  To  obtain  the  mathematical  expression  of  this  law,  it  is 
only  necessary  to  imagine  a  given  weight  of  gas  with  initial  con- 
ditions PI,  Vi,  7*1,  changing  to  final  conditions  P2,  Vz,  T%,  in  two 
steps;  first,  at  constant  temperature  TI,  to  F2  and  some  inter- 
mediate pressure  P/,  and  second,  at  constant  volume  F2,  to  PZ 
and  TV 

The  result  of  the  first  change  is  given  by  Boyle's  law  as  follows : 

V       P  ' 
With  temp,  constant  at  TI,    -=^  =  -=^» 

K2  Pi 

from  which  Pi'=£.     -     •     •    •    •     •     (I0) 


32  HEAT-POWER  ENGINEERING 

Here  PI  is  the  resulting  pressure  of  the  gas  when  its  volume  is 
changed  to  V2  and  its  temperature  remains  7\.  Then  using 
Charles'  law  for  the  second  change, 

•p   f  "T1 

with  volume  constant  atF2,       -^-  =  -^i 

•LZ  *2 

from  which  Pt»^i.  ".     .  '.^V    .     (it) 

1\ 

Here  P2  is  the  resulting  pressure  of  the  gas  when  its  temperature 
changes  to  T2  and  its  volume  remains  V2. 

If  now  the  value  of  PI  from  (10)  be  substituted  in  (n),  the 
resultant  expression  is 

p       PiVi    T* 

"TT"55 

giving,  on  rearrangement, 


i\       r2 

which  is  the  expression  sought.     In  general  this  becomes 

•     •     ~^-JJ  =  Constant.  .     .     (13) 


P2F2      P3F3 


(c)  The  value  of  this  constant  for  any  given  gas  will  vary 
directly  with  the  weight  of  gas  dealt  with ;  for,  at  any  given  tem- 
perature and  pressure,  two  pounds  of  gas  must  occupy  twice  the 
volume  occupied  by  one  pound,  three  pounds  three  times  the 
volume,  etc.     For  convenience  it  is  customary  to  tabulate,  for 
all  the  commercial  gases,  the  value  of  this  constant  obtained  by 
substituting  in  (13)  the  volume  of  one  pound  of  gas  and  the  tem- 
perature and  pressure  at  which  the  volume  was  experimentally  de- 
termined.    This  constant,  commonly  represented  by  R,  will  be 
found  to  be  of  great  importance. 

To  distinguish  the  volume  of  any  given  weight  from  the 
volume  of  a  unit  weight  of  gas,  the  former  will  hereafter  be  desig- 
nated by_Fjind  the  latter  by  V.-  The  expression  of  the  law  for 
one  pound  ofideal  gas  then  is 

PV 

TT-*.  .     .     (14) 

(d)  It  makes  no  difference  what  units  are  adopted  in  such  an 
expression  as  (13),  provided  the  same  units  are  consistently  used 
throughout  all  the  calculations,  but  in  (14)  a  constant  .R  is  dealt 


THE  LAWS  OF  GASES  33 

with  whose  values  have  been  calculated  and  tabulated,  hence  it 
is  necessary  to  employ  the  same  units  as  those  used  in  calculating 
R.  In  English-speaking  countries, 

P   =  pressure  in  pounds  per  square  foot ; 

V    =  volume  of  one  pound  of  gas,  in  cubic  feet;  and 

T   =  absolute  temperature  in  Fahrenheit  degrees. 

(e)  The  "  cons tant  "  in  equation  ( 1 3)  may  now  be  i  nterpre ted  as 
WR  where  W  represents  the  number  of  pounds  of  gas  represented 
by  Vi,  Vz,  .  .  .    Vn.     This  applies  in  all  cases  in  which  P  stands 
for  pressure  in  pounds  per  square  foot,  V  for  volume  in  cubic  feet, 
and  T  for  degrees  Fahrenheit  above  absolute  zero. 

(f)  Boyle's  law  as  previously  stated  may  now  be  seen  to  be  only 
a  special  form  of  equation  (13)  or  (14).     Writing  these 

PV  =  WRT       and      PV  =  RT, 

it  becomes  evident  that  the  right-hand  member  is  a  more  complete 
expression  for  the  "  constant  "  of  equation  (6). 

21.  The  Specific  Heats  of  Ideal  Gases.    As  a  result  of  the 
assumption  regarding  the  constitution  of  ideal  gases  (see  page  29), 
it  follows  that,  if  a  quantity  of  heat,  A(),  is  added  to  an  ideal 
gas  in  such  manner  that  it  does  not  alter  the  gas  chemically  nor 
change  its  motion  as  a  whole,  equation  (i)  must  become 

A<2  =  AS  +  AE        (15) 

because,  as  there  are  no  positive  or  negative  internal  forces  to 
overcome  in  such  a  gas,  no  heat  is  needed  for  doing  internal  work; 
hence  A/  equals  zero.  Therefore  the  specific  heat  of  an  ideal  gas, 
or  the  heat  required  when  the  temperature  of  an  ideal  gas  is 
raised  one  degree,  can  only  supply  that  needed  to  increase  the 
temperature  and  to  do  the  external  work  corresponding  to  any 
resultant  volume  change  with  the  displacement  of  surrounding 
media. 

22.  Constant- Volume  Specific  Heat  of  Ideal  Gas  (£„).     (a)  If 
the  volume  of  an  ideal  gas  is  maintained  constant  while  the 
temperature  is  raised,   the  pressure  will   increase  according  to 
Charles'  law.     As  the  volume  does  not  change,  no  external  work 
can  be  done  because  no  external  media  are  displaced.     All  the 
heat  supplied  must  then  be  used  for  changing  the  temperature; 


34  HEAT-POWER  ENGINEERING 

that  is,  using  Aft  to  designate  the  heat  supplied  with  volume 
maintained  constant, 

Aft  must  equal  AS,. 

If  Cv  represents  the  specific  heat  of  an  ideal  gas  when  heated 
at  constant  volume,  this  equation  may  be  written 

Aft  =  AS,  =  WC.  (T2  -  Ti),       ....     (16) 
from  which 

Aft 


W  as  before  standing  for  the  weight  of  the  gas  and  (T2  —  Ti) 
being  the  temperature  change.  As  already  explained,  the  value 
of  Cv  thus  obtained  might  be  either  a  real  constant  or  it  might 
be  an  average  over  the  range  from  TI  to  TV 

(b)  Obviously  this  specific  heat  is  a  True  Specific  Heat  as 
defined  on  page  15.     Also,  it  is  not  only  the  heat  required  to 
raise  the  temperature  of  one  pound  one  degree  at  constant 
volume,  but  is  likewise  the  amount  given  out  when  the  tem- 
perature drops  one  degree  under  the  same  conditions. 

(c)  The  symbol  Cv  denotes  a  certain  quantity  of  heat  energy 
measured  in  British  thermal  units,  but  as  it  is  sometimes  neces- 
sary to  refer  to  the  same  quantity  of  energy  in  the  mechanical 
form  it  is  convenient  to  have  a  symbol  for  that  purpose.     For 
this  Kv  is  used.     As  Cv  stands  for  a  certain  number  of  thermal 
units,  each  of  which  is  equal  to  778  foot-pounds  (see  page  6), 
it  follows  that  Kv  must  numerically  be  778  times  as  large  as  Cv\ 
that  is, 

778CV  =  KV      .......     (18) 

expresses  the  relation  between  the  constant-volume  specific  heat 
in  heat  units  and  in  units  of  mechanical  energy. 

(d)  It  is  now  pertinent  to  inquire  whether  Cv  is  a  constant  for 
all  conditions  of  the  same  gas.     That  is,  whether  it  takes  the 
same  amount  of  heat  to  raise  the  temperature  of  unit  weight 
one  degree  at  constant  volume  when  the  gas  is  at  a  high  tem- 
perature and  when  it  is  at  a  low  temperature;  whether  it  takes 
the  same  amount  of  heat  with  the  gas  at  a  low  pressure  but 
occupying  a  large  volume  as  it  does  with  the  gas  at  a  high  pressure 
but  occupying  a  small  volume. 

Experiment  and  reasoning  lead  to  the  belief  that  Cv  may  be 
considered  constant  for  all  temperatures  and  pressures  in  the 


THE  LAWS  OF  GASES  35 

case  of  the  ideal  gas,  that  is,  one  having  only  the  properties 
assigned  to  that  material  in  previous  paragraphs. 

In  the  case  of  real  gases,  experiments  prove  Cv  to  change 
with  variation  of  temperature  and  pressure;  but  for  ordinary 
gases  through  usual  temperature  ranges  the  variations  are 
negligible.  With  exceptionally  high  temperatures,  such  as 
those  occurring  in  furnaces  and  the  cylinders  of  internal -com- 
bustion engines,  the  increase  in  the  values  of  Cv  is  very  noticeable. 
Therefore  it  is  customary  to  treat  Cv  as  a  constant  for  real 
gases  except  when  making  accurate  calculations  for  very  high 
temperature  conditions. 

(e)  Since,  as  shown  on  page  n,  the  intrinsic  heat  energy  of  a 
substance  depends  only  upon  the  content  of  sensible  heat  and 
the  heat  expended  on  internal  work,  it  follows  from  the  fore- 
going that  in  the  case  of  ideal  gases  the  intrinsic  heat  energy  depends 
only  on  the  temperature.  It  is  impossible  to  measure  the  total 
intrinsic  heat  energy  of  a  gas  because  it  cannot  be  completely 
removed.  It  is,  however,  possible  to  measure  the  quantities 
concerned  in  changes  of  intrinsic  energy,  and  this  is  what  is 
commonly  done.  Whatever  the  conditions  of  the  change,  if  the 
temperature  of  W  pounds  of  gas  is  altered  from  T\  to  T2,  the 
Change  of  Intrinsic  Heat  Energy  is 

Aft,  =  WCV  (T2  -TJ (19) 

23.  Constant-Pressure  Specific  Heat  (Cp).  (a)  If  the  pres- 
sure of  an  ideal  gas  is  maintained  constant  while  the  temperature 
is  raised,  the  volume  will  increase  according  to  Charles'  law. 
As  the  volume  changes,  surrounding  media  must  be  moved  under 
the  constant  pressure  they  exert  upon  the  gas,  and  hence  heat  is 
expended  not  only  in  adding  intrinsic  energy,  but  also  in  doing 
external  work  AEP.  The  amount  of  heat  required  is,  then, 

AQP  =  ASP+  AEP  =  WCP  (T2  -  rO,  .     .     .     (20) 
from  which  the  specific  heat  at  constant  pressure  Cp  is, 

AQP 

Lp~  W(TZ-  7*1) ' 

Here,  as  in  the  preceding  case,  the  specific  heat  may  also  be 
given  in  units  of  mechanical  energy,  in  which  case  the  symbol 
Kp  is  used.  Evidently 

P=KP.        .    :. (22) 


36  HEAT-POWER  ENGINEERING 

(b)  It  was  shown  in  Eq.  (19)  that   the  change  of  intrinsic 
energy  depends  only  on  temperature  change  and  is  independent 
of  pressure  and  volume  conditions.     Hence,  whether  an  ideal 
gas  is  heated  one  degree  at  constant  pressure  or  at  constant 
volume,  the  change  of  sensible  heat  is  exactly  the  same,  and  it 
follows  that  the  constant-pressure  specific  heat  exceeds  the  constant- 
volume  specific  heat  by  just  the  quantity  of  energy  necessary  to 
do  external  work,  AEP.     That  is,  for  any  temperature  variation, 
T!  to  T2, 

giving  AQP  =  AQV  -h  ADP, 

and  Cp  =  C*  +  W(xf-  Ti) (23) 

(c)  A  simple  expression  may  be  obtained   for  the   external 
work  done  when  a  gas  is  heated  at  constant  pressure.     Imagine, 
for  instance,  that  one  pound  of  gas  with  conditions  Fi,  PI,  TI,  is 
confined  in  a  cylinder  with  a  movable  piston  of  area  F  square 
feet.     The  length  of  the  portion  of  the  cylinder  lying  between 
the  inside  of  the  head  and  the  face  of  piston  must  be 


If  now  the  gas  is  heated  at  constant  pressure  to  Tz  the  volume 
will  increase  to  V*  and  the  piston  must  move  out  so  that  the 
distance  from  the  inside  of  the  cylinder  head  to  the  face  of  the 
piston,  becomes 


But  the  piston  will  have  moved  through  the  distance  L2  —  LI 
against  a  force  P\  pounds  per  square  foot;  then  the  work  done  is 

External  work  =  FPi  (L*  -  LI) 

=  Pl  (PL*  -  FLO 

=  Pi(V2-  FOft.-lbs.;       .     .     .     (24) 

hence  the  external  work  done  when  a  gas  is  heated  at  constant  pres- 
sure is  the  product  of  that  constant  pressure  and  the  change  of 
volume,  the  result  being  in  foot-pounds.  If  measured  in  thermal 
units  it  would  be 

External  work  =  AEP  =  P(F2~  Fl)  B.t.u.,  (25) 

770 


THE  LAWS  OF  GASES  37 

and  if  this  be  substituted  in  Eq.  (23),  understanding  Vi  and  V2 
to  stand  for  the  volumes  before  and  after  a  one-degree  change, 
and  remembering  that  the  equation  must  be  written  in  terms  of 
the  volume  of  one  pound  of  gas,  there  results 

r       r    |   P(Vi-Vi)    ' 

CP=  C*  -t      —      --  .       •     -   .     .     (26) 


Using  the  foot-pound  symbols 

Kp=Kv  +  P(Vz-V,}.       .     .     ...     (27) 

(d)  The  constant-pressure  specific  heat  may  now  be  shown  to 
be  a  constant  for  an  ideal  gas.  It  has  been  seen  that  the  con- 
stant-volume specific  heat  may  be  considered  constant;  then,  if 
P  (V2  —  Vi)  can  be  shown  to  be  independent  of  temperature  and 
pressure  conditions,  Kp  and  Cp  must  be  constant.  This  amounts 
to  proving  that  AEP  per  degree  is  constant  at  all  temperatures, 
pressures,  and  volumes. 

To  do  this,  imagine  one  pound  of  a  gas  with  conditions  Vi, 
PI,  TI,  first  heated  one  degree  to  T\  with  volume  changing  to  V/ 
and  pressure  remaining  constant.  The  external  work  done  will 

be 

External  work  =  Pi  (Vi'-Vi)     ....     (28) 

Then,  if  the  condition  of  the  same  gas  is  changed  to  V2,  P2,  Tz, 
which  may  be  any  values  different  from  Vi,  PI,  7\,  and  if  its 
temperature  is  then  raised  one  degree  to  TV  with  the  volume 
changing  to  V2'  and  the  pressure  remaining  constant,  the  ex- 
ternal work,  as  before,  will  be 

External  work  =P2(V2'-  V2)  .....     (29) 
But  by  the  law  of  ideal  gases 


7\  Ti'          T2          T2' 

Substituting  from  this  in  Eqs.  (28)  and  (29)  gives 

Work  in  first  case       =  R  (TV  -  7\)  =  R, 
Work  in  second  case  =  R  (  T2'  —  T2)  =  R, 

so  that  the  work  is  the  same  in  each  case.  It  follows  that  when 
the  temperature  of  one  pound  of  a  perfect  gas  is  raised  one  degree 
at  constant  pressure,  the  work  done  is  always  the  same  and  is  inde- 
pendent of  the  values  of  P,  V,  and  T;  that  is,  &EP  per  degree  is 
constant. 


3g  HEAT-POWER  ENGINEERING 

More  than  this,  it  appears  that  R,  previously  known  only  as 
the  constant  in  the  law  of  ideal  gases,  is  really  equal  to  the  foot- 
pounds of  external  work  done  when  the  temperature  of  one  pound 
of  gas  is  raised  one  degree  at  constant  pressure.  From  this 

KP  =  KV  +  R,  .....     •     -     (30) 

D 

and  Cp=Cv 


24.  The  Ratio  7.     The  ratio  between  the  two  specific  heats 
of  gases  just  considered  is  of  great  importance  and  is  designated 
by  the  letter  7,  thus, 

f?  =  ^  =  7,    .......  '    (32) 

Kv        Ct, 

from  which  it  is  evident  that  7  must  always  be  a  quantity  greater 
than  unity. 

By  means  of  the  ratio  7  a  form  of  expression,  which  will  be 
very  convenient  later,  can  now  be  developed  from  Eq.  (30). 
Rearranging  the  latter  and  dividing  by  Kv,  there  results 

l=Kp_R_=      _R_, 
Kv      Kv  Kv 

D 

from  which  Kv  =  —  —  j-,    ......     (33) 

which  is  the  expression  sought. 

25.  Table  of  Gas  Constants,    (a)  The  Gas  Constants  most 
commonly  used  by  the  engineer  are  given  in  Table  I.     In  it  all 
columns  with  headings  haying  the  same  subscript  are  based  upon 
data  of  the  same  character.     Columns  headed  with  the  same 
letter,  as  BI,  B2,  B3,  contain  values  of  the  same  quantity,  for 
each  gas,  determined  in  different  ways.     In  the  first  column  of 
each  of  the  groups  B,  C,  and  D  is  a  closely  approximate  value 
calculated  from  data  given  in  column  AI  rounded  off  to  the 
nearest  half-unit.     Column  A2  gives  molecular  weights  based  on 
the  1909  International  Atomic  Weights,  and  all  other  columns 
headed  with  the  subscript  2  contain  values  computed  from  these 
weights.     Columns  headed  with  subscript  3  give  experimentally 
determined  values. 

(b)  The  calculated  columns  for  Density  depend  on  the  Law  of 
Avogadro.  This  law  states  that  equal  volumes  of  all  gases,  at 
the  same  temperature  and  pressure,  contain  an  equal  number  of 


THE  LAWS  OF  GASES  39 

molecules.  Hence  the  densities  of  different  gases  must  be  in  the 
same  proportions  as  the  molecular  weights.  The  Weight  per 
Cubic  Foot,  and  Cubic  Feet  per  Pound,  columns  C  and  D,  can 
be  obtained  from  the  density  columns. 

(c)  While  the  specific  heat  Cp  would  be  constant  for  an  ideal 
gas,  it  is  not  constant  for  real  gases.     Experiment  shows  it  to 
vary  with  temperature  and  pressure.     The  values  tabulated  in 
column  Es  are  average  values  for  ordinary  temperature  ranges  at 
atmospheric  pressure. 

The  values  of  7,  however,  which  are  usually  determined  from 
the  velocity  of  sound  in  the  gas,  are  generally  for  some  definite 
temperature.  Therefore  the  numbers  tabulated  in  column  Gs 
are  not  really  on  the  same  temperature  basis  as  those  given  in 
column  E3;  hence,  since  the  most  satisfactory  way  of  obtaining 

values  of  Cv  is  by  using  the  equation  Cv  =  —  ,  the  values  given 

in  column  Fa  must  be  in  error  with  respect  to  the  rest  of  the 
data. 

This  is  well  shown  by  the  variation  of  values  for  R  in  column 
Is'  from  those  in  columns  1%  and  I3.  The  values  in  I3'  are  ob- 
tained from  the  equation  Kp  —  Kv  =  R,  which  should  give  very 
accurate  results  and  the  numerical  values  show  wide  variations 
from  those  determined  in  other  ways. 

In  general,  it  may  be  said  that  the  amount  by  which  the  experi- 
mental results  vary  from  the  exact  calculated  values  is  a  measure 
of  the  degree  of  imperfection  of  the  gas  under  consideration. 

(d)  For  average  engineering  work  it  will  suffice  to  use  the  ap- 
proximate or  observed  columns,  dropping  all  but  three  significant 
figures;  further  figures  are  given  in  the  table  to  correspond  to  the 
supposed  standard  of  accuracy  of  experimental  determinations. 

(e)  The   method   of   calculating   the   values   in   the   several 
columns  is  as  follows: 

A  =  i/Ci 
D,  = 


Bz  =  Observed  E3  =  Observed 

d  =  .080725  X  Bl  F3  =  E*/G3 

C2  =  .080725  X  Bz  G3  =  Observed 

C3  =  .080725  X  B3  H  =  Theoretical 


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HEAT-POWER  ENGINEERING 


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42  HEAT -POWER  ENGINEERING 

It*  (Calculated  from  Inter.  Atom.  Wts.  using  Air  as  a  Base.) 

_  12.387  X  14.696  X  144  y.   i        R 

491.4=  (273  X9/5)        B* 
Is  (Calculated  from  Specific  Heats.) 

=  778  Cp  -  778  Cv  =  R. 
78*  (Calculated  from  Observed  Volumes.) 

D3  X  14.696  X  144  =  R 
491.4  =  (273  X  9/5) 

*  Although  the  value  492°  is  used  in  other  parts  of  this  book  as  the  absolute 
temperature  corresponding  to  32°  F.,  the  value  used  in  computing  the  quantities 
given  in  columns  7  2  and  73  is  491.4,  because  this  corresponds  to  273°  C.,  which  is 
used  in  most  experimental  determinations. 


CHAPTER   V. 


Isobari ) 


PiV, 


EXPANSIONS  AND   COMPRESSIONS  OF  GASES. 

26.  Volume  Changes,  (a)  The  law  of  ideal  gases  expressed 
by  Eq.  (13)  shows  that  there  are  three  inter -related  variables  which 
define  the  condition  of  a  gas;  namely,  pressure,  volume,  and  tem- 
perature. The  fixing  of  any  two  of  these  determines  the  third. 
For  the  study  of  heat  engines  it  is  convenient  to  consider  the 
behavior  of  the  gas  while  the  volume  changes  in  various  ways 
and  to  note  the  accompany- 
ing variations  of  the  other 
two  quantities. 

(b)  Certain  diagrams  are 
useful  in  studying  such 
changes,  the  most  common 
one  being  called  the  pres- 
sure-volume diagram  or  PV- 
diagram.  To  construct  this 
diagram  pressures  are  plot- 
ted vertically  and  volumes 
horizontally  as  in  Fig.  6. 

Assume,  for  instance,  that 
the  volume  and  pressure  of  a 
given  weight  of  a  certain  gas 
are,  PI,  Fi,  as  plotted  at  A.  The  volume  of  this  gas  may  be  in- 
creased or  decreased  in  different  ways.  For  example,  volume 
might  be  made  to  increase  or  to  decrease  while  pressure  is  main- 
tained constant.  If  the  various  volumes  assumed  are  plotted  at 
constant  pressure  PI,  the  resulting  points  must  lie  on  the  line 
AB  or  on  the  line  AC.  Either  one  line  or  the  other  would  then 
show  graphically  the  relations  of  pressure  and  volume.  The 
temperature  at  any  point  as  P2  F2,  where  P2  =  PI  in  this  case, 
could  be  found  by  substitution  in  Eq.  (13)  or  (14),  remembering 
that  if  the  form  involving  R  is  used  V  stands  for  the  volume  of 
one  pound  of  gas. 

43. 


Volumes 

Fig.  6.  — PV-Diagram. 


44  HEAT-POWER  ENGINEERING 

(c)  Volume-changes  with  volume  increasing  are -known  as  ex- 
pansions;  volume-changes  with   volume  decreasing  are  known 
as  compressions.     Inspection  of  Fig.  6  shows  that  any  number 
of  different  kinds  of  expansions  are  possible;  any  line  drawn 
from  A  in  the  field  to  the  right  of  DE  represents  a  possible  ex- 
pansion.    Similarly,  any  line  drawn  from  A  in  the  field  to  the 
left  of  DE  represents  a  possible  compression.     Really,  all  the 
expansions  commonly  used  lie   in   the  quadrant  between  AB 
and   AE  and   all    the    usual    compressions   between   AD    and 
AC. 

(d)  Since  there  are  thus  an  infinite  number  of  possible  methods 
of  changing  volume,  it  is  impossible   to  analyze  all   of  them. 
Fortunately,  the  study  of  four  characteristic  methods  of  change 

-  including  the  limiting  case  with  volume  constant  —  suffices 
for  the  elementary  consideration  of  heat  engines.     They  are: 

1.  Volume  changes,  in  which   the   pressure  is  constant;   or, 
otherwise  stated,  in  which  the  volume  changes  most  rapidly 
with  respect  to  pressure.     These  are  known  as  Isobaric  Changes 
and  are  represented  by  the  graph  AB  or  AC,  Fig.  6. 

2.  Pressure  changes,  in  which   the  volume   is   constant;   or, 
otherwise  stated,  in  which  the  pressure  changes  most  rapidly 
with  respect  to  volume.     These  are  known  as  Isovolumic  Changes 
and  are  represented  by  the  graph  AD  or  AE. 

3.  Volume  changes  at  constant  temperature,  known  as  Iso- 
thermal Changes. 

4.  Volume  changes  known  as  Adiabatic  Changes  (to  be  de- 
fined later). 

27.  Constant-Pressure  or  Isobaric  Changes  of  Gases.  As 
just  explained,  the  graph  of  such  changes  is  a  horizontal  line  on 
the  PV-diagram.  In  Fig.  7  an  isobaric  expansion  of  gas  with 
initial  conditions  PiVi  would  be  represented  by  the  line  AB  and 
a  similar  compression  by  the  line  AC. 

Equation  for  Isobaric  Changes. 

(a)  It  is  evident  from  an  inspection  of  the  graph  of  such  a 
change,  or  from  the  definition,  that  its  equation  in  P  V  coordinates 
is 

P  =  Constant (34) 


EXPANSIONS  AND  COMPRESSIONS  OF  GASES 


45 


Change  of  Associated  Heat  during  Isobaric  Changes  of  Gases. 

(b)  During  these  volume  changes   at  constant  pressure  the 
temperature  must  vary  according  to  Charles'  law;  that  is,  the 

absolute    temperature   must      , ( i 1 

vary  directly  as  the  volume. 
But  when  a  unit  weight  of 
gas  has  its  temperature 
raised  or  lowered  one  degree 
at  constant  pressure,  it  ab- 
sorbs, or  gives  out,  a  quan- 
tity of  heat  equal  to  its  con- 
stant-pressure specific  heat, 
Cp.  Then  for  any  weight  W 
of  gas  changing  volume  from 
Vi  to  Vz  at  constant  pressure 
with  a  corresponding  change 
of  temperature  from  T\  to 
T2,  the  change  of  associated 
heat  (in  thermal  units)  is 


PiV, 


P2Vo 


Volumes 
Fig.  7.  —  Constant-Pressure  Changes 


A<2=  wcp(Tz-  ro (35) 

If  the  volume  change  is  an  expansion  the  result  will  be  positive 
because  T2  will  be  greater  than  T\\  but  if  the  volume  change  is 
a  compression  Tz  will  be  less  than  TI  and  the  result  will  be 
negative.  Negative  heat  change  must  be  interpreted  as  heat 
given  out  or  liberated,  so  that  the  equation  as  stated  is  true  for 
compressions  as  well  as  expansions. 

Work  during  Isobaric  Changes. 

(c)  It  was  shown  in  Eq.  (24)  that  the  external  work  in  foot- 
pounds done  by  a  gas  when  its  temperature  increases  with  pres- 
sure constant  is  given  by  the  equation 

External  Work  =  778  AE  =  P  ( F2  -  Fi)  ft.-lbs.     .     .     (36) 

This  is  the  equation  for  work  done  during  a  constant-pressure 
volume  change.  The  equation  gives  a  positive  result  for  expan- 
sion, and  a  negative  one  for  compression;  that  is,  a  gas  expand- 
ing at  constant  pressure  does  work,  and  work  must  be  done  to 
compress  a  gas  at  constant  pressure. 


46 


HEAT-POWER  ENGINEERING 


(d)  Obviously,  the  product  P  •  (F2  —  Fi)  is  represented  in 
Fig.  7,  by  the  crosshatched  area  under  the  line-  showing  the 
volume  change  from  Vi  to  F2,  hence  the  area  under  that  line, 
expressed  in  foot-pounds,  is  equal  to  the  work  done  during  the 
volume  change.  For  an  expansion  the  area  is  interpreted  as 
positive,  that  is,  as  the  area  ABGF;  for  a  compression  from 
P2  F2  to  PI  Fi,  as  negative,  that  is,  the  area  BAFG.  This  prop- 
erty of  representing  work  by 
area  is  common  to  all  PV- 
diagrams  and  makes*]  them 
very  useful.  / 


"Volumes 
Fig.  8.  —  Constant-Volume  Changes 


28.   Const  ant- Volume  or 
Isovolumic  Changes  of  Gases. 

(a)  With  volume  constant 
the  pressure  will  increase  as 
the  absolute  temperature  in- 
creases, and  decrease  as  that 
temperature  decreases.  The 
graph  of  such  changes  plotted 
to  P  V  coordinates  is  a  verti- 
cal line  like  ED  in  Fig.  8. 
There  being  no  volume  change,  there  can  be  no  expansion  or 
compression.  A  line  drawn  vertically  upward,  as  AD,  means 
pressure  increase,  and  a  line  drawn  vertically  downward  means 
pressure  decrease. 

Equation  for  Isovolumic  Changes. 

(b)  The  equation  of  constant-volume  changes  in  terms  of  P 
and  V  must  be 

V  -  Constant.     .     .     .     .     .     .     »     (37) 

Changes  of  Associated  Heat  during  Isovolumics  of  Gases. 

(c)  To  increase  the  temperature  of  one  pound  of  gas  one 
degree  at  constant  volume  requires  a  heat  addition  equal  to 
Cv  thermal  units,  and  to  decrease  the  temperature  one  degree  an 
amount  of  heat  equal  to  Cv  must  be  withdrawn.     Then  if  the 
pressure  of  W  pounds  of  gas  changes  from  Pl  to  P2  at  constant 
volume,  while  the  temperature  varies  according  to  Charles'  law 


EXPANSIONS  AND  COMPRESSIONS  OF  GASES 


from  TI  to  T-t,  the  change  of  associated  heat  (in  thermal  units) 

A<2  =  WC,  (T,  -  TO (38) 

For  a  pressure  increase  Charles'  law  shows  that  T2  must  be 
greater  than  TI  and  the  result  will  be  positive.  For  a  pressure 
decrease,  T2  will  be  less  than  TI  and  the  result  will  be  negative; 
that  is,  heat  must  be  supplied  to  cause  increase  of  pressure  at 
constant  volume,  and  must  be  abstracted  to  cause  decrease  of 
pressure  at  constant  volume. 

Work  during  Isovolumic  Changes. 

(d)  Since  there  is  no  change  in  volume,  —  that  is,  no  displac- 
ing of  surrounding  media,  —  there  can  be  no  external  work 
done.  Then  for  this  case,  in  foot-pounds, 

External  Work  =  778  AE  =  0.     .    .     .     (39) 

In  the  figure  given  there  is  no  area  under  the  line  represent- 
ing the  change,  and  therefore,  since  area  on  the  pressure-volume 
diagram  represents  work,  it  follows  that  the  work  equals  zero. 

29.   Constant-Temperature  or  Isothermal  Changes  of  Gases. 

(a)    If  the  temperature  of  a  gas  is  maintained  constant,  while  its 
pressure  and  volume  change, 
Boyle's  law  applies  and  gives 
the    relation    between    these 
two  variables  as 

PV  =  Constant. 


If,  starting  with  PI  V\  in 
Fig.  9,  different  values  be 
substituted  for  V  in  this 
equation  and  the  resulting 
pressures  are  computed  and 
plotted  against  these  vol- 
umes, the  graph  obtained 
will  be  CB,  which  is  a  rec- 
tangular hyperbola.  The  line 
from  A  to  B  shows  an  iso- 
thermal expansion  from  P\V\  and  the  line  from  A  to  C  repre- 
sents an  isothermal  compression  from  the  same  point. 


I 


Volumes 

Fig.  9.  —  Isothermal    Changes    for    Ideal 
Gases 


48  HEAT-POWER  ENGINEERING 

Equation  for  Isothermal  Changes  of  Gases. 

(b)  The  equation  of  these  changes,  in  terms  of  pressure  and 
volume,  must  be  that  just  given, 

PV=  Constant  ......  '   .     .     (40) 

Work  during  Isothermal  Changes  of  Gases. 

(c)  Since   there  is  a   change  of   volume  during  isothermal 
changes,  external  work  must  be  done.     If  in  Fig.  9  the  two  closely 
spaced  vertical  lines  represent  a  volume  change  d  V,  from  V\  to 
Vz',  so  small  that  the  pressure  may  be  assumed  constant  while  it 
is  taking  place,  the  external  work  in  foot-pounds  during  that  small 
change  must  be 

778  5£  =  P  (V2f  -  Vi')  =  P  [(Vi'  +  5V)-  V,'}  =  P5V 
and  for  a  finite  change  of  any  size,  from  V\  to  Vz 

778  A3  =   CV*PdV  ......     (41) 

«/  Vi 

To  integrate  this  expression,  it  is  necessary  to  substitute  for 
P  in  terms  of  V.  Assuming  P  and  V  as  the  values  for  any  point 
on  the  curve  and  PI  and  V\  as  the  values  with  which  the  expan- 
sion starts, 

PiVi  =  PV 
from  which 

P=W 
V 

Substituting  this  value  in  the  expression  (41)  gives 


*  ft.-lbs.    .....     (42) 

If  the  ratio  of  volumes  (Vz/  Vi)  in  the  last  expression,  known  as 
the  ratio  of  expansion  or  of  compression,  is  designated  by  the 

*  It  is  usually  more  convenient  to  use  logw  instead  of  loge.  Since  log*  = 
*-3°2  logio,  Eq.  (42)  may  be  written  =  P1V1X  2.302  loglo  ~  •  The  other  logarith- 
mic equations  which  are  to  follow  may  be  similarly  transformed. 


EXPANSIONS  AND  COMPRESSIONS  OF  GASES  49 

letter  r,  the  equation  for  work  done  by  any  weight  of  gas  may  be 
written 

778AE  =  P1F1logerft.-lbs.      .     .     (43a) 

For  unit  weight  778  AE  =  RTi  loge  r  ft.-lbs.  .     .     .     (43b) 

If  the  expansion  is  negative,  that  is,  if  there  is  compression, 
the  work  done  by  the  gas  must  be  negative;  thus  work  must  be 
done  upon  it  to  decrease  its  volume. 

rv2 

i      It  should  be  noted  that  I     PdV  is  the  general  expression  for 

«/Ft 

the  area  under  a  curve  drawn  to  P  V  coordinates  and  hence  in 
Fig.  9  the  crosshatched  area  on  the  diagram  is  a  measure  of 
work  done. 

Change   of   Associated   Heat   during   Isothermal   Changes   of 

Gases. 

(d)  In  order  that  a  gas  may  expand  and  do  work,  an  amount 
of  energy  equivalent  to  the  work  done  must  be  supplied  from 
some  internal  or  external  source.  The  only  heat  energy  asso- 
ciated with  an  ideal  gas*  is  that  associated  with  it  as  sensible 
heat,  and  that  stored  in  surrounding  media  as  a  result  of  previous 
expansion  to  the  present  volume. 

In  isothermal  expansion  temperature  is  constant  by  definition, 
and  since  under  this  condition  the  internal  energy  of  an  ideal 
gas  is  constant,  it  follows  that  there  can  be  no  change  in  the 
store  of  sensible  heat  of  the  expanding  gas,  and  therefore  that 
this  store  cannot  be  the  source  of  energy  for  the  doing  of  work. 

In  any  expansion  the  energy  stored  in  external  media  is  in- 
creased, and  therefore  this  store  cannot  be  a  source  of  energy  to 
do  work,  during  the  expansion. 

Hence  a  gas  doing  work  can  expand  isothermally  only  if  it 
receives  from  an  external  source  an  amount  of  energy  equal  to  the 
work  done,  and  this  energy  can  only  be  received  as  heat.  It 
follows,  then,  that  an  ideal  gas  expanding  isothermally  and  doing 
work  receives  from  surrounding  media  during  the  expansion  a 
quantity  of  heat  equal  to  the  external  work  done,  hence,  from  Eq. 
(43a),  for  any  weight  of  gas, 

B.t.u.      .     .     (44a) 


*  It  is  assumed  that  no  chemical,  change  occurs  nor  any  change  of  motion 
of  the  gas  as  a  whole. 


50  HEAT-POWER  ENGINEERING 

And  for  unit  weight, 


(44b) 


Thus  during  isothermal  expansion  there  is  no  change  of  heat  in 
the  gas  itself;  the  gas  merely  serves  as  a  conveyor  of  the  added 
heat  A<2;  and  this  heat  may  be  considered  as  external  work  AE, 
in  the  solution  of  problems.  Hence,  during  isothermal  expansion 
in  a  piston  engine  the  work  delivered  through  the  piston  rod 
is  equal  to  this  A(). 

(e)  If  a  gas  is  forced  to  expand,  and  to  do  external  work,  with- 
out a  supply  of  heat  energy  from  some  external  source,  it  derives 
the  necessary  quantity  from  its  own  internal  store  of  sensible 
heat;  but  this  is  accompanied  by  a  temperature  drop  and  the 
expansion  cannot  be  isothermal. 

Isothermal  compression  is  the  reverse  of  isothermal  expansion 
and  the  work  done  on  the  gas  appears  as  heat,  which  must  be 
removed  as  fast  as  it  is  generated;  otherwise  the  gas  will  absorb 
this  energy  as  sensible  heat,  with  rise  in  temperature,  and  the 
operation  cannot  then  be  isothermal. 

It  may  seem  at  first  sight  as  if  isothermal  expansion  of  a  per- 
fect gas  furnished  an  exception  to  the  second  law  of  thermo- 
dynamics. It  is  certainly  true  that  all  the  heat  energy  supplied 
to  the  gas  under  such  conditions  is  completely  converted  into 
mechanical  energy,  but  it  is  equally  true  that  this  process  cannot 
continue  indefinitely.  That  is,  such  a  transformation  cannot 
go  on  continuously,  and  must  stop  in  general  when  the  pressure 
of  the  expanding  material  has  reached  that  of.  the  surrounding 
media. 

30.  Adiabatic  Volume  Changes  of  Gases,  (a)  During  adia- 
batic  expansion  or  compression  no  energy,  in  the  form  of  heat, 
is  supplied  to,  or  withdrawn  from,  the  expanding  gas,  as  would  be 
the  case  if  the  walls  of  the  vessel  surrounding  the  gas  were  of 
material  which  is  perfectly  nonconducting  as  regards  heat. 
Therefore  all  heat  that  is  transformed  into  external  work  by 
such  expansion  must  come  from  the  sensible  heat  store  of  the 
working  gas,  and  all  work  that  is  transformed  into  heat  by  such 
compression  goes  to  increase  the  store  of  sensible  heat  of  the  gas. 

More  briefly  —  the  external  work  done  by  the  adiabatic  ex- 
pansion of  a  gas  has  its  energy  source  in  the  sensible  heat  of  the 


EXPANSIONS  AND  COMPRESSIONS  OP  GASES  $1 

gas.     The   heat   resulting   from   work  done   in   adiabatic  com- 
pression is  stored  as  sensible  heat  in  the  gas. 

To  illustrate  adiabatic  changes,  imagine  a  gas  confined  in  a 
cylinder  permanently  closed  at  one  end  and  supplied  with  a 
frictionless  piston.  Assume  that  the  apparatus  is  all  made  of 
material  that  will  neither  absorb  nor  transmit  heat.  If  the  pis- 
ton moves  out,  the  volume  of  the  gas  will  increase  adiabatically 
and  external  work  will  be  done;  if  the  piston  moves  in,  the  volume 
will  decrease  adiabatically  and  work  will  be  done  upon  the  gas. 

(b)  During  adiabatic  volume  increase  against  resistance  —  that 
is,  during  adiabatic  expansion  with  the  doing  of  external  work  — 
the  temperature  of  the  gas  must  fall   because   external  work  is 
done  at  the  expense  of  sensible  heat.     During  adiabatic  volume 
decrease  —  adiabatic    compression  —  the    temperature    must   rise 
because  the  heat  equivalent  of  the  work  of  compression  goes  to 
increase  the  sensible  heat  of  the  gas.     Obviously,  in  this  imagi- 
nary operation,  the  heat  that  disappears  during  expansion  equals 
the  external  work  done;  and  during  compression  the  work  of 
compression  equals  the  heat  increase  in  the  gas. 

Equation  for  Adiabatic  Changes  of  Gases. 

(c)  The  equation  representing  the  adiabatic  change  of  a  gas 

has  the  form 

PVn  =  Const  .......     (45a) 

which  may  be  rewritten 


in  which  n  =  7,  as  will  be  shown  when  Eq.  (48)  is  derived. 

Work  during  Adiabatic  Changes  of  Gases. 

(d)  Using  reasoning  similar  to  that  which  led  to  Eq.  (41),  the 
expression  for  work  done  during  an  adiabatic  change  must  be 

rv2 

778  AE  =  /     PdV. 
Jv, 

P\V\n 
Substituting  in  this  P  =  ,  obtained  from  Eq.  (45),  gives 


(46) 


HEAT-POWER  ENGINEERING 


This  can  be  simplified  by  performing  the  multiplication  indi- 
cated in  the  numerator,  then  substituting  from  the  relation 


and  cancelling,  thus  obtaining  for  any  weight  of  gas, 

778A£  =  Pl^~^F2ft.-lbs.  .    ...    (4?a) 
and  for  one  pound  of  gas, 

£=*(7~)fZlbs  .....     (47b) 


These  equations  cannot  be  used  numerically,  however,  until 
the  value  of  n  is  known.  This  will  now  be  determined. 

(e)  Since  the  sensible  heat  lost  by  a  gas  when  expanding 
adiabatically  and  doing  external  work  must  equal  the  work 
done,  and  since,  in  any  case,  the  sensible  heat  energy  lost  per 
pound  of  a  gas  which  is  changing  temperature  in  any  way  from 
TI  to  a  lower  value  Tz,  must  equal  Kv  (J\  —  T%)  ft.-lbs.,  —  it 
follows  that 


and  substituting  for  Kv  its  value  from  Eq.  (33) 


(y  -  1)  (n  -  1) 

from  which  it  follows  that 

n  =  y  ..........     (48) 

Then  the  equation  of  an  adiabatic  change  is,  as  was  mentioned 
in  connection  with  Eq.  (45), 

PV  =  Constant.     .     .     .     „'    .     .     (49) 
(f)  The  work  done  is,  from  Eq..(47a),  for  any  weight  of  gas, 

778  AE  =  Pff  ~  ™   (ft.-lbs.)    .     .     .     (5oa) 
and  for  one  pound  is,  from  Eq.  (47b), 


778  A£  =  j     »     (ft.-lbs.) 


EXPANSIONS  AND  COMPRESSIONS  OF  GASES  53 

Temperature  Change  of  Gas  during  Adiabatics. 

(g)  Since  during  an  adiabatic  process  the  stock  of  sensible 
heat,  and  hence  also  the  temperature,  is  constantly  changing,  - 
dropping  during  an  expansion  and  rising  during  a  compression,  - 
it  is  necessary  to  find  some  means  of  determining  the  extent  of 
this  temperature  variation.     If  a  gas  changes  adiabatically  from 
PiFk  to  P2F2,  Eq.  (49)  gives 

PiIV  =  P2lV;     or     J^=l     •     •     •     •     (a) 
and  the  law  of  ideal  gases  gives 


If  the  last  forms  of  expressions  (a)  and  (b)  be  multiplied  to 
gether,  there  results 

1        y~1 

=r    ....... 


and  substitution  for  -^  from  the  first  form  of  (a)  gives 

•i 

~ (52) 


Either  Eq.  (51)  or  (52)  can  be  used  for  finding  the  tempera- 
ture resulting  from  an  adiabatic  change  if  the  initial  temperature 
is  known. 

31.  General  Expression  for  Volume  Changes,  (a)  All  the 
common  volume  changes  of  gases  can  be  represented  with  neces- 
sary accuracy  by  the  general  form  of  expression, 

PVn  =  Constant. 

It  is  of  course  assumed  that  n  will  have  a  special  numerical 
value  for  each  different  type  of  change.  The  truth  of  this 
proposition  for  the  changes  so  far  developed  can  be  seen  by 
writing  the  equations  in  the  following  fashion: 

For  pressure  const.,  P  =  Const,  may  be  written  PV°  =  Const. 
For  volume  const.,  V  =  Const,  may  be  written  PFoo  =  Const. 
For  isothermal,  .  PV  =  Const,  may  be  written  PV1  =  Const. 
For  adiabatic,  .  PVy  =  Const,  is  ....  PV^  =  Const. 


54 


HEAT-POWER  ENGINEERING 


(b)  A  comparison  of  the  expansion  curves  (Fig.  10)  will  show 
that  as  the  graph  of  the  different  expansions  considered  swings 

down  through  the  quadrant 
BAE  the  exponent  increases 
in  size.  The  facts  that  any 
equation  with  n  <  1  >  o  gives 
a  graph  less  steep  than  the 
isothermal  and  that  any  equa- 
tion with  n  >  1  <  oo  gives  one 
steeper  than  the  isothermal  are 
very  useful  and  should  be 
memorized.  The  idea  of 
steepness  in  this  statement  is 
important,  as  in  general  one 
curve  cannot  be  said  to  lie 

above  or  below  another.    For 
Fie.  10.  —  Showing  Effect  of  Value  of  n  in  ,      .  r    ,  •      T^« 

Equation  PV»  =  Const.  examPle' lf  the  CUrVCS  m  F^' 

10  are  continued  as  compres- 


Volumes 


sions,  to  the  left  from  the  point  A 
position  are  reversed. 


their  relations  as  to  vertical 


32.  Construction  of  Lines  Representing  Volume  Changes. 
(a)  In  dealing  with  heat  engines  it  is  frequently  necessary  to 
construct  the  lines  representing  graphically  the  changes  already 
discussed  and  others  of  similar  character.  This  can  always  be 
done  by  substituting  assumed  volumes  or  assumed  pressures  in 
the  equation  for  the  type  under  consideration,  solving  for  the 
other  quantity  and  plotting  the  resulting  points.  The  curve 
joining  these  points  is  the  graph  sought.  An  exponential  form 
of  equation  involves  the  use  of  logarithms  and  in  some  cases  the 
calculations  become  a  little  more  troublesome. 

It  is  therefore  convenient  to  know  graphical  methods  of  de- 
termining directly  the  curves  representing  the  various  changes. 

Graphical  Construction  of  Curve     PV  =  Constant. 

(b)  In  Fig.  n,  with  coordinates  P  and  V  as  before,  let  it  be 
desired  to  draw  an  equilateral  hyperbola  through  point  A .  For 
doing  this  two  methods  will  be  given.  First  Method:  —  Draw 
through  the  point  A  horizontal  and  vertical  lines  ppi  and  ViVi\ 
next,  from  the  origin  0  draw  any  number  of  rays  (such  as  Od) 


EXPANSIONS  AND   COMPRESSIONS  OF  GASES 


55 


to  intersect  these  lines  (as  at  a  and  b) ;  then  horizontal  and  ver- 
tical lines  drawn  through  these  points  of  intersection  will  meet 
at  points  (such  as  B)  on  the  desired  curve.  For  expansion  from 
point  A,  the  rays  fall  below  A ;  for  compression,  they  fall  above. 
Second  Method:  —  Through  A,  Fig.  12,  draw  any  number  of 


Figs,  ii  and  12. —  Construction  of  Curve      PV  =  Constant  on  PV-Chart. 

lines,  as   bbi,  cci,  etc.;   make  b\B  =  Ab,  CiC  =  Ac  and  so  on; 
then  the  points  A,  B,  C,  etc.,  will  be  on  the  desired  curve. 

Construction  of  Curve    PVn  =  Const,  by  Using  Logarithmic 
Cross-Section  Paper. 

(c)  The  equation  PVn  =  K  =  const.,  if  solved  by  logarithms, 
takes  the  form  log  P  =  —  n  log  V  +  log  K.  Then  letting  y  = 
log  P,  x  =  log  V,  and  k  =  log  K,  the  last  equation  may  be  re- 
written y  =  —  nx  +  k.  This  is  the  equation  of  a  straight  line 
with  negative  slope  n  and  ^-intercept  k.  It  is  shown  in  Fig.  13 
by  KS,  drawn  to  the  ordinary  uniform  scales  Ox  and  Oy-  The 
abscissa  of  any  point  A  on  KS,  measured  on  the  scale  Ox,  gives 
the  logarithm  of  the  value  of  V  represented;  its  ordinate  on 
scale  Oy  is  the  logarithm  of  the  value  of  P. 

If  now  new  scales  Lv  and  Lp  are  constructed  in  such  a  manner 
that  the  lengths  1-2  and  1-3,  etc.,  represent  the  logarithms  of  2, 
3,  etc., — as  is  done  on  the  scale  of  the  slide  rule,  —  then  these 
logarithmic  scales  may  be  used  for  reading  directly  the  numerical 
values  of  P  and  V  corresponding  to  points  on  KS.  To  the 
scale  Lp,  the  ^-intercept  of  this  line  is  the  constant  K,  and  to 
the  uniform  scale  the  slope  is  n.  Since  the  values  of  P  and  V 


HEAT-POWER  ENGINEERING 


may  be  read  directly  on  the  logarithmic  scales,   the  uniform 
scales  are  not  usually  given  on  charts  of  this  character. 

Any  straight  line  can  be  lo- 
cated on  the  logarithmic  chart 
if  the  PV  values  for  two 
points  are  known;  or  if  one 
point  and  the  slope  n  are 
given;  but  in  the  latter  case 
it  must  be  remembered  that 
the  slope  is  laid  off  using  the 
uniform  scale.  For  one  of  the 
points  it  is  sometimes  conven- 
ient to  use  the  ^-intercept,  K. 
After  the  line  has  been 
drawn  the  simultaneous  values 


%L 

p 

* 

.     ' 

K 

V 

\ 

\ 

A 

\ 

1 

\ 

1 

s 

3 

4 

5 

6 

7 

8   1 

10 

t 

1         1 

I 

1 

: 

lu 

1 

1       2       : 

4 

5     e 

" 

8 

9 

10 

Fig.  13. — Logarithmic  Chart. 


.35 


S'     Q' 


of  P  and  V  may  be  read,  and 
these   may   then   be   used  in 
drawing  the  P  V  curve  on  ordinary  cross-section  paper. 

The  chart  in  Fig.  13  is  arranged  for  numbers  between  I  and  10, 
but  it  may  be  used  for  numbers  between  .1  and  i,  between  10 
and  100,  100  and  1000,  and 
so  on,  by  merely  changing  1 
the  scales  to  suit. 

When  a  wider  range  of  ffi 
numbers  is  under  considera-  10 
tion  (as  from  .1  to  100)  a 
"  checkerboard  "  composed  of 
several  similar  logarithmic 
charts  may  be  used.  Thus  1 
in  Fig.  14,  let  each  of  the 
squares  contain  such  a  chart 
and  let  the  one  surrounded 
by  heavy  lines  correspond  to 
Fig.  13,  with  KS  reproduced. 
In  the  lower  tier  of  charts 
the  ordinates  are  for  numbers  from  .1  to  I,  in  the  middle  tier 
they  are  from  i  to  10,  and  in  the  upper  from  10  to  100.  The 
abscissas  for  the  vertical  columns  progress,  from  left  to  right,  by 
multiples  of  ten  also. 

The  coordinates  of  a  point  anywhere  on  the  checkerboard  can 


\ 


U'    S\  Q' 


ioov 


Fig.  14.  —  Checkerboard  of  Logarithmic 
Charts. 


EXPANSIONS  AND  COMPRESSIONS  OF  GASES  57 

be  read  directly  on  the  proper  scales.  For  example,  point  B 
has  coordinates  P=  25  and  V=  .35;  for  point  C  the  value  of 
P  is  .14  and  V  is  13. 

As  all  the  squares  are  cross-ruled  the  same,  and  differ  only  as 
to  scales  (and  that  by  multiples  of  10),  it  is  evident  that  if  S'T' 
is  drawn  in  the  central  chart  in  a  position  similar  to  that  of 
ST  in  the  square  below,  it  can  be  used  in  place  of  the  latter  line 
provided  points  on  it  are  read  to  a  scale  TV  that  used  for  KS. 
Similarly,  T"Uf,  K'Q',  and  Q"Mf  may  be  drawn  to  correspond 
to  TU,  KQ,  and  QM  respectively,  and  may  be  used  instead  of 
them  with  proper  change  in  scale.  Thus  a  single  logarithmic 
chart  may  be  used  in  place  of  the  checkerboard.  Obviously, 
when  the  curve  crosses  a  horizontal  boundary  line  the  scale  of 
ordinates  changes;  and  when  it  crosses  a  vertical  boundary  the 
scale  of  abscissas  changes. 

If  n  =  i,  as  in  the  case  of  the  equilateral  hyperbola,  the  slope 
of  the  line  is  —  45°.  If  the  exponent  is  greater  than  i,  the  slope 
is  steeper,  and  vice  versa. 


BEAT-POWER  ENGINEERING 


& 
J** 


si 


PQ 


00 


ft} 


CO 


^  c;  r 
-3  o  £ 

5  wJ! 


i      £ 


ii 
> 


> 


a 


8 

^S 


a 


K 

cS 


•38, 
•gi 
26 


0   *- 


.a    ^ 


0 

S    u 


- 


05 


>>  OJ    C 

<*So.S 


CHAPTER   VI. 

REVERSIBILITY.* 

33.  Definition,  (a)  Processes,  or  series  of  changes,  which 
may  be  made  to  occur  with  materials  and  their  associated 
energies  are  broadly  divided  into  two  kinds: 

1.  Irreversible  processes,  and 

2.  Reversible  processes. 

An  Irreversible  Process  is  one  which  affects  the  participating 
materials  and  energies  in  such  a  way  that  after  its  total  or 
partial  completion  it  would  be  impossible  to  return  those  mate- 
rials and  energies  to  initial  conditions,  without  leaving  changes 
in  other  materials  and  their  associated  energies.  All  the  actual 
processes  with  which  the  engineer  has  to  deal  are  of  this  character. 
It  is,  however,  possible  to  imagine  some  of  these  processes  as 
taking  place  under  ideal  conditions  in  such  a  way  that  after  their 
completion  everything  can  be  again  returned  to  starting  condi- 
tions without  leaving  changes  in  anything,  even  though  it  be 
entirely  extraneous  to  the  system  under  investigation.  Such 
ideal  changes  are  called  Reversible  Processes. 

(b)  A  good  mechanical  example  of  a  reversible  change  is 
furnished  by  a  pendulum  swinging  on  a  frictionless  support  and 
in  a  perfect  vacuum.  Each  cycle  of  the  pendulum  is  accom- 
panied by  a  change  of  kinetic  to  potential  energy,  and  then  a 
reversal  of  this  process  so  as  to  bring  everything  concerned  to 
exactly  the  conditions  pertaining  at  the  start.  This,  then,  is  a 
process  which  may  be  said  to  be  by  nature  reversible. 

A  real  pendulum  can  never  reproduce  this  ideal  process  exactly, 
because  of  friction  at  the  support  and  more  or  less  friction  in 
the  enveloping  medium.  These  resistances  change  some  of  the 
kinetic  energy  of  the  pendulum  into  heat  which  in  the  usual 
case  leaves  the  system  by  radiation.  Thus,  the  end  of  each 
cycle  finds  the  pendulum  system  poorer  in  energy  by  the  amount 

48  The  study  of  this  chapter  may  be  deferred  until  Section  49  (h)  is  reached 

59 


60  HEAT-POWER  ENGINEERING 

of  heat  which  has  been  lost;  and  surrounding  materials  must  of 
course  have  gained  a  corresponding  amount  of  energy.  The  real 
process  does  not  therefore  fulfill  the  requirements  of  a  reversible 
process.* 

(c)  It  will  be  observed  from  the  preceding  paragraph  that  the 
ideally  reversible  process  becomes  imperfectly  reversible  as  soon 
as  losses  are  assumed  to  occur.     Although  the  process  could  never 
be  performed  in  reality  without  such  losses,  this  does  not  in- 
validate the  determination  of  the  laws  of  the  ideal  pendulum,  - 
laws  which  are  very  valuable  for  investigations  of  a  certain  type. 
Since  a  reduction  of  losses  in  a  real  process  of  this  character  will 
cause  the  process  to  approach  the  ideal  reversible  one  more 
closely,  it  is  evident  that  the  reversible  process  and  the  laws 
derived   for  it  may  be  regarded  as  the  ideal  limiting  case  of 
the  real  process  and  of  the  laws  governing  it.     This  applies  to 
processes  of  a  certain  character  only. 

(d)  There  are  many  other  processes  of  such  character  that 
no  assumptions  of  ideal  mechanisms  and  no  reasonable  assump- 
tions as  to  the  elimination  of  losses  can  reduce  them  to  limiting 
reversible  processes,  as  was  done  in  the  case  of  the  pendulum. 
Such  processes  are  the  irreversible  ones,  examples  of  which  will 
be  given  later. 

(e)  In   the   investigation   of   certain   thermodynamic    trans- 
formations  accompanying   pressure,    volume,  and    temperature 
changes,  it  is  often  possible  and  desirable  to  assume  all  losses 
absent  so  that  the  process  may  be  considered  reversible.      The 
assumptions  as  to  the  elimination  of  loss  must  be  reasonable  ones, 
however,  —  those  not  involving  changes  in  the  intrinsic  character 
of  the  process.     Thus  it  is  permissible  to  assume  that  there  is 
an  absence  of  friction,  and  that  one  may  use  a  material  which 
does  not  conduct  heat,  as  was  done  in  previous  chapters;  but  an 
assumption  that  there  is  no  internal  heat  energy  lost  when  a  gas 
does  work  by  expanding  adiabatically  behind  a  piston  would 
have  been  unreasonable,  as  it  would  have  been  absolutely  con- 
trary to  the  intrinsic  character  of  the  process. 

*  The  process  might  still  be  considered  reversible  if  there  was  any  way  of  gather- 
ing up  the  energy  lost  as  heat,  converting  all  of  it  into  mechanical  form,  and  return- 
ing this  to  the  pendulum.  But,  even  assuming  that  the  heat  could  all  be  caught, 
the  second  law  of  thermodynamics  states  that  it  cannot  all  be  again  converted 
into  the  mechanical  form,  and  the  statement  made  above  must  therefore  be  correct 


REVERSIBILITY  6l 

The  study  of  an  ideal  reversible  process  in  lieu  of  a  real  im- 
perfectly reversible  one  greatly  simplifies  problems  and  makes 
possible  the  development  of  laws  which  would  otherwise  be 
obtainable  only  with  great  difficulty. 

(f)  For  thermodynamic  purposes  a  reversible  process  may  be 
defined  as  follows: 

A  thermodynamically  reversible  process  is  one  involving  heat 
and  mechanical  energy  transformations  which  are  of  such 
character  that,  after  completion,  they  can  be  carried  through  in 
the  opposite  sense,  without  resulting  in  any  changes  in  anything 
extraneous  to  the  system  under  consideration. 

The  practical  application  of  this  simple  definition  is  often 
confusing.  There  are  certain  processes  which  are  obviously 
reversible  in  this  sense  and  certain  others  which  are  as  obviously 
irreversible;  but  there  are  also  many  about  which  a  decision  is 
difficult.  A  few  reversible  and  irreversible  thermodynamic 
processes  are  given  in  the  succeeding  sections. 

34.  Some  Reversible  Processes,  (a)  A  good  example  of  an 
ideal  thermodynamically  reversible  process  is  as  follows:  Imagine 
a  perfect  gas  inclosed  in  a  cylinder  made  of  material  that  will 
neither  absorb  nor  conduct  heat  and  let  it  be  fitted  with  a  friction- 
less  piston  of  the  same  material.  If  the  gas  expands  it  must 
*do  so  adiabatically,  since  the  heat  insulation  is  assumed  to  be 
perfect.  The  temperature  will  drop,  the  volume  will  increase,  and 
work  will  be  done  in  driving  the  piston  outward  against  what- 
ever resistance  is  offered  —  for  instance,  the  raising  of  a  weight. 

If,  after  the  piston  has  reached  a  certain  point,  the  work  which 
has  been  done  by  the  gas  is  returned  to  drive  the  piston  back  to 
its  original  position  —  for  instance,  by  the  dropping  of  the  lifted 
weight,  —  the  gas  will  be  compressed  adiabatically  to  its  original 
condition  and,  in  the  ideal  case,  nothing  in  the  universe  need  have 
been  changed  by  the  process. 

Such  a  process  is  thermodynamically  reversible.  It  is  evi- 
dently ideal  and  can  only  be  approximated  in  real  cases,  for  every 
material  known  absorbs  and  conducts  heat,  and  no  piston  can  be 
frictionless.* 

*  It  is  really  necessary  to  further  stipulate  that  the  expansion  and  compression 
of  the  gas  in  this  process  take  place  at  infinitely  slow  rates,  to  make  it  perfectly 
reversible  in  theory.  This  is  necessary  in  order  to  exclude  any  degree  of  what  is 
termed  "  free  expansion,"  an  irreversible  phenomenon  which  will  be  treated  in  a 
later  paragraph. 


62  BEAT-POWER  ENGINEERING 

(b)  Again,  imagine  a  body  which  is  at  a  certain  temperature, 
and  is  so  arranged  that  the  withdrawal  of  heat  from  it  does  not 
change  its  temperature.     The  steam  in  a  boiler  is  a  body  of 
material  approximating  this  conception.     If  a  confined  body  of 
gas  is  kept  in  contact  with  this  source  of  heat,  or  hot  body, — 
as  in  a  steam- jacketed  cylinder  made  of  perfectly  conducting 
material, —  and  if  it  is  allowed  to  expand  and  do  external  work, 
such  as  driving  out  a  piston  against  resistance,  the  expansion 
must  be  isothermal.     During  the  process  heat  wrill  be  drawn  from 
the  hot  body  and  appear  as  mechanical  energy  to  do  external 
work.     This  work   may   be  returned   by   compressing  the  gas 
isothermally   and   restoring   the   resulting   heat   to   its   original 
source.     The  ideal  process  is  thermodynamically  reversible,  but 
practically  some  heat  must  have  been  radiated  and  some  lost 
as  friction,  so  that  the  reversibility  is,  as  before,  ideal  only. 

(c)  A  reconsideration  of  the  simple  ideal  expansions  discussed 
in   Chapter  V  will    now  show  that  all  of  these  may  be  made 
reversible  processes. 

35.  Some  Irreversible  Processes,  (a)  One  of  the  best  ex- 
amples of  an  intrinsically  irreversible  process  is  furnished  by 
the  passage  of  heat  from  one  body  to  another  which  is  at  a  lower 
temperature.  Consider  two  bodies  at  different  temperatures' 
brought  into  contact  and  thermally  isolated  from  the  rest  of 
the  universe.  Experience  shows  that  the  colder  body  will  receive 
heat  from  that  having  the  higher  temperature,  and  that  this  proc- 
ess will  continue  until  the  two  temperatures  become  the  same; 
also  it  shows  that  certain  physical  changes  will  accompany  this 
passage  of  heat.  Thus  there  may  be  a  change  of  state,  as 
would  be  the  case,  for  instance,  if  the  colder  body  is  ice  at 
the  melting  point;  or  again,  there  may  be  simply  changes  in 
volume  accompanying  the  doing  of  external  work. 

No  matter  what  the  conditions,  no  method  has  yet  been 
devised  to  reverse  this  process  thermodynamically;  that  is,  to 
make  heat  flow  from  the  previously  cool  body  to  the  other  so 
as  to  leave  them  at  different  temperatures,  return  them  to  the 
initial  physical  conditions,  and  leave  no  change  in  anything 
else.  The  process  is  then  irreversible  by  definition. 

(b)  Another  example  of  an  intrinsically  irreversible  process  is 
the  free  expansion  of  a  perfect  gas  similar  to  that  which  occurs 


REVERSIBILITY  63 

in  Joule's  experiment.*  Imagine  two  vessels  of  equal  size 
joined  by  a  pipe  containing  a  valve,  all  made  of  non-heat-con- 
ducting material.  Imagine  further  that  one  vessel  contains  a 
quantity  of  perfect  gas  at  some  given  pressure  and  temperature 
and  that  the  other  vessel  is  absolutely  empty.  If  the  valve  in 
the  connecting  pipe  is  opened,  the  gas  will  rush  from  the  high- 
pressure  vessel  into  the  other  one  and  ultimately  both  will 
contain  the  same  quantity  of  gas  at  the  same  pressure  and 
temperature.  To  make  this  possible,  the  gas  originally  contained 
in  one  vessel  must  have  expanded  until  its  volume  became  suffi- 
cient to  fill  the  two.  Since  the  volume  occupied  by  the  gas  is 
now  greater  than  before,  the  pressure  must  be  lower  unless  the 
temperature  has  risen,  and  it  will  be  found  that  this  has  not 
occurred.  Further,  since  the  vessels  and  connecting  pipe  are 
nonconducting,  and  since  the  system  is  so  arranged  that  no 
disturbance  of  surrounding  media  can  be  caused,  it  follows  that 
there  can  have  been  no  loss  of  heat  energy  by  the  gas. 

The  heat  energy  associated  with  the  system  must  therefore  be 
the  same  before  and  after  the  change.  Since,  however,  as  was 
shown  in  connection  with  the  specific  heat  of  gases,  the  intrinsic 
heat  energy  of  a  perfect  gas  is  always  the  same  at  the  same 
temperature,  it  follows  that  the  temperature  of  the  gas  must  be 
the  same  when  filling  two  vessels  as  when  filling  one. 

To  make  this  process  reversible,  it  must  be  possible  to  com- 
press the  gas  again  into  one  vessel,  keep  the  temperature  the 
same,  and  have  no  change  in  anything  outside  the  system  of  two 
vessels  and  contained  gas.  This  is  impossible,  as  work  would 
have  to  be  done  upon  the  gas  to  compress  it,  and  there  would 
then  either  be  a  rise  in  temperature  or  the  heat  of  compression 
would  have  to  be  absorbed  by  some  body  outside  the  system. 
This  heat,  though  equal  to  the  work  of  compression,  could  not 
be  returned  to  the  engine,  or  device  doing  that  work,  as  an 
equivalent  of  the  work  done.  This  is  so  because  (according  to 
the  Second  Law  of  Thermodynamics)  no  engine  could  deliver 
in  mechanical  form  all  the  heat  supplied  it. 

Obviously  the  process  is  intrinsically  irreversible  because  it  is 
impossible  to  imagine  its  thermodynamic  reversal  even  with 
ideal  mechanism. 

*  This  is  not  to  be  confused  with  Joule's  experiment  for  the  determination  of 
the  mechanical  equivalent  of  heat. 


64  HEAT-POWER  ENGINEERING 

(c)  The  process  of  free  expansion  is  one  of  the  most  interest- 
ing and  is  worthy  of  more  detailed  study.  What  really  happens 
is  best  considered  in  two  parts. 

The  gas  in  the  high-pressure  vessel  begins  to  expand  as  soon 
as  the  valve  in  the  connecting  pipe  is  opened,  and  it  acquires 
a  high  velocity  with  rapid  drop  of  pressure  as  it  flows  into  the 
empty  vessel.  The  kinetic  energy  associated  with  this  velocity 
must  come  from  the  intrinsic  heat  energy  possessed  by  the  gas. 
The  expansion  is  in  reality  adiabatic,  and  the  intrinsic  heat 
energy,  which  during  expansion  behind  a  piston  would  have 
been  converted  into  mechanical  work,  is  here  converted  into 
the  kinetic  energy  acquired  by  the  gas  itself.  The  temperature 
of  the  gas  drops  just  as  in  the  other  adiabatic  expansions  already 
considered;  thus,  the  material  entering  the  empty  vessel  has 
the  low  temperature  which  corresponds  to  the  low  pressure  and 
is  deducible  directly  from  the  law  of  adiabatic  expansion. 

Considering  next  the  receiving  vessel,  —  the  gas  with  low 
pressure  and  temperature  enters  with  high  velocity  but  imme- 
diately becomes  churned  up,  impinges  on  the  walls,  etc.,  and 
slowly  comes  to  rest.  The  energy  originally  possessed  by  virtue 
of  its  velocity  cannot  be  destroyed,  but  is  reconverted  into  heat. 
It  is  absorbed  as  sensible  heat  by  the  gas  and  raises  its  tempera- 
ture. Given  sufficient  time,  equilibrium  will  be  established 
between  the  material  in  the  two  vessels,  and  then  the  gas,  with 
the  same  stock  of  heat  as  before,  will  have  returned  to  the  tem- 
perature it  had  initially.* 

*  The  importance  of  the  footnote  on  page  61  can  now  be  appreciated.  If 
gas,  expanding  adiabatically  behind  a  piston,  is  allowed  to  acquire  an  appreciable 
velocity,  some  of  the  heat  energy  which  has  previously  been  assumed  as  doing 
external  work  will  be  used  to  impart  this  velocity  to  the  gaseous  molecules.  In 
just  so  far  as  this  occurs  the  process  will  be  irreversible.  In  all  real  piston  engines 
the  velocity  acquired  is  so  small  that  the  heat  thus  used  is  negligible.  Hence  no 
attention  is  ever  given  the  phenomenon  from  this  viewpoint,  and  it  need  not  be 
considered  in  discussing  the  elementary  cycles  in  the  following  chapters. 


CHAPTER   VII. 

ENTROPY. 

36.  Explanatory.     In  the  more  advanced  discussions  of  ther- 
modynamic  theory  a  certain  property  of  substances,  know  as 
their  "Entropy"   (represented  by  <£),  is  found  to  be  of  great 
importance.     The  solution  of  most,  if  not  all,  engineering  prob- 
lems involving  thermodynamic  changes  can  be  obtained  with- 
out employing  entropy;  but  its  use  enables  scientists  to  draw 
certain  sweeping  conclusions  with  regard  to  natural  phenomena, — 
conclusions  which  would  otherwise  be  difficult  to  formulate,  and 
which  materially  assist  in  developing  the  laws  governing  thermo- 
dynamic transformations.     The  consideration  of  entropy  also 
serves  the  useful  purpose  of  giving  the  engineer  a  broader  view- 
point with  regard  to  the  processes  he  makes  use  of.     For  these 
reasons  it  is  introduced  here. 

37.  Definition,     (a)  It  has  been  seen  that  it  is  impossible  to 
measure  the  absolute  amount  of  associated  heat  energy   (0, 
and  that  all  cases  can  be  analyzed  when  the  discussion  is  limited 
to  changes  of  energy  (dQ,  dQ,  or  A@).     Later  it  will  be  shown  that 
entropy  is  a  similar  function  ;  therefore  the  treatment  will  be 
limited  to  entropy  changes  (d<f>,  S<£,  A0),  rather  than  to  consider 
the  absolute  amount. 

(b)  To  a  student  unable  to  distinguish  between  heat  and  cold 
and  not  familiar  with  the  phenomena  accompanying  tempera- 
ture changes,  it  would  be  very  difficult  to  convey  a  conception 
of  what  a  temperature  change  really  is.  Probably  the  best 

definition  would  be  the  mathematical  one  dT  =  -* »  which  would 

o 

be  unsatisfactory  and  troublesome  to  the  student  until,  by 
experience,  he  became  familiar  with  the  phenomena  accompany- 
ing changes  in  temperature.  The  same  difficulty  occurs  in 
attempting  to  define  any  unfamiliar  physical  quantity  or  prop- 
erty, and  applies  equally  well  to  entropy.  Hence,  the  best 

65 


66  HEAT-POWER  ENGINEERING 

that  can  be  done  at  present  is  to  give  a  mathematical  definition 
of  entropy  and  rely  on  the  experience  and  familiarity,  which 
will  come  from  the  solution  and  discussion  of  problems  involving 
its  use,  to  give  a  more  or  less  concrete  conception  of  the  physical 
meaning  and  properties. 

(c)  The  Mathematical  Expression  for  an  Infinitesimal  Change 
of  Entropy  is 


l*y  rj~> 

in  which   the  numerator   indicates  the  summation  of   the  in- 
finitesimal changes  indicated, 

T  =  absolute  temperature  of  material  during  these  infinites- 
imal changes,  and 
A  =  1/778,  introduced  to  keep  all   terms  in  numerator  in 

same  units. 
A  finite  change  of  entropy  will  then  be 

A    D    JIT 

....     (54) 


It  is  often  convenient  to  first  evaluate  per  pound  and  then 
for  the  weight  concerned.  If  A<£i  is  for  unit  weight, 

A0J7  =  W  A0i (55) 

(d)  It  will  be  observed  during  the  further  development  of 
thermodynamic  phenomena  that  all  those  processes  which  occur 
"  naturally,"  i.e.,  spontaneously,  are  accompanied  by  an  increase 
of  entropy.  Any  process  which  results  in  a  decrease  of  entropy 
must  be  forced  in  some  way,  and  is  in  that  sense  "  unnatural." 
Hence  it  may  be  said  that  the  entropy  of  every  substance  tends 
to  increase. 

A  somewhat  analogous,  though  not  a  parallel,  case  may  be 
cited  from  mechanics.  It  is  well  known  that  the  potential 
energy  of  mechanical  systems  always  tends  to  decrease,  for 
there  is  a  tendency  for  the  centers  of  mass  of  all  terrestial  bodies 
to  approach  the  earth's  center  as  closely  as  conditions  will 
permit.  Given  a  mechanical  system,  in  which  processes  result- 
ing in  change  of  the  position  of  the  center  of  gravity  can  take 
place,  that  change  will  occur  which  will  make  the  potential 
energy  of  the  system  least,  unless  external  forces  impose  a 
different  behavior. 


ENTROPY  67 

38.  Entropy  Changes  for  Reversible  Processes  with  Ideal 
Gases,  (a)  It  was  mentioned  (in  Section  340)  that  the  ideal 
expansions  considered  in  Chap.  V  may  be  made  reversible  proc- 
esses; and  a  further  consideration  will  show  that  in  every 
such  case  the  external  work,  dE,  can  be  represented  asAPdV. 
Further  study  will  show  that  for  all  reversible  processes 

APdV  =  dE  and  A  f  'P dV  =  AE. 


•JT 


Then,  since  dl  =  o  for  an  ideal  gas,  the  numerator  of  Eq.  (53) 
becomes  dS  +  dE  =  dQ.  And  the  infinitesimal  entropy  change 
experienced  by  an  ideal  gas,  during  a  reversible  process,  is  then 

dS+dE      dQ 
d<t>  =  --  j,  --  =  y  ......     (56) 

The  finite  change  is 

"  •'•  •  •  •  •  (57) 


or,  if  dQ  be  assumed  to  refer  to  unit  weight,  see  Eq.  (55), 

.   ......     (58) 


(b)  It  must  be  noted  that  the  last  three  equations  are 
proved  only  for  reversible  processes,  and  for  the  present  they  will 
be  considered  as  applicable  only  to  ideal  gas.  They  may  be 
used  for  finding  the  entropy  change  experienced  by  a  given 
weight  of  ideal  gas  which,  while  expanding  behind  a  piston,  is 
undergoing  one  of  the  reversible  processes,  such  as  those  de- 
scribed in  Chapter  V;  they  are  not  applicable  for  determining 
the  entropy  change  when  a  given  weight  of  gas  experiences  an 
irreversible  process,  such  as  the  free  expansion  of  Joule's  experi- 
ment, Section  35  (b).  In  such  cases  the  entropy  change  must 
be  determined  in  other  ways  which  will  be  presented  later. 

39.   Sign  of  Entropy  Changes  during  Reversible  Processes. 

(a)  The  integration  of  Eq.  (57)  between  the  limits  I  and  2  for 
any  assumed  process  will  result  in  a  difference  of  two  quantities; 
thus  the  sign  of  the  right-hand  member  will  depend  upon  which 
of  these  quantities  is  the  larger.  The  sign  of  this  number  indi- 
cates whether  the  process  in  question  will  increase  or  decrease 
the  entropy  of  the  material. 


68  HEAT-POWER  ENGINEERING 

(b)  A  reversible  increase  of  heat  energy  would  give  a  positive 
value  for  the  right-hand  member  of  the  equation,  —  a  positive 
value  of  A0,  —  and  this  corresponds  to  an  increase  of  entropy. 

(c)  A  reversible  rejection  of  heat  results  in  a  negative  value 
of  A0,  indicating  a  decrease  of  entropy. 

(d)  Eq.  (57)  would  show  no  change  of  entropy  for  any  revers- 
ible process  involving  no  change  of   associated  heat,  but  this 
could  only  be  true  of  an  adiabatic  process  (in  which  dQ  =  o,  see 
Section  30  (a)  ).     An  ideal  gas,  therefore,  experiences  no  change 
of  entropy  during  a  reversible  adiabatic  process. 

(e)  Although  it  is  the  entropy  change  which  is  really  con- 
sidered in  thermodynamic  calculations  in  which  entropy  is  con- 
cerned, yet  engineers  are  accustomed  to  speak  of  the  "total 
entropy  "  of  the  substance  for  the  particular  conditions  of  tem- 
perature, pressure,  and  volume  pertaining.     They  do  this  because 
they  have   by  common  consent  agreed    that   the  entropy  of 
materials  shall  be  measured  above  a  certain  arbitrarily  chosen 
datum,  which  is  taken  as  zero  for  convenience.     Thus  the  term 
"  total   entropy  "    (<£)    refers  to   the  total   entropy  change   ex- 
perienced by  the  material  in  passing  reversibly  from  the  arbi- 
trarily chosen  datum  to  the  conditions  in  question.     As  the 
entropy  difference  (<fe  —  #1)  is  dealt  with,  any  datum  whatever 
may  be  selected  provided  the  same  one  is  used  for  both  of  the 
entropy  quantities,  <fc  and  0i. 

40.  Entropy  Changes  during  Reversible  Isobarics  of  Gases. 
In  Eq.  (56)  the  numerator  of  the  right-hand  member  can  be 
replaced  by  the  product  of  specific  heat  into  an  infinitesimal 
temperature  change,  thus  for  unit  weight 

,         dQ      CdT  ,     , 

d(f>  =  -^  =  —  ^-  1    ......     (59) 

the  symbol  C  representing  the  proper  specific  heat  for  the  par- 
ticular change  under  consideration. 

For  a  change  at  constant  pressure  C  becomes  Cp  and  the 
differential  equation  for  entropy  change,  per  unit  weight,  is 


(60) 


Assuming  Cp  a  constant  as  before,  the  total  change  of  entropy 
is,  per  unit  weight, 


ENTROPY  69 

Thus  A0  =  (fc  -  00  =  Cp  (log.  T2  -  loge  ri).     .     (6ib) 

=  Cploge*p (6ic) 

*i 

Eq.  (6ib)  or  (6ic)  will  indicate  by  the  algebraic  sign  of  its 
right-hand  member  whether  a  positive  01  negative  entropy 
change  is  under  consideration.  Increase  of  associated  heat  will 
make  T2  greater  numerically  than  T\  and  the  right-hand  mem- 
ber of  the  equations  will  then  have  a  positive  sign,  which 
indicates  an  increase  of  entropy.  Reduction  of  associated  heat 
will  make  T2  less  than  T\  and  the  right-hand  member  of  the 
equations  will  have  a  negative  sign. 

The  equations  can  then  be  trusted  to  give  not  only  the  numeri- 
cal value  of  the  entropy  change,  but  also  to  signify  whether  it 
increases  or  decreases  the  total  entropy  of  the  material  under 
consideration. 

41.   Entropy  Changes  during  Reversible  Isovolumics  of  Gases. 

In  this  case  the  specific  heat  C  in  Eq.  (59)  becomes  Cv  and  the 
resulting  differential  equation  is 

=        1.    .  '•/.    ....     (62) 


J. 
The  total  change  of  entropy  is,  therefore,  per  unit  weight, 


or  A0  =  (02  -  &)  =  C,  (log,  T2  -  loge  7*1).  .     .       (63) 

=  C,  log,  p-      .....     (63a) 

1  1 

As  before,  the  algebraic  sign  of  the  right-hand  member  of  this 
equation  will  indicate  whether  an  increase  or  decrease  of  entropy 
is  under  consideration. 

42.  Entropy  Changes  during  Reversible  Isothermals  of  Gases. 
During  an  isothermal  change  the  temperature  is  constant  by 
definition;  that  is,  T  in  Eq.  (56)  is  the  same  for  each  of  the  differ- 
ential heat  changes  dQ.  Then 


*  It  is  usually  more  convenient  to  use  logio  instead  of  loge.  As  loge  =  2.302  logio, 
Eq.  (6ic)  may  be  written  A0  =  CP  X  2.302  logio  (TV T,).  The  other  logarithmic 
equations  which  are  to  follow  may  be  similarly  transformed. 


70  HEAT-POWER  ENGINEERING 

.j; 

becomes 

A* -(*-#£ -^-7^.    •    ;     •     •     (64) 

Thus,  for  isothermal  changes,  since  ((?2  —  Qi)  =  A<2, 

A*-^.  '.--..     .. (65) 

The  entropy  change  will  obviously  have  the  same  sign  as  A<2, 
indicating  increase  of  entropy  with  increase  of  associated  heat 
and  decrease  of  entropy  with  decrease  of  associated  heat. 

43.  Entropy  Changes  during  Reversible  Adiabatics  of  Gases. 

An  adiabatic  change  being  one  which  occurs  under  conditions  of 
heat  insulation,  that  is,  one  during  which  heat  energy  is  neither 
given  to  nor  abstracted  from  the  substance,  it  follows  that 
dQ  =  o,  and  therefore 

^  =  ^2  =  o (66) 

Thus  during  a  reversible  adiabatic  change  there  is  no  entropy 
change,  just  as  during  an  isothermal  process  there  is  no  tem- 
perature change.  Reversible  adiabatics  are  therefore  often  called 
Isentropics,  and  these  two  terms  may  be  used  interchangeably. 

44.  Irreversible  Adiabatic  Processes  of  Ideal  Gas,  and  the 
Corresponding   Entropy   Changes,     (a)    Besides    the    reversible 
adiabatic  expansion  already  discussed,  there  are  an  unlimited 
number  of  adiabatic  processes  which  are  irreversible.     These 
are  thermodynamic  processes  which  ideal  gas  undergoes  when 
confined  in  vessels  which  are  nonconducting  as  regards  heat, 
that  is,  in  those  which  neither  permit  the  gas  to  receive  nor  to 
surrender   any   heat   through    the   surrounding   walls.     Of   the 
processes  which  are  strictly  adiabatic,  those  which  are  isentropic 
are  the  only  ones  that  are  reversible. 

(b)  As  an  example  of  an  irreversible  adiabatic  change  of  ideal 
gas,  assume  the  process  similar  to  the  free  expansion  of  Joule's 
experiment,  discussed  in  Section  35  (b).  During  such  a  process, 
the  entropy  change  experienced  by  unit  weight  of  gas  cannot 
be  found  by  Eqs.  (56)  and  (57),  as  they  apply  only  to  reversible 
processes.  An  attempt  to  use  them  would  give  the  zero  entropy 


ENTROPY  71 

change  that  was  obtained  in  Section  43,  which  is  very  far  from 
being  correct,  as  the  next  paragraph  will  show. 

(c)  Recourse  must  then  be  had  to   the  original  definition, 
Eq.  (53),  which  may  be  rewritten  as 

dS  +  dl  ,    APdV. 
d<t>  =  -—^  ---  ^A~Y~  ......     (a) 

In  the  process  under  discussion  there  can  be  no  change  in  the 
sensible  heat  because  the  temperature  of  the  gas  is  the  same  after 
as  before  the  change,  and  dl  is  of  course  zero  for  ideal  gas. 
Hence  dS  +  dl  =  o  and  Eq.  (a)  becomes 


(b) 


The  P  VT  changes  in  a  unit  weight  of  ideal  gas  are  represented 
by  the  expression 


Thus  P  =  RT/V 

and  P(N  =  RT~ 

This  value  of  PdV  may  now  be  substituted  iri  Eq.  (b),  which 
then  becomes 

,.        ARTdX       ARdV 
d<j>  =  A-jr  y-=A-^-. 

Integrating  this  between  the  limits  I  and  2  gives  the  true  entropy 
change,  per  pound  of  material, 

As  the  volume  V2  occupied  when  the  gas  fills  the  two  vessels 
is  greater  than  the  volume  Vi  which  it  had  when  confined  in  one 
of  them,  the  process,  as  shown  by  Eq.  (c),  must  result  in  an 
increase  of  entropy  despite  the  fact  that  the  conditions  are 
adiabatic.  This  is  quite  different  from  the  zero  value  obtained 
by  applying  the  equation  for  reversible  changes  in  which  A  PdV 
=  dE.  This  emphasizes  the  statement  already  given  that  only 
reversible  adiabatics  are  isen  tropic  processes. 

(d)  The  free  expansion  of  a  gas  may  be  called  a  "  natural  " 
process.  It  was  seen  to  be  accompanied  by  an  increase  in 


/z      fj\r 
R^=AR(lozeV2-  \oZeVJ  .       .     .     (c) 


72  HEAT-POWER  ENGINEERING 

entropy  of  the  materials  concerned.  A  similar'  increase  also 
occurs  with  all  other  natural  processes,  such  as  the  flow  of  heat 
from  a  higher  temperature  body  to  one  at  lower  temperature. 
Thus  the  entropy  of  all  substances  always  tends  to  increase. 
These  facts  will  become  more  apparent  as  the  subject  is  developed. 

45.  Entropy  Changes   Independent   of   Path,     (a)    The   in- 
tegration of  Eq.  (54)  results  in  a  difference  in  two  quantities, 
the  values  of  which  depend  merely  on  the  conditions  of  the 
substance  before  and  after   the  change.     Evidently,  then,  the 
entropy  change  is  in  no  way  dependent  on  the  method  of  changing 
from  the  one  set  of  conditions  to  the  other.     Thus  the  entropy 
change  experienced  by  a  material  in  passing  from  some  definite 
set  of  conditions  I  to  another  definite  set  2  will  always  be  the 
same,  no  matter  what  path  is  pursued  on  the  graphical  repre- 
sentation of  the  process. 

(b)  This  fact  is  often  of  great  importance,  as  the  entropy 
change  experienced  by  a  substance  when  undergoing  any  very 
complicated  set  of  changes  can  be  determined  by  finding  the 
entropy  change  accompanying  any  simple  change,  or  group  of 
changes,  which  will  carry  the  body  from  the  same  initial  to 
the  same  final  conditions.  It  is,  however,  very  essential  to 
make  sure  that  the  final  conditions  are  the  same  in  both  cases, 
as  mistakes  are  easily  made  in  just  this  point. 

46.  Temperature-Entropy  Diagrams,     (a)   Just  as  pressure- 
volume  diagrams  are  useful  as  a  means  of  graphically  represent- 
ing  certain   changes,   so   diagrams   with   absolute  temperature 
plotted  vertically  and  entropy  change  plotted  horizontally  are 
capable   of   visualizing   some   very   important   transformations. 
They  are  known  as  T0-diagramr. 

There  is  a  peculiarity  about  the  plotting  of  diagrams  with 
temperature  and  entropy  coordinates,  to  which  attention  should 
be  called.  In  the  PV-diagram  the  intersection  of  the  coordi- 
nate axes  represents  zero  pressure  and  zero  volume,  and  this 
is  possible  because  both  absolute  pressure  and  absolute  volume 
can  be  determined.  In  the  T^-diagrams,  however,  although 
absolute  temperature  can  be  determined  inferentially,  as  pre- 
viously shown  on  p.  30,  the  absolute  quantity  of  entropy  is  inde- 
terminate like  the  absolute  quantity  of  associated  heat.  As 
already  shown,  the  equations  give  change  of  entropy,  A<£,  and  not 


ENTROPY 


73 


absolute  quantity  of  entropy,  <j>.  It  is  this  A</>  which  is  used  in 
plotting.  The  abscissas  thus  represent  entropies  of  a  substance 
above  some  conveniently  chosen  datum,  such  as  that  at  32°  F. 

(b)  In  Fig.  15,  the  point  A  represents  the  temperature- 
entropy  conditions  of  a  substance  as  Tifa.  This  means  that  at 
temperature  7\  the  entropy  of  the  substance  is  <fr,  above  what- 


Fig.  15.  —  T^-Curves  for  Gases. 

ever  value  has  been  decided  on  as  zero  of  entropy,  — just  as  in 
the  PV-diagram,  Fig.  6,  V\  represents  the  volume  of  the  sub- 
stance above  absolute  zero  of  volume  when  its  pressure  is  PI. 

Isobaric  Changes. 

(c)  The  line  AB,  Fig.  15,  represents  the  temperature-entropy 
changes  of  a  gas  expanding  at  constant  pressure,  or  it  is  the  graph 
of  Eq.  (61),  and  is  obtained  by  substituting  various  increasing 
values  for  T2.    Similarly,  the  line  AC  is  the  graph  of  a  constant- 
pressure  compression. 

Isovolumic  Changes. 

(d)  The  line  AD  represents  a  rise  of  pressure  at  constant 
volume  and  is  obtained  by  means  of  Eq.  (63) ;  while  the  line  AE 
is  the  same  curve  continued  backward,  and  represents  a  con- 
stant-volume pressure  drop. 

Isothermal  Changes. 

(e)  During  an  isothermal  change  T  is  constant  but  entropy 
becomes  greater  as  associated  heat  increases,  which  occurs  as 
volume  grows  larger.     The   graph  of   an   isothermal  expansion 


74  HEAT-POWER  ENGINEERING 

from  Tifa  must  then  be  a  horizontal  line  to  the  right  of  A ;  and 
similarly  an  isothermal  compression  must  be  shown  by  the  hori- 
zontal line  to  the  left. 

Adiabatic  Changes. 

(f)  The  entropy  change  is  zero  during  a  reversible  adiabatic 
change,  therefore  A<£  equals  zero,  and  such  a  change  must  be 
shown  by  a  vertical  line  on  the  T<£-diagram.     Further,  since  the 
temperature  of  a  gas  decreases  during  adiabatic  expansion,  as 
previously  shown,  the  line  A  H  must  represent  such  an  expansion 
from   Ti(f>i  conditions,  and  the  line  A I  a  similar  compression 
from  the  same  point. 

Area  equivalent  to  AQ. 

(g)  From  Eq.  (56)   dQ  =  Td<f>,  for  reversible  processes,  and 
hence  for  such  a  process, 

/*2  /»2 

j    dQ  =  j    Tdj, 
and  A()  =  ft  -  (?i  =  f  *  Td^.      .     .     (67) 

The  last  term  of  this  equation  is,  however,  the  mathematical 
expression  for  the  area  under  a  curve  drawn  to  ^-coordinates. 
It  therefore  follows  that  area  on  the  T$-diagram  represents 
heat  change  during  reversible  processes,  and  inspection  of  the 
graphs  already  given  will  show  that  area  under  a  line  traced  from 
left  to  right  represents  heat  given  to  a  substance,  while  area 
under  a  line  from  right  to  left  represents  heat  abstracted  from 
a  substance. 

One  of  the  great  conveniences  resulting  from  the  use  of  the 
T<£-diagram  in  engineering  may  now  be  seen.  The  PV-diagram 
shows  by  the  area  beneath  the  expansion  line  the  total  external 
work  associated  with  a  process;  while,  for  reversible  processes 
at  least,  the  T<£-diagram  shows  by  the  area  beneath  the  corre- 
sponding line  the  change  of  total  associated  heat  occurring  during 
the  same  processes.  The  engineer  is  thus  enabled  to  quickly 
solve  many  problems  by  simple  inspection  of  these  two  dia- 
grams, and  can  avoid  the  necessity  of  making  long  mathematical 
calculations  with  the  ever-present  possibility  of  error. 

It  may  be  objected  that  it  involves  more  work  and  time  to 
construct  the  necessary  diagrams  than  it  would  to  make  the 


ENTROPY  75 

calculations  direct.  It  will,  however,  be  discovered  in  a  later 
chapter  that  certain  standard  diagrams  can  be  constructed  for 
the  solution  of  by  far  the  larger  class  of  problems  in  which  the 
conception  of  entropy  change  is  particularly  helpful.  These 
diagrams,  once  constructed,  can  be  used  indefinitely  without 
further  calculation. 


CHAPTER   VIII. 

GAS  CYCLES. 

47.  Definition  of  a  Cycle,  (a)  As  already  stated,  man  re- 
quires far  more  energy  than  his  body  can  supply,  and  this  energy 
is  obtained  from  Nature's  stores.  Energy  as  used  by  the  engi- 
neer is  always  associated  with  some  substance,  body,  or  "  sys- 
tem ":  kinetic  energy  with  moving  masses;  potential  mechanical 
energy  with  masses  by  virtue  of  position;  heat,  sensible  or  latent, 
with  soh'ds,  h'quids,  cr  gases. 

(b)  When  energy  is  used  for  the  doing  of  work  the  material 
with  which  it  is  associated  is  called  the  working  substance.     Thus 
in  a  hydraulic  power  plant,  water  is  the  working  substance;  gas 
is  the  working  substance  in  a  gas  engine;  and  water  is  the  working 
substance  in  a  steam  engine. 

(c)  If  a  given  quantity  of  a  working  substance,  with  its  asso- 
ciated energy,  be  used  so  as  to  obtain  all  the  work  possible  under 
given  circumstances,  the  same  amount  of  work  cannot  be  again 
obtained  under  the  same  circumstances  unless  the  substance  is 
first  returned  to  its  initial  condition.     Thus  a  pound  of  water 
falling  a  given  distance  will  develop  a  certain  amount  of  work, 
and  that  work  will  be  the  greatest  obtainable  under  the  circum- 
stances when  the  water  falls  to  the  lowest  possible  point.     To 
again  develop  the  same  amount  of  work  with  the  same  pound 
of  water,  it  must  first  be  raised  to  the  height  from  which  it  origi- 
nally fell.     Or  similarly,  if  one  pound  of  gas  does  work  by  ex- 
panding adiabatically  from  a  temperature  T\  to  a  temperature 
r2,  which  is  the  lowest  possible  under  the  conditions,  it  cannot 
again  do  the  same  amount  of  work  in  the  same  way  until  its 
temperature  is  again  raised  to  the  initial  value  T\. 

(d)  In  order  to  deliver    work   continuously  as    is   generally 
required,   there   are   obviously   only   two   possible   methods   of 
operation:  either  (i)  the  working  substance  must  be  periodically 
returned  to  initial  conditions,  or  (2)  new  quantities  of  working 

76 


GAS  CYCLES  77 

substance  must  be  supplied  at  regular  intervals.  The  latter  is 
the  simpler  and  is  often  used,  but  it  is  not  Nature's  method.  If 
man  uses  falling  water  to  develop  power  and  allows  the  water 
to  run  to  waste  at  the  lower  level,  Nature  immediately  begins  to 
lift  it  by  evaporation,  so  that  sooner  or  later  it  will  be  again 
available.  If  man  burns  carbon  in  air,  getting  hot  CO2  and  N2, 
and  then,  after  obtaining  work  by  lowering  the  temperature, 
discharges  the  gas  as  useless,  Nature  through  the  agency  of  plant 
growth  decomposes  the  cold  CO2  into  C  and  O2  so  that  they  can 
again  be  combined  to  evolve  the  same  amount  of  heat  energy 
as  before. 

Thus  without  man's  agency  all  working  substances  periodically 
return  to  the  same  starting  conditions,  that  is,  pass  through 
cycles. 

A  cycle  is  any  series  of  operations  which  periodically  brings  the 
working  substance  back  to  initial  conditions. 

It  is  customary  to  speak  of  Open  and  Closed  Cycles,  but  there 
are  really  no  open  cycles  in  engineering.  If  the  engineer  carries 
a  working  substance  through  any  series  of  changes  which  does 
not  return  it  to  initial  conditions,  Nature  kindly  closes  the  cycle 
for  him. 

(e)  One  difficulty  here  confronts  the  beginner:  Experience 
shows  that  it  requires  at  least  as  much  energy  to  pump  water 
between  levels  as  can  be  obtained  from  it  in  flowing  down  again ; 
this  being  true,  how  is  man  to  obtain  available  work  from  a 
substance  if  equal  work  has  to  be  returned  to  raise  the  material 
to  starting  conditions?  There  are  two  solutions  which  amount 
to  the  same  thing  in  the  end: 

1.  Allow  Nature  to  do  the  pumping,  as  in  the  case  of  the  water- 
fall; or 

2.  Imitate  Nature  in  finding  some  way  of  pumping  that  does 
not  require  the  return  of  the  identical  energy  which  has  been 
obtained  from  the  cycle. 

When  a  heat  engine  is  used  heat  energy  is  available  but  mechani- 
cal energy  is  sought.  Most  of  the  methods  in  use  for  returning 
the  working  substance  to  initial  conditions  in  such  cases  depend 
upon  the  use  of  a  small  amount  of  the  generated  mechanical 
energy  and  a  large  amount  of  the  available  heat  energy  for  this 
purpose;  or  they  employ  some  group  of  processes  which  are  the 
substantial  equivalent  of  this. 


HEAT-POWER  ENGINEERING 


48.  Diagram  of  a  Cycle.  (a)  Cycles  are  conveniently  rep- 
resented diagrammatically,  as  has  already  been  done  for  pres- 
sure-volume changes  or  temperature-entropy  changes.  The 
coordinates  used  are  generally  either  P  V,  or  T<f>. 

Assume  for  instance  that  the  point  A,  in  Fig.  16,  represents 
the  pressure  and  volume  conditions  PiVi,  at  temperature  T\, 

of  one  pound  of  gas  used  as  a 
working  substance  in  a  cylinder 
fitted  with  a  frictionless  piston, 
as  shown  in  the  figure.  If  the 
gas  expands  to  conditions  PJft 
at  B,  according  to  such  a  law 
that  AB  is  the  graph  of  pres- 
sure-volume changes,  the  area 
ABEF  must  measure  the  ex- 
ternal work  done  upon  the  pis- 
ton while  it  moves  from  position 
a  to  position  b.  If  the  gas  then 
expands  further  according  to 
some  other  law  BC  so  as  to 
arrive  at  the  point  C  with  con- 
ditions PsV3,  the  additional  ex- 
ternal work  done  upon  the  piston 
while  moving  from  b  to  c  must  be 
represented  by  the  area  BCGE. 
By  compression  the  working  substance  may  then  be  brought  to 
some  conditions  PJIt  according  to  the  law  represented  by  the 
graph  CD  while  the  piston  moves  from  c  to  d,  but,  to  do  this, 
work  represented  by  the  area  CDHG  must  be  done  by  the  piston 
upon  the  gas.  From  point  D  compressing  in  the  proper  way  will 
bring  the  working  substance  to  starting  conditions  at  A,  with  an 
expenditure  of  work  shown  by  the  area  DAFH.  The  return  of 
the  gas  to  starting  conditions  at  A  completes  a  cycle;  the  pres- 
sure, volume,  and  temperature  of  the  gas  are  again  PiVi7\  and 
the  piston  is  back  to  position  a.  There  is  then  no  reason  why 
the  same  process  may  not  be  repeated  again  and  again  indefi- 
nitely. Observe,  however,  that  the  total  external  work  done  by 
the  gas  is 

Positive  Work  =  ABEF  +  BCGE  =  ABCGF  ft.-lbs., 


a,'         d)  6       c1 

Fig.  16.  —  PV-Diagram  of  Cycle. 


GAS  CYCLES 


79 


while  the  total  work  done  upon  the  gas  is 

Negative  Work  =  CDHG  +  DAFH  =  CDAFG  ft.-lbs. 
leaving 

Net  or  Available  Work  =  ABCGF  -  CDAFG 
=  A  BCD  A  ft.-lbs. 
=  A  rea  inclosed  by  lines  of  cycle. 

(b)  Four  successive  processes  as  represented  by  the  four  lines 
in  Fig.  1 6  are  not  necessary  for  a  working  cycle.  Any  number 
of  processes  between  an  infinite  number  and  two  may  inclose 
an  area  and  therefore  could  represent  a  cycle  delivering  work. 
Four  lines  are,  however,  employed  in  most  of  the  cycles  used  in 
ordinary  heat  engines. 

49.  The  Carnot  Cycle  for  Gases,  (a)  This  cycle,  named  from 
Sadi  Carnot,  the  man  who  first  investigated  it,  represents  the 
best  that  can  possibly  be  done  in  the  conversion  of  heat  energy 
into  mechanical  energy.*  It  cannot  be  used  in  any  actual 
engine  and  is  therefore  only  of  theoretical  interest  as  a  criterion  of 
the  maximum  result  obtainable. 

(b)  For  performing  such  a  cycle  with  gas  it  is  necessary  to  have 

1.  The  gaseous  working  substance; 

2.  Certain  apparatus,  to  be  specified  below. 

The  working  substance  may  be  any  gas  far  enough  removed 
from  its  point  of  liquefaction  to 
sensibly   obey   the    laws  already 
developed  for  perfect  gases. 

The  necessary  apparatus  is 
shown  in  Fig.  17  and  may  be  de- 
scribed as  follows: 

U  is  a  body  at  high  tempera- 
ture T\  and  so  arranged  that  this 
temperature  remains  constant  de- 
spite withdrawal  or  addition  of 
heat  energy.  An  ordinary  fur- 
nace with  a  controllable  fuel  and 


U 


Fig.  17.  —  Machinery  of  Carnot 
Engine. 


*  This  statement  must  not  be  interpreted  to  mean  that  no  other  cycle  can  do 
as  well;  it  means  only  that  no  other  cycle  can  do  better.  It  will  be  shown  later 
that  there  are  a  number  of  cycles  equally  efiLcient  as  energy  transformers. 


8o 


HEAT-POWER  ENGINEERING 


air  supply  approximates  these  conditions.     The  body    U  will 
hereafter  be  called  the  Hot  Body. 

X  is  a  body  at  temperature  r2,  lower  than  Ti,  and  this  tem- 
perature T2  remains  constant  despite  addition  or  removal  of 
heat  energy.  A  vessel  jacketed  with  flowing  water  at  tem- 
perature 7*2,  or  arranged  like  the  condenser  shown  in  Fig.  3, 
would  approximate  these  conditions.  The  body  X  will  here- 
after be  called  the  Cold  Body. 

Y  is  a  cylinder,  Z  is  a  removable  plate  which  may  be  used  to 
cover  the  end  of  the  cylinder,  and  F2  is  a  frictionless  piston. 
These  parts  are  made  of  material  that  will  neither  absorb  nor 
conduct  heat.  Yi  is  a  cylinder  head  made  of  material  that 
offers  no  resistance  to  flow  of  heat. 


Operation  of  Carnot  Engine. 

(c)  Imagine  first  that  one  pound  of  gas  is  inclosed  in  the  cylin- 
der Y  at  conditions  PaVa  and  Ta,  as  shown  at  a  in  Fig.  18,  Ta 

being  equal  to  TI,  the  tem- 
perature of  the  hot  body. 
(i)  Remove  cover  Z,  apply 
the  hot  body  to  the  conduct- 
ing head  FI,  and  allow  the 
gas  to  expand  isothermally  to 
some  lower  pressure  Pb  at 
volume  V&  as  shown  at  b  in 
the  figure.  The  necessary 
heat  supply  must  have  come 
from  the  hot  body  and  may 
be  called  A<2i. 

(2)  Next  remove  the  hot 
body,  apply  the  nonconduct- 
ing cover  Z,  and  allow  the 

Fig..i8.  — PV-Diagram  of  Carnot  Cycle,     Sas    to    expand    adiabatically 

until     its     temperature     has 

dropped  to  Tc,  equal  to  T2,  the  temperature  of  the  cold  body. 
The  gas  will  then  have  conditions  PCVC. 

(3)  Again  remove  the  cover  Z,  apply  the  cold  body  X,  and 
drive  the  piston  back,  compressing  the  gas  isothermally  to  some 
higher  pressure  Pd  at  volume  Vd.  (The  value  of  Pd  will  be  con- 


Volumes 


GAS   CYCLES  8  1 

sidered  in  the  next  paragraph.)     The  heat  generated  must  be 
absorbed  by  the  cold  body  and  may  be  called  Aft. 

(4)  For  the  fourth  and  completing  operation,  remove  the 
cold  body,  replace  the  nonconducting  head  Z,  and  drive  the  piston 
back,  compressing  the  gas  adiabatically  until  its  temperature  has 
again  risen  to  that  of  the  hot  body,  which  was  the  starting 
temperature  of  the  cycle.  To  close  the  cycle,  the  pressure  and 
volume  must  return  to  P0Va  when  T\  is  reached.  This  can  only 
be  attained  if  the  isothermal  compression  is  stopped  at  such  a 
point  d  that  the  subsequent  adiabatic  compression  will  return 
the  gas  to  the  starting  conditions. 

Work  Developed  by  Carnot  Engine. 

(d)  The  area  crosshatched  upward  from  left  to  right  in  Fig.  18 
represents  work  done  by  the  gas,  while  that  crosshatched  down- 
ward from  left  to  right  represents  work  done  upon  the  gas.  The 
foot-pounds  of  net  work  resulting  from  one  cycle  is  shown  by  the 
inclosed  area  abed.  If  this  cycle  is  carried  through  n  times  per 
minute,  the  total  net  work  done  by  the  gas  will  be  n  times  the 
area  abed.  The  mathematical  expression  for  net  work  done  per 
cycle  can  be  obtained  by  using  the  formulas  already  developed 
for  isothermal  and  adiabatic  changes.  The  results  are  tabulated 
below. 

Before  consulting  this  table,  however,  note  that  this  cycle 
consists  of  two  isothermals  joined  by  two  adiabatics.  The 

TI  isothermal  is  an  expansion  with  ratio  ^~  =  r,    and    the    T2 


c 
isothermal  is  a  compression  with  ratio  r^r  =  rf.     These  two  ratios 

must  be  equal  because  by  Eq.  (51) 


r2     TV" 

j  •*  i     -*  « 

and  —  =  —  : 

-/2  -/d 

Vc      V,  Vft      Vc 

giving  A^^Va'        °r      V^  =  V^' 

so  that  r  =  r' . 

By  means  of  the  last  equation  the  tabulated  results  give  simple 
expressions  for  net  work  as  indicated  below  the  table. 


82 


HEAT-POWER  ENGINEERING 


Line. 

Kind. 

Heat  Received 
(Ft.-lbs./lb.  gas). 

Work  Done 
(Ft.-lbs./lb.  gas). 

ab 

Isothermal 
Expansion 

+  RTt  loge  r 

+  RTiloger 

be 

Adiabatic 
Expansion 

O 

I   RTl~Tz 

*    T-l 

cd 

Isothermal 
Compression 

-RT2loge(r'=r) 

-RT2loge(r'=r) 

da 

Adiabatic 
Compression 

0 

rt-r2 

R    7-1 

Net  Work  =  R^  loge  r  -  RT2  loge  r' 
=  (T1-T2)R\oger  ft.-lbs. 


(68) 


Efficiency  of  Carnot  Engine. 

(e)  Efficiency  is  denned  as  the  ratio  of  useful  result  to  expendi- 
ture or  effort  made  to  obtain  that  result.  That  is 

rrr     '  T?_c  ReSUlt 

Efficiency  =  £/.  =  _. 

The  result  obtained  from  the  operation  of  this  Carnot  engine 
is  the  net  work  done  by  the  gas  and  the  expenditure  made  is  the 
heat  supplied  by  the  hot  body.  Then 

trr  <~         4.  r*     i         Foot-pounds  represented  by  abed    ,.     N 
Ef.  Carnot  Cycle  =  -  778  Aft  '  (69a) 


(69b) 


_  B.t.u.  represented  by  area  abed 
Aft 

The  heat  supplied  per  unit  weight  of  gas  is  Aft  =  RT±  \oger 
foot-pounds  and  the  net  work  is  given  by  Eq.  (68).  Hence: 

„,  Net  Work       _  (Ti  -  T2)  R  \oger      7\  -  T2 

=  Heat  Supplied  "          T,R  loge  r  ~T\~ '     (69c) 

Objection  is  often  made  to  the  expressions  of  efficiency  just 
developed  because  it  seems  as  though  the  engine  ought  to  be 
credited  with  the  heat  given  to  the  cold  body.  The  fallacy  of 
this  appears  when  it  is  understood  that  the  heat  given  to  the 
cold  body  leaves  the  engine  at  a  low  temperature,  T2,  whereas  to 
operate  the  engine  heat  must  be  available  at  a  high  temperature 
Tlt  The  heat  rejected  to  the  cold  body  could  not,  therefore,  be 


GAS  CYCLES  83 

directly  used  again  in  the  engine,*  and  hence  should  not  appear 
in  the  expression  for  efficiency. 

(f)  To  make  this  heat  available  again  for  use  in  the  same 
engine,  it  would  have  to  be  raised  to  the  high  temperature  7\  and 
be  returned  to  the  engine  by  way  of  the  hot  body  at  that  tem- 
perature, but  experience  shows  that  heat  will  not  flow  of  its  own 
accord  from  any  body  to  one  at  a  higher  temperature.   ^From  the 
discussion  which  follows,  it  will  be  seen  that  at  least  as  much 
mechanical  energy  would  be  consumed  in  causing  such  a  flow  as 
could  be  obtained  by  using  the  elevated  heat  in  a  heat  engine.     It 
will  be  discovered  that  this  is  all  in  accord  with  the  Second  Law 
of  Thermodynamics. 

The  case  is  analogous  to  that  in  which  water  leaving  a  water 
wheel  is  pumped  again  to  the  original  height  in  the  attempt  to 
utilize  the  energy  still  possessed  by  the  water  when  leaving  the 
wheel.  Obviously,  in  this  case  the  energy  leaving  the  wheel 
with  the  effluent  water  is  of  no  further  use  to  that  wheel,  and 
exactly  the  same  thing  is  true  of 
the  heat  energy  leaving  the  engine. 

(g)  Fig-  19  is  intended  to  show 
the  energy  changes  of  the  Carnot 
cycle  graphically.     If  vertical  dis- 
tances between  heat  reservoirs  T\ 
and  T2  in  the  figure  represent  tem- 
perature,  and  widths  of   streams 
represent  quantities  of  energy,  the 
sense  of  the  foregoing  discussion 
becomes  graphically  evident. 

The  dotted  part  of  the  figure 
shows  how  a  part  of  the  effluent 
energy  might  be  used  if  another  cold  body  with  temperature  TZ, 
lower  than  T2,  could  be  obtained. f     The  ultimate  limit  to  this 

*  In  a  real  case  the  hot  body  would  derive  the  heat  to  maintain  its  temperature 
from  some  form  of  fuel,  and  the  cost  of  that  fuel  would  be  the  expenditure  made  to 
obtain  the  work  delivered  by  the  engine. 

t  The  possibility  of  the  existence  of  cold  body  T3  immediately  suggests  the  use 
of  only  one  engine  operating  between  temperatures  Ti  and  T3.  There  is  no  theo- 
retical objection  to  this,  but  sometimes  when  analogous  schemes  are  tried  with 
real  engines  a  number  of  practical  considerations  dictate  the  use  of  several  engines 
in  series  as  above,  rather  than  one  engine  working  through  the  entire  temperature 
drop.  The  reasons  will  be  considered  later. 


Worl— 778AE' 
-Ft.-Lb. 
J 

Fig.  19.  —  Energy  Flow  in  Carnot 
Engine. 


84  HEAT-POWER  ENGINEERING 

arrangement  would  be  an  engine  having  a  cold  body  with  tem- 
perature at  absolute  zero. 

It  is  of  interest  to  note  that  in  this  limiting  case  the  Second  Law 
of  Thermodynamics  would  no  longer  be  true  because  the  last  engine 
of  the  series  would  reject  no  heat,  having  reduced  the  temperature 
of  its  working  substance  to  absolute  zero.  All  the  heat  entering 
the  group  of  engines  could  then  be  completely  and  continuously 
converted  into  mechanical  energy.  //  is  obviously  an  impossible 
proposition,  arising  in  this  case  from  the  impossible  ideal  gas,  the 
assumptions  made  as  to  the  properties  of  that  material,  and  the 
absurd  assumption  that  any  body  can  be  maintained  indefinitely 
at  absolute  zero  of  temperature  without  the  expenditure  of 
work  in  a  continuous  process  of  refrigeration. 

From  Fig.  19 

Aft  +  AE  =  Aft;     ......     (70) 

hence  the  efficiency  might  be  written, 


and  this  will  be  found  to  express  the  efficiency  of  any  heat-engine 
cycle.  From  Eqs.  (6Qc)  and  (71)  it  is  evident  that  in  the  case  of 
the  Carnot  engine  with  gaseous  working  substance 

Aft  -  Aft  _  T,-T, 

Aft  ~TT  (72) 

Reversibility  of  Carnot  Engine. 

(h)  Each  part  "of  the  process  carried  on  in  a  Carnot  engine  is 
thermodynamically  reversible.  In  fact  the  cycle  is  made  up  of 
the  two  processes  which  were  cited  in  Section  34  (a)  and  (b)  as 
typical  examples  of  reversible  processes.  The  entire  cycle  must 
therefore  be  reversible;  that  is,  it  must  be  possible  to  operate 
the  engine  starting  at  the  point  a  in  Fig.  18,  and  following  the 
cycle  backwards  in  the  direction  adcb. 

There  is  no  reason  why  the  gas  cannot  (i)  expand  adiabatically 
from  a  to  d  and  then  (2)  isothermally,  at  temperature  T2,  from 
d  to  c.  During  the  latter  process  it  would  absorb  heat  Aft  from 
the  cold  body.  If  the  necessary  mechanical  energy  is  available 
the  gas  can  be  (3)  compressed  adiabatically  from  c  to  b,  and  then 
(4)  isothermally  in  contact  with  the  hot  body  to  the  starting 
point.  During  the  isothermal  compression  the  gas  must  give  to 


GAS  CYCLES  8$ 

the  hot  body  the  amount  of  heat  Aft  exactly  equal  to  that  previously 
removed  during  the  direct  operation. 

In  the  diagram  (Fig.  18)  the  work  done  by  the  gas  during 
the  two  expansions  must  be  represented  by  the  area  adcef,  and 
that  done  on  the  gas  during  the  two  compressions  must  be  shown 
by  the  area  ecbaf.  The  net  result  must  then  be  the  absorption 
of  external  work  equal  to  that  given  out  in  the  direct  cycle  and 
represented  by  the  area  adcb.  Tabulation  of  the  results  of 
operation,  first  direct  and  then  reversed,  gives 

Direct  Operation.  Reversed  Operation. 

Heat  absorbed  from  hot  body  =  A@i   =  Heat  delivered  to  hot  body. 

Heat  discharged  to  cold  body  =  AQ2  =  Heat  absorbed  from  cold  body. 

Mechanical   energy  delivered  =  (AQi  —  A@2)  =  Mechanical  energy  absorbed. 

Thus  the  Carnot  engine  reversed  can  remove  heat  at  low 
temperature  from  the  cold  body  and,  having  absorbed  a  certain 
quantity  of  available  mechanical  energy,  can  deliver  the  sum  of 
these  two  energies  to  the  hot  body  as  heat  at  high  temperature. 
It  is  therefore  a  heat  pump. 

Carnot  Engine  as  a  Source  of  Perpetual  Motion  of 
Third  Type. 

(i)  Imagine  now  two  Carnot  engines  exactly  alike,  one  working 
as  an  engine,  and  the  other,  with  operation  reversed,  working  as 
a  "  heat  pump."  The  engine  will  remove  heat  from  the  hot 
body,  deliver  a  part  of  it  as  mechanical  energy,  and  discharge 
the  remainder  to  the  cold  body.  The  pump  will  absorb  from 
the  cold  body  the  same  quantity  of  heat  that  this  latter  received 
from  the  engine ;  it  will  require  for  its  operation  the  same  quantity 
of  mechanical  energy  that  was  delivered  by  the  engine;  and  it 
will  discharge  to  the  hot  body  the  sum  of  the  two  energies,  — 
that  is,  an  amount  of  heat  equal  to  that  which  the  engine  removed 
from  the  hot  body.  If  the  two  pieces  of  apparatus  can  be  con- 
nected so  that  the  engine  drives  the  pump,  a  device  results  which, 
theoretically  devoid  of  friction  and  radiation  losses,  can  go  on 
moving  forever,  though  delivering  no  useful  work.  This  is  what 
was  called  in  Section  9  perpetual  motion  of  the  third  type, 
which,  though  conceivable,  cannot  be  materialized. 

50.  All  reversible  engines  have  the  same  efficiency  as  the 
Carnot  engine  when  working  between  the  same  temperature 
limits. 


86 


HEAT-POWER  ENGINEERING 


There  are  many  possible  types  of  reversible  and  irreversible 
ideal  engines.  It  will  now  be  proved  that,  when  working  between 
the  same  temperature  limits,  —  i.e.,  receiving  heat  from  a  hot 
body  at  the  same  temperature  as  that  supplying  the  Carnot 
engine  and  rejecting  heat  to  a  cold  body  at  the  same  tempera- 
ture as  that  used  with  the  Carnot  engine, —  (i)  no  engine  what- 
ever can  have  higher  efficiency  than  the  Carnot  engine  and  (2)  the 
efficiency  of  all  reversible  engines  equals, the  efficiency  of  the  Carnot 
engine. 

To  prove  (i):  Assume  that  any  engine,  A,  is  more  efficient 
than  the  Carnot  engine,  C.  Obviously  A  could  deliver  more 
mechanical  energy  than  could  C,  although  receiving  the  same 
amount  of  heat;  and  the  heat  rejected  by  A  to  the  cold  body 
would  evidently  be  less  than  that  delivered  by  C  by  an  amount 
equal  to  the  difference  between  the  quantities  of  mechanical 
energy  delivered  by  A  and  C* 

Let  A,  operating  as  an  engine,  drive  C  reversed,  that  is,  as 
a  heat  pump.  This  is  shown  diagrammatically  in  Fig.  20,  in 


Fig.  20.  —  Heat  Flow  Diagram  to  show  that  no  engine  can 
have  a  greater  efficiency  than  the  Carnot. 

which  the  width  of  stream  is  supposed  to  be  a  measure  of  the 
energy  flow.  From  the  combination  there  would  result  an 
excess  of  mechanical  energy  AEz  which  could  be  used  outside 

*  Because  heat  received  =  heat  discharged  +  mechanical  energy  delivered. 
With  the  left  member  of  the  equation  constant,  neither  term  of  the  right  member 
can  vary  except  at  the  expense  of  the  other. 


GAS  CYCLES  87 

the  system.  This  excess  mechanical  energy  would  be  exactly 
equal  to  the  only  heat  supplied  the  system,  that  is,  to  AE2'  given  by 
the  cold  body.  Therefore  the  combination  could  continuously 
convert  into  mechanical  energy  all  the  heat  supplied  it;  but  this 
would  be  Perpetual  Motion  of  the  Second  Type,  and  is  contrary 
to  human  experience  as  expressed  in  the  Second  Law  of  Thermo- 
dynamics. Since  the  assumption  that  A  is  more  efficient  than 
C  results  in  this  impossibility,  it  follows  that  that  assumption 
must  be  incorrect,  and  that  no  heat  engine,  reversible  or  irrevers- 
ible, can  have  an  efficiency  greater  than  that  of  the  Carnot 
engine.  Hence  statement  (i)  is  correct. 

To  prove  (2),  that  if  the  engine  A  is  reversible  it  must  have 
the  same  efficiency  as  the  reversible  Carnot  engine  C  working 
between  the  same  temperature  limits,  imagine  it  to  have  an 
efficiency  less  than  that  of  C*  Being  reversible,  it  can  be  used 
as  a  heat  pump  driven  by  C.  Then,  if  the  pump  can  be  less 
efficient  than  the  engine,  perpetual  motion  of  the  second  type 
again  appears.  Hence,  neither  engine  can  be  more  efficient  than 
the  other,  so  the  efficiencies  of  all  reversible  engines  working 
between  the  same  temperature  limits  must  be  the  same,  which 
proves  (2). 

51.   Comparision  of  Carnot  Engine  and  Real  Engine.    The 

Carnot  engine  as  described  above  is  evidently  only  an  ideal 
mechanism,  for  the  material  assumed  for  the  parts  does  not 
exist  and  a  perfect  apparatus  could  not  be  constructed.  It  is 
possible,  however,  to  approach  such  ideals  and  they  may  there- 
fore be  regarded  as  limiting  cases  for  actual  constructions. 
Comparing  the  real  engines  with  the  Carnot  as  a  standard  gives 
a  measure  of  the  perfection  of  attainment. 

In  any  actual  engine,  the  piston,  which  itself  meets  with 
frictional  resistance,  is  connected  to  a  friction-burdened  mech- 
anism. In  the  real  engine,  provision  must  also  be  made  for 
storing  part  of  the  energy  delivered  during  the  expansion,  to  be 
returned  for  the  compression  of  the  working  substance,  and  this 
storage  and  return  always  involves  waste.  In  the  reciprocating 
engine,  for  instance,  this  energy-storing  device  is  usually  a  fly- 
wheel, and  some  of  the  energy  stored  is  lost  in  friction  and 
windage. 

*  It  has  already  been  proved  that  its  efficiency  cannot  be  greater  than  that  of  C. 


88  HEAT-POWER  ENGINEERING 

Obviously  there  must  be  the  following  losses  in  any  real  engine: 

1.  Some  of  the  heat  received  from  the  hot  body  must  be  lost 
as  heat  through  conduction  and  radiation  by  the  material  of  the 
engine. 

2.  Some  of  the  mechanical  energy  delivered    to   the  piston 
must  be  lost  by  friction  in  the  mechanism  of  the  engine. 

3.  Some  of  the  energy  stored  for  compressing  the  working  sub- 
stance must  be  lost  by  friction  during  its  storage  and  its  return. 

Recalling  the  meanings  of  the  three  types  of  perpetual  motion 
(page  7) ,  it  is  evident  — 

(a)  That  no  ideal  engine  can  give  perpetual  motion  of  the  first 
or  second  type; 

(b)  That  any  ideal  reversible  engine  combined  with  another  of 
similar  character  can  give  perpetual  motion  of  the  third  type  only;  but 

(c)  That  no  real  engine  can  give  perpetual  motion  of  any  of  the 
three  types. 

52.  T<£-Diagram  of  Carnot  Cycle,  (a)  The  Carnot  cycle, 
being  made  up  of  two  reversible  isothermals  and  two  reversible 
adiabatics,  must  be  represented  by  a  rectangle  when  drawn  to 
T<f>  coordinates.  Such  a  diagram  is  given  in  Fig.  21,  in  which 
the  horizontal  lines  ab  and  cd  represent  the  reversible  isothermal 
reception  and  rejection  of  heat  and  the  vertical  lines  be  and 
da  show  the  reversible  adiabatic  changes.  The  corresponding 
corners  of  the  cycle  are  for  convenience  lettered  the  same  as  in 
Fig.  i 8. 

(b)  Since  for  reversible  changes  with  ideal  gases, 

*2 

Td<t> 

i 

the  area  abef  under  the  isothermal  expansion  ab  represents  heat 
Aft  received  from  the  hot  body,  and  the  area  cefd  is  similarly 
proportional  to  heat  Aft  rejected  to  the  cold  body  during  the 
isothermal  compression  cd.  The  difference  abed  is  the  area  of 
the  cycle  and  represents  heat  converted  into  work.  Then 

Aft  =  T\  (fa-  fa)    and   Aft  =  T2  (fa  -  fa)  =  T2  (fa  -  fa) 

and 

=  Aft  -  Aft  =  Ti  (fa  -  fa)  -  T,  (fa  -  fa) 
Aft  T\  (fa  -  fa) 

=       ^ — -»   as  before. 


/ 


GAS  CYCLES  89 

53.   Criterion  of  Maximum  Efficiency.     That  an  ideal  engine 

T>  nr> 

may  have  the  maximum  possible   efficiency, 


Tl 


when 


re- 


ceiving heat  from  a  body  at  temperature  TI  and  rejecting  heat 
to  a  body  at  temperature  T2,  it  is  necessary  that  — 

(1)  All  heat  received  from  the  hot  body  be  taken  when  the  working 
substance  has  the  same' temperature  as  that  body;  and 

(2)  All  the  heat  rejected  to  the  cold  body  be  given  it  when  the 
working  material  has  the  same  temperature  as  that  body. 

This  is  easily  proved  from 
the  T</>-diagram,  Fig.  21.  Im- 
agine heat  to  be  received  re- 
versibly  along  some  such  line 
as  dr  a'  b,  with  the  tempera- 


ture of  the  working  substance 
varying  from  TV  to  7\.  Obvi- 
ously less  heat  is  received  than 
if  the  reception  had  been  iso- 
thermal, because  the  area  fdf 
a' be  ( =  fabe  —  ad! a'}  is  less 
than  the  area  fabe.  The  work 
done  is  also  less  because  the 
area  dd'a'bcd  ( =  dabc  —  ad' a') 
is  less  than  dabc.  But  since 
the  area  ad' a'  is  lost  in  both 
cases,  and  since  the  (smaller)  area  representing  work  is  affected 
more  than  the  (larger)  area  representing  heat  received,  it  follows 
that 


Entropy 

Fig.  21. —  T<£-Diagram  of  Carnot  Cycle. 


a'bcdd'       abed 
a'bcefd'       abef 


and     Ef<  Ef. 


A  similar  proof  would  show  that  the  rejection  of  heat  along  a 
line  such  as  b'c'  also  gives  a  cycle  which  is  less  efficient  than  that 
with  isothermal  heat  rejection.* 

*  Confusion  is  sometimes  caused  by  the  apparent  contradiction  of  these  state- 
ments and  those  given  as  propositions  (i)  and  (2)  in  Section  50.  It  should,  how- 
ever be  noted  that  a  very  distinct  limitation  is  put  upon  the  reversible  engines 
considered  in  that  section.  They  receive  all  their  heat  at  temperature  TI  from  the 
hot  body  in  reversible  fashion  and  reject  reversibly  to  a  cold  body  at  temperature 
TZ.  On  the  other  hand,  engines  receiving  heat  along  such  a  line  as  d'a',  Fig.  21, 
could  only  do  so  reversibly  by  employing  a  string  of  hot  bodies  with  temperatures 


HEAT-POWER  ENGINEERING 


54.  The  Constant- Volume  Regenerative  or  Stirling  Cycle,  (a) 
In  this  cycle,  which  is  drawn  to  PV-coordi nates  in  Fig.  22, 
the  gas  receives  heat  from  the  hot  body  and 
rejects  heat  to  the  cold  body  along  the  iso- 
thermals  ab  and  cd  exactly  as  in  the  case  of 
the  Carnot  engine.  The  two  adiabatics  of 
this  latter  case  are,  however,  replaced  by  the 
two  constant  volume  lines  be  and  da. 

The  line  be  is  supposed  to  be  obtained  by 
allowing  the  working  substance  to  reject  heat 
to  a  body  so  arranged  that  it  stores  that  heat 
in  such  a  manner  that  (i)  each  part  of  the 
body  is  always  at  the  same  temperature  as 
the  contiguous  gas,  (2)  the  temperature  of 
each  part  remains  constant,  and  (3)  each  in- 
crement of  heat  after  storing  is  maintained  at 
the  temperature  of  reception.  The  line  da  is 


operation. 

(b)  Such  a  heat  storing  and  restoring  body 
is  known  as  a  Regenerator  and  in  its  perfect 


Volumes 


Fig.  22.  —  PV-Dia-  supposed  to  be  obtained  by  the  return  of  the 
gram  of  Constant-Vol-  stored  heat  to  the  gas  by  a  reversal  of  this 
ume  Regenerative 
Cycle.  Air  as  work- 
ing substance.  Same 

pressure   range  as  in 
Flg  lg  state  is  of  course  purely  ideal.     It  may  be  ap- 

proximated, however,  by  a  long  pipe  of  heat- 
insulating  material  filled  with  wire  gauze  or  equivalent,  and  with 
temperature  7\  at  one  end  and  T2  at  the  other.  As  hot  gas 
flows  through  in  the  direction  T^TZ  it  will  impart  heat  to  the 
walls  and  filling  at  a  progressively  decreasing  temperature  and 
give  the  change  be;  while  da  may  be  obtained  by  causing  gas  to 
flow  through  the  regenerator  in  the  opposite  direction. 

The  Mechanism  of  the  Stirling  Engine. 

(c)  The  machinery  necessary  for  the  carrying  out  of  such  a 
cycle  is  shown  in  Fig.  23.  The  cylinders,  Y  and  Y\,  and  the  hot 
and  cold  bodies,  U  and  X,  are  similar  to  those  used  in  the  Carnot 
engine.  The  tube  R  is  the  regenerator  just  described  and  its 

varying  from  7Y  to  Ta'  by  infinitesimal  elements,  so  that  the  gas  might  without 
sensible  error  be  said  to  receive  each  element  of  heat  when  at  the  same  temperature 
as  the  body  supplying  it.  This  is  distinctly  contrary  to  the  assumptions  of  Section 
50  as  reiterated  above. 


GAS  CYCLES 


91 


YI 


contained  volume  is  assumed  to  be  negligible  compared  with 
that  of  either  cylinder. 

Imagine  the  piston  in  FI  at  the  bottom  of  the  cylinder  and 
that  in  F  at  the  top,  as  the  result  of  the  expansion  ab,  Fig.  22. 
F  is  then  filled  with  a  gas  with  conditions  shown  at  b.  Now 
drive  the  right  piston  down,  thus 
forcing  the  gas  through  the  regen- 
erator, and  allow  the  left  piston  to 
rise  at  just  the  rate  necessary  to 
keep  constant  the  total  volume  of 
the  gas.  During  this  process  the 
regenerator  will  absorb  heat  and 
its  temperature  will  grade  from  Tb 
at  the  right  to  Tc  at  the  left. 
When  the  piston  in  F  has  reached 
the  bottom  of  its  stroke  all  the 
gas  will  be  in  FI,  the  piston  in  the 


Fig.   23.  —  Machinery  of  Constant- 
Volume  Regenerative  Cycle. 


latter  will  be  at  the  top  of  the  stroke,  and  the  constant-volume 
line  be  will  have  been  produced.  Now  hold  the  right  piston  sta- 
tionary, bring  the  cold  body  up  to  cylinder  FI  and  force  the  pis- 
ton into  this  cylinder,  until  the  volume  occupied  by  the  gas  is 
that  shown  at  d,  in  Fig.  22.  This  will  produce  the  isothermal  com- 
pression. Free  the  piston  in  F,  continue  the  downward  motion  of 
that  in  FI  until  it  reaches  the  bottom  of  its  cylinder,  and  simul- 
taneously allow  the  right  piston  to  rise  as  much  as  is  necessary  to 
keep  the  volume  constant.  This  will  give  the  line  da  of  the  dia- 
gram, and  the  gas  in  passing  through  the  regenerator  will  rise  in 
temperature  from  Td  ( =  Tc)  toTa(=  Tb).  Finally  fix  the  left  pis- 
ton in  its  position,  bring  the  hot  body  up  to  cylinder  F,  and  allow 
the  gas  to  expand  isothermally  from  a  to  b,  completing  the  cycle. 

Work  Obtained  per  Unit  Weight  of  Gas  by  Use  of 
Constant-Volume  Regenerative  Cycle. 

(d)  The  work  theoretically  available  from  an  engine  using  this 
cycle  can  be  found,  as  in  the  case  of  the  Carnot  engine  (see 
Section  49  (d),  by  summing  up  the  quantities  of  work  done 
during  each  process  of  the  cycle.  This  is  done  in  the  following 
tabulation  in  which  the  letters  in  the  first  column  refer  to  Fig. 
22.  It  is  evident  from  the  figure  that,  as  before,  the  ratios  of 
expansion  and  compression  are  equal.  Thus,  using  unit  weight, 


HEAT-POWER  ENGINEERING 


Work  Done 

Line. 

Process. 

/Ft.-Lbs.\ 

\Lb.-Gas/  ' 

ab 

Isothermal  Expansion 

+  RTi  loge  T 

be 

Isovolumic  Change 

0 

cd 

Isothermal  Compression 

-  RT2  loge  r' 

da 

Isovolumic  Change 

0 

Net  work  per  cycle  =  RTi  logc  r  —  RTZ  logc  r1 ',  and  since  r  =  r', 

=  (7\  -  T2)  #  loge  r  ft.-lbs.  .     .     .     (73) 
Thus 

A£  =  (ri"^10gC'   B'tJI-     '     •     '     (74) 

Efficiency  of  the  Constant-Volume  Regenerative  Engine. 

(e)  With  an  ideal  regenerator  the  isovolumic  processes  be  and 
da  would  be  thermodynamically  reversible,  and   the   isothermal 
compression  and  expansion,  as  in  the  Carnot  engine,  are  also 
reversible.     The  cycle  as  a  whole  must  then  be  reversible,  and 
therefore  its  efficiency  must  equal  the  efficiency  of  the  Carnot  cycle. 
This  may  be  proved  as  follows : 

(f)  With  unit  weight  of  gas,  the  heat  received  from  the  hot 

~D  T"*     1 

body  may  be  called  Aft,  and  as  before  it  must  equal  —  • 

778 

The  heat  rejected  to  the  cold  body  is  similarly  Aft  and  is  equal  to 

R  T2  loge  r'          R  T2  loge  T        .  , 

-  =  -         *     i  since  r  is  equal  to  r. 
770  775 

The  external  work  done,  or  the  mechanical  energy  made 
available,  must  equal  the  difference  between  the  work  done  by 
the  gas  during  the  isothermal  expansion  and  the  work  done 
upon  it  during  the  isothermal  compression,  hence  it  must  be 

778  AE  =  RT,  loge  r  -  RT,  loge  r. 
Then  the  efficiency  is 

i  -  Aft  _  RT,  loge  r  -  RT2  loge  r  _  TI  -  T2 
Aft  RTi  loge  r  TI 


(75) 


There  is  often  difficulty  at  first  in  realizing  that  this  cycle, 
which  has  the  same  efficiency  as  the  Carnot  cycle,  fulfills  the 
criterion  of  maximum  efficiency  stated  in  Section  53.  Careful 
study  will  show,  however,  that  the  statements  in  that  section 
apply  only  to  heat  transfers  between  the  working  substance  and 


GAS   CYCLES 


93 


bodies  external  to  the  actual  engine  — i.e.,  the  hot  and  cold 
bodies.  The  heat  given  up  or  received  by  the  gas  during  the 
constant-volume  changes,  i.e.,  C,(Ti-  T2),  is  really  stored  and 
restored  reversibly  and  does  not  enter  or  leave  the  system. 

T0-Diagram  of  Constant-Volume  Regenerative  Cycle. 

(g)    Fig.  24  shows  the  T^-diagram  of  this  cycle  as  abed  super- 
imposed upon  that  of  the  Carnot  cycle  abc'd' .     For  convenience 


Entropy 

Fig.  24.  —  T$-Diagram  of  Constant-Volume  Regenerative  Cycle. 
Same  temperature  range  as  in  Figs.  18  and  21. 

in  comparison  the  two  cycles  are  drawn  for  the  same  temperature 
range. 

The  lines  be  and  da  are  obtained  from  Eq.  (63)  and  are  evi- 
dently parallel  curves.  The  areas  bc'c  and  ad'd  are,  therefore, 
equal,  hence  abed  must  equal  abc'd'.  Each  of  these  areas,  how- 
ever, represents  the  heat  converted  into  mechanical  energy.  The 
heat  supplied  in  each  case  is  shown  by  the  area  under  ab.  There- 
fore, the  heat  supplied  in  each  cycle  being  the  same,  and  the  work 
done  being  the  same,  the  efficiencies  are  equal. 

55.   The  Constant-Pressure  Regenerative,  or  Ericsson,  Cycle. 

The  PV-diagram  for  this  cycle,  shown  in  Fig.  25,  differs  from 
the  cycle  last  considered  only  in  the  fact  that  the  regenerator  proc- 
esses are  carried  on  at  constant  pressure  instead  of  at  constant 


94 


HEAT-POWER  ENGINEERING 


volume.  The  same  mechanism  may  be  used  as  in  the  last  case, 
and  the  cycle,  being  reversible,  must  have  the  same  efficiency. 
The  T$-diagram  of  this  cycle  is  similar  to 
that  of  the  constant-volume  cycle  shown  in 
Fig.  24.  The  curves  corresponding  to  be  and 
da  of  that  figure  are  obtained  from  Eq.  (61) 
and  of  course  have  a  different  slope;  other- 
wise nothing  is  altered,  and  statements  con- 
cerning one  of  these  cycles  are,  in  general, 
true  of  both. 


\ 


56.  The  Constant-Volume  Heat-Change, 
Otto,  or  Beau  de  Rochas  Cycle,  (a)  This 
cycle,  the  PV-diagram  of  which  is  shown  in 
Fig.  26,  consists  of 
two  adiabatics  be  and 
da  and  two  constant 
volume  lines  ab  and 
cd.  Heat  is  received 
from  the  hot  body 
>,  the 

pressure  and  temper- 
ature rising  while  the 


Volumes 

Fig.  25.  —  PV-Dia- 
gram  of  Constant  Pres- 
sure Regenerative  Cy- 
cle. Air  as  working  ajQng  the  Hne 
substance.  Same  vol- 
ume range  as  in  Fig. 
22. 

volume  remains  con- 
stant. Heat  is  rejected  to  the  cold 
body  along  the  line  cd,  the  pressure  and 
temperature  dropping  while  the  volume 
remains  constant. 

(b)  The  reception  of  heat  is  irreversi- 
ble, since  the   temperature  of   the  hot 


Volumes 


Fig.  26.  —  PV-Diagram  of 
body  is  at  least  as  high  as  that  which  Otto  Cycle.  Air  as  working 
the  gas  attains  when  reaching  condition  substance.  Conditions  at  b 
b,  and  therefore  must  be  higher  than  same  as  those  at  a  in  Fis-  l8 

,1  r  .Li-  j      •        ^i  ^  and  lowest  pressure  same  as 

that  of  the  gas  during  the  entire  recep-  .    .,    . 

,  .  m  that  case. 
tion  of  heat  A(A.     The  same  is  true  for 

the  rejection  of  heat  along  cd,  the  cold  body  having  a  tempera- 
ture at  least  as  low  as  that  of  the  gas  at  d.  This  case  is  the 
first  one  cited  in  Section  35  as  a  process  intrinsically  irreversible. 
This  cycle  is  not  only  irreversible,  but,  as  is  evident,  it  does 
not  fulfill  the  criterion  for  maximum  efficiency  (Section  53),  and 


GAS  CYCLES 


95 


hence  has  an  efficiency  lower  than  that  of  the  cycles  previously 
described.  It  is,  however,  the  only  one  of  the  four  gas  cycles 
so  far  considered  which  is  of  any  great  practical  importance. 

Mechanical  Energy  Obtained  per  Unit  Weight  of  Gas 
Operating  in  Otto  Cycle. 

(c)  The   following   tabulation   gives   the   mechanical   energy 
changes  for  each  line  per  unit  weight  of  gas: 


Line. 

Type  of  Change. 

Work  in  Ft.-lbs.  Done  by 
Gas. 

ab 

Constant-  Volume  Pressure  Rise 

O 

be 

Adiabatic  Expansion 

R(Tb-  Tc) 

7-1 

cd 

Constant-  Volume  Pressure  Drop 

O 

da 

Adiabatic  Compression 

R   Ta  -  Td) 

7-1 

The  summation  of  the  last  column  gives  the  net  work  per  cycle 
per  unit  weight  of  gas,  as 

Network  =  -^-  (Tb  -  Tc  -  Ta  +  Td)  ft.-lbs.    .     (76) 


-D 

FromEq.  (33),  —^  is  equal  to  Kv,  giving 

Network  =  778  AE  =  Kv  (Tb  -  Tc  -  Ta  +  Td).    .     (77) 

(d)  This  same-result  could  have  been  obtained  more  briefly  as 
follows:  The  mechanical  energy  obtained  must  equal  Aft  -  Aft, 
when  measured  in  heat  units;  that  is,  AE  =  Aft  -  Aft.  Since 
the  heat  changes  take  place  at  constant  volume,  Aft  =  Cv 
(Tb  -  To)  and  Aft  =  Cv  (Tc  -  Td), 
hence,  in  ft.  Ib.  units, 

778  AE  =  Kv  (Tb  -  Ta)  -  Kv  (Te  -  Td) 
=  K,(Tb-  Ta-  Tc+Td) 

which  is  the  same  as  Eq.  (77)- 


96  HEAT-POWER  ENGINEERING 

Efficiency  of  Otto  Cycle. 
(e)  Writing 


and  substituting  in  the  last  form  gives 

_,  _C,(Tb-Ta)-C\(Tc-Td) 

'  c,  (n  -  r.)  ' 

=  l-^P (78) 

lb  —    la 

This  expression  can  be  further  transformed  and  simplified 
so  that  important  conclusions  can  be  easily  deduced.     Since  the 
curves  be  and  da  are  adiabatics,  Eq.  (51)  gives 
T       A  FA7-1  Td      /FaV"1 

J.  c  /    '  b  \  i  •*•«  i^*l 

r. =  (vj        and    T, '  (TJ 

Since  Fa  =  Vb  and   Fc  =  Fd 


and  therefore 


i       Tc-  Td  _  Td  /     N 

ana  r  ~     «  •      •     •     •     v/vy 


Substituting  from  this  in  (78)  gives 

Ef.  =  1-^  =  ^^.       ....     (80) 

•La  J-  a 

CV  \7-l 
-^j          .......     (81) 

Thus  it  is  evident  — 

(1)  That  the  efficiency  of  this  cycle  is  independent  of  the  upper 
temperature,  but  depends  only  upon  the  temperature   range  of 
adiabatic  compression. 

(2)  That  with  the  same  value  of  Pd,  the  less  the  volume  of 
one  pound  of  gas  at  the  end  of  compression  the  higher  the  efficiency. 

(3)  That  with  the  same  temperature  Td,  the  higher  the  tem- 
perature at  the  end  of  compression  the  higher  the  efficiency. 

Eq.  (81)  shows  that  the  efficiency  of  the  cycle  may  vary  with 
different  real  gaseous  working  substances  because  the  value  of  7, 
as  shown  in  Table  I,  is  not  the  same  for  different  gases.  This 
is  in  marked  contrast  to  the  cycles  previously  considered,  where 
the  efficiency  could  be  expressed  entirely  in  terms  of  the  tern- 


GAS  CYCLES 


97 


peratures  of  the  hot  and  cold  bodies,  and  where  the  efficiency 
was  independent  of  the  individual  characteristics  of  the  gaseous 
working  substances. 

Writing  the  Carnot  efficiency 


and  the  Otto  efficiency 

Ta-    Td 


I* 

Ta 


T  ' 

•L  a 


inspection  shows  that  for  the  same  upper  and  lower  tempera- 
tures the  Otto  efficiency  must  be  the  smaller,  as  Ta  must  be  less 
than  Ti. 

T<i>  -Diagram  of  Otto  Cycle. 

(f)  In  reality  the  1>-diagram  of  this  cycle  cannot  be  drawn 
by  the  same  means  that  was  used  in  the  preceding  cases,  for  the 

reason  that  in  Chapter  VII  the  equation  A<£  =    I  -~  was  proved 

for  reversible  processes  only, 
whereas  two  processes  in 
this  cycle  are  irreversible 
(see  (b)). 

It  is  possible,  however,  to 
draw  a  T<|>-diagram  for  this 
case  by  making  use  of  the 
fact  that  the  entropy  change 
accompanying  an  alteration 
from  any  given  condition  to 
another  must  always  be  the 
same,  no  matter  how  the 
change  from  the  first  state  to 
the  second  occurs. 

To    find    the    entropy 

,  .  ,  Entropy 

changes  occurring  as  the  gas 

receives  heat  along  the  line      r*  *7- -T*-Dhg»m  of  Otto  Cycle. 
7   .      ^.  .     .       ,  .      Air  as  working  substance.     Same  tempera- 

ab  in  Fig.  27,  it  is  then  only  ture  range  as  that  in  Figs   l8  and  2I 

necessary   to  discover  some 

reversible  method  of  supplying  the  same  amount  of  heat  in  such  a 
way  that  the  condition  of  the  gas  at  every  individual  point  on 
ab  will  be  the  same  as  when  the  heat  supply  is  irreversible. 


98 


HEAT-POWER  ENGINEERING 


Such  a  heating  process  would  result  from  the'  use  of  a  series 
of  reservoirs  with  temperatures  graded  from  Ta  to  Tb.  The  gas 
can  then  receive  each  increment  of  heat  from  a  reservoir  having 
the  same  temperature  as  it  possesses  at  the  instant,  and  there- 
fore the  gas  can  thus  be  heated  reversibly. 

The  total  entropy  change  would  then  be 


and  by  the  use  of  this  equation  the  T0-diagram  can  be  drawn  as 
in  Fig.  27.  The  diagram  in  this  figure  shows  the  same  changes 
as  are  represented  by  PV-coordinates  in  Fig.  26.  The  dotted 
rectangle  is  the  Carnot  cycle  originally  given  in  Fig.  21. 

57.  The  Constant-Pressure  Heat  -Addition,  Brayton,  or  Joule 
Cycle,  (a)  This  cycle,  like  the  last,  is  an  irreversible  one  in  the 
thermodynamic  sense,  but  it  is  impor- 
tant because  of  its  practical  application 
to  certain  purposes  which  will  be  con- 
sidered later.  It  is  now  necessary  to 
derive  the  type  equations  for  the  cycle, 
as  has  been  done  in  the  preceding  cases. 
Fig.  28  shows  the  Joule  cycle  drawn 
to  PV  coordinates.  Starting  at  a,  heat 
is  added  to  the  working  substance  by 
the  hot  body,  volumes  and  temperature 
increasing  at  constant  pressure,  until  the 
point  b  is  reached.  Obviously  the  tem- 
perature 7"i,  of  the  hot  body,  must  be 
at  least  as  high  as  that  of  the  gas  at  b, 
and  therefore  higher  than  that  of  the 
gas  at  a.  The  heat  addition  is  there- 
fore irreversible. 

From  b  the  gas  expands  adiabatically 
to  c,  then  rejects  heat  irreversibly,  main- 
taining constant  pressure  until  the  vol- 
ume Vd  is  reached,  and  is  then  compressed  adiabatically  to  a, 
completing  the  cycle. 


Volumes 

Fig.  28.  —  PV-Diagram  of 
Joule  Cycle.  Air  as  working 
substance.  Adiabatic  expan- 
sion with  same  pressure  range 
as  in  Fig.  26. 


GAS  CYCLES 


99 


Mechanical  Energy  Obtained  per  Unit  Weight  of  Gas 
Operating  in  Joule  Cycle. 

(b)    As  before,  the  useful  effect  per  unit  weight  of  gas  can  be 
found  by  tabulation.     Thus: 


Line. 

,    Type. 

Mechanical  Energy  (Ft.-lbs.) 
Made  Available. 

ab 
be 
cd 
da 

Constant-Pressure  Expansion 
Adiabatic  Expansion 
Constant-Pressure  Compression 
Adiabatic  Compressicn 

+  Pa  (Vfr  -  V«) 
,    PbVb  -  PcVc 

7-1 

-  PC  (Ve  -  Vd) 
PaVa  ~  PdVd 

7-1 

The  summation  of  the  last  column  gives  for  the  cycle 

PbVb  -  PCVC 


Net  Work  =  Pa  (V»  -  V.)  + 


-  Pc  (Vc  -  Vd)  - 


7-  l 

PnVn- 


T- 


ft.-lbs.      (82) 


(c)  This  expression  could  be  simplified,  but  it  is  hardly  worth 
while,  as  a  shorter  one  can  be  obtained  more  easily  in  the  follow- 
ing manner. 

Writing  available  mechanical  energy,  or  work  done,  as 


AE  =  (Aft  -  A<22)  B.t.u., 
it  follows  from  the  character  of  the  lines  ab  and  cd  that 

AE  =  Cp  (Tb  -  To)  -  Cp  (Tc  -  Td) 
=  Cp(Tb-  Ta-  Tc+  Td)  B.t.u. 


and 


778  AE  =  Kp  (Tb  -  Ta)  -  Kp  (Tc  -  Td) 

=  Kp  (Tb  -  Ta  -  Tc  +  Td)  ft.-lbs. 


(83) 


(84) 


IOO 


(d)   Since 


HEAT-POWER  ENGINEERING 
Efficiency  of  Joule  Cycle. 


Ef.  = 


it  must  be  in  this  case, 


Aft  -  Aft 
Aft 


„,      Cp(Tb-  Ta)-CP(Tc-  Td) 

Cp(Tb-  Ta) 
Tc  -  TV 


T 

lb  — 


(85) 


This  can  be  further  simplified  by  using  Eq.  (52).     From  this 

y-l  T-l 

Tc          /Pc\y  i         Td          /Pd\    V 

Tfr  =   -FT         and     -=r  =  ( rrr- 


then,  since 

Pa  -  Pb     and     Pd  = 

T\  _  Td,  _  Tc  —  Ta 

Tb~    Ta~    Tb~    Ta 

Substituting  this  in  Eq.  (85)  gives 


(86) 


a  result  similar  to  that  obtained  for  the 
Otto  cycle. 

The  last  equation  can,  by  simple  sub- 
stitution, also  be  written 

/17\7-1 

Ef-  =  l-(f)        (87) 

which  is  likewise  similar  to  the  corre- 
sponding form  for  the  Otto  cycle. 

T</>-Diagram  of  Joule  Cycle. 

(e)    By  replacing  the  irreversible  iso- 
barics  by  equivalent  reversible  proces- 
ses, the  T</>-diagram  to  represent  this 
Fig    29  -PV-Diagram  of          ,e  can  fae  constructed    as  was  done 
Diesel  Cycle.    Air  as  working    r         .       „. 

substance.  The  lines  be  and  !°r  the  .Otto  cycle»  but  as  this  diagram 
cd  coincide  with  the  lines  sim-  ls  °f  h'ttle  practical  value  it  will  be 
ilarly  lettered  in  Fig.  26.  omitted. 

58.   The  Diesel  Cycle,     (a)    This  cycle,  drawn  to  PV-coordi- 
nates,  is  shown  in  Fig.  29.    The  heat  is  added  from  the  hot  body 


Volumes 


GAS  CYCLES 


101 


during  the  constant-pressure  expansion  ab,  and  then  the  gas,^-, 
pands  adiabatically  from  b  to  c.  Heat  is  discharged  to  the  cold 
body  while  the  pressure  of  the  working  substance  decreases  from 
c  to  d  at  constant  volume.  The  cycle  is  closed  by  the  adiabatic 
compression  da.  The  Diesel  cycle  is  irreversible  for  the  same 
reasons  that  the  Otto  and  Joule  cycles  are. 

Mechanical  Energy  Obtained  per  Unit  Weight  of  Gas 
Operating  in  Diesel  Cycle. 

(b)    As  before,  the  amount  of  mechanical  energy  made  avail- 
able can  be  found  by  tabulating: 


Line. 

Character. 

Work  (Ft.-Lbs.)  Done  by 
Unit  Weight  Gas. 

ab 

Constant-Pressure  Expansion 

+  Pa  (Vfc  -  Va) 

be 

Adiabatic  Expansion 

7-1 

cd 

Constant-  Volume  Pressure  Drop 

O 

da 

Adiabatic  Compression 

PaVa  -  PrfVd 

7  -  1 

The  summation  of  the  last  column  gives  for  the  cycle 


Net  Work  =  778  AE  =  Pa  (V6  -  V«)  +  - 


PbVb  -  PCVC 


y  -  1 


P  V   — 

-L  a  »  a 


7-  1 


ft.-lbs. 


(88) 


(c)  This  expression  need  not  be  simplified,  since,  as  in  previous 
cases,  there  is  a  more  convenient  way  of  finding  a  short  ex- 
pression for  the  work  done.  Writing 


AE  =  (Aft  -  A<22)  B.t.u., 
it  follows  that,  in  the  case  of  the  Diesel  cycle, 

AE=  Cp(Tb-  Ta)-Cv(Tc-Td)  B.t.u.    .     .     (89) 
and 

778  AE  =  Kp  (Tb  -  Ta)  -KV(TC-  Td)  ft.-lbs,    .     (90) 


'.. ."IO2 


(d)    Writing 


HEAT-POWER  ENGINEERING 
•.*  Efficiency  of  Diesel  Cycle. 


Aft  - 


the  efficiency  in  this  case  must  be 

•         Cp(Tb-  Ta)-Cv(Tc-Td) 
Cp(Tb-  Ta) 


\C,     Tc  -  Td] 

=  1  —     TT  •   ^  -  T=T 

\_Cp        Tb  —    -TaJ 


Tc  -  T 


-  TV] 

T~ 

—    1  aj 


This  has  the  same  form  as  Eq.  (85),  for  the  efficiency  of 
the  Joule  cycle,  with  the  exception  of  the  introduction  of  1/7. 
It  should,  however,  be  noted  that  the  temperature  term  is  not 
numerically  the  same  in  both  cases,  on  account  of  the  difference 
in  the  shape  of  the  two  cycles. 

(e)  By  substituting  reversible  processes  for  the  irreversible 
ones,  a  1>-diagram  equivalent  to  this  cycle  can  be  constructed. 


GAS  CYCLES  -TABLE  III 


CYCLE 

WORK-FT.LBS. 
PER   LB.  OF  GAS. 

EFFICIENCY 

NAME 

PV-DIAGRAM 

GENERAL 

1               Any  Number 
\?\      of  Processes 
^^        Enclosing 
1  an  Area,  A 

=  Area  Enclosed  (A) 
=  AQjX  Eff.x  778. 
=778  AE 
=778(AQ,-AQ2) 

=Kesult  -J-  Effort 
=(^0^-^02)  4-  AQj 

CARNOT 

I    -j-           Isothermals 

M^&v                 and 
y^         Adiabatics 

=  CT-T2)Rloger 

=  ^=1-^ 

STIRLING 

^/T.        Isothermals 
\               and 
T.pt          Jsovolumics 

1  1 

t  ( 

ERICSSON 

T      Isothermals 

^             and 
1  T2              Isobarics 

<  c 

<  c 

OTTO 

1  ^          Adinbatics 

\\c           and 
™d     Isovolumics 

=  Kr(T6-T-Tc+Td) 

.i-ftLi-^l^ 

1    PW          vj 

BRAYTON 
OR 
JOULE 

1  db          Adiabatics 

1    &*           and 

Isobarics 

=  KP(T6-T-VTd) 

ii 

DIESEL 

1  ah          Adiabatics 
^^C     Isobaric  and 
d     Isovolumic 

^K/VT^MVT,) 

1  P  T«-T"1 

rv\J 

CHAPTER   IX. 

VAPORS. 

59.  Vapors   and   Gases.     When   materials   change   from   the 
liquid*  to  the  gaseous  state  they  do  not  immediately  reach  the 
condition  in  which  their  behavior  even  approximately  obeys  the 
laws  of  ideal  gases.     It  is  customary  to  designate  materials  as 
Vapors  when  in   this   intermediate   condition.     It  will  appear 
later  that  when  strictly  interpreted  the  term  vapor  will  apply  to 
many  of  the  materials  with  which  the  engineer  deals  and  which 
he  is  accustomed  to  call  gases. 

60.  Formation  of  Vapor,     (a)    When  a  liquid  is  heated  under 
constant  pressure  its  temperature  will  first  rise  until  it  reaches  a 
certain  temperature  which  is  dependent  upon  the  pressure  under 
which  it  exists;  after  which  further   addition  of  heat  will  cause 
some  of  the  material  to  change  physical  state  at  constant  tem- 
perature, this  temperature  being  the  one  fixed  by  the  pressure 
existing.     The  amount  of  material  that  has  changed  state  will 
increase  as  this  further  addition  of  heat  progresses,  and  if  sufficient 
heat  is  added  all  the  liquid  present  will  thus  change  its  state. 
The  material  formed  during  this  change  of  state  is  called  a  vapor. 

(b)  Considering  the  process  for  the  first  time,  one  would 
recognize  two  possible  methods  of  formation  of  vapors,  a\id 
without  previous  knowledge  would  not  be  able  to  decide  be- 
tween them.  Thus: 

(1)  The  liquid  as  a  whole  might  gradually  change  from  liquid 
to  vapor,  all  of  it  being  at  any  one  time  in  exactly  the  same  con- 
dition of  transformation.     Or, 

(2)  Parts  of  the  liquid  might  progressively  change  to  vapor  as 
the  necessary  heat  became  available,  leaving  the  remainder  still 
in  the  form  of  liquid. 

Usually  vaporization  occurs  by  method  (2),  and  as  heat  is 
added  more  and  more  vapor  appears  at  the  expense  of  liquid. 

*  Or  directly  from  the  solid,  as  in  "  sublimation." 
103 


Fig.  30. 


HEAT-POWER  ENGINEERING 


Thus  when  one-fourth  of  the  total  heat  necessary  for  complete 
vaporization  is  added  one-fourth  of  the  liquid  will  be  vaporized, 
and  so  on  until  vaporization  is  complete. 

(c)  In  the  sections  which  follow  the  generation  of  vapor  may 
be  conveniently  studied  by  imagining  the  process  carried  out  in 

the  device  illustrated  in  Fig.  30.  It 
consists  of  a  vertical  cylinder  with 
closed  end  down,  containing  a  friction- 
less  piston  of  given  weight,  —  all  being 
placed  under  a  bell  jar  in  which  a  per- 
fect vacuum  is  maintained. 

Assume  now  that  one  pound  of  liq- 
uid is  inclosed  in  the  cylinder  beneath 
the  piston.  The  total  pressure  on  the 
upper  surface  of  this  liquid  will  be 
that  due  to  the  weight  of  the  piston, 
and  since  it  is  evenly  distributed  over 
3  the  entire  surface  it  may  be  desig- 
nated as  P  pounds  per  square  foot  of 
surface. 

Any  liquid  may  be  used  and,  in  general,  may  have  any  tem- 
perature between  that  of  solidification  and  that  of  vaporization 
at  the  chosen  pressure.  It  is,  however,  customary  to  assume  the 
temperature  at  a  convenient  value  dependent  on  the  physical 
characteristics  of  the  liquid  dealt  with. 

In  the  case  of  water,  and  of  all  other  liquids  for  which  such  a 
temperature  is  at  all  convenient,  the  engineer  is  accustomed  to 
refer  all  vaporization  phenomena  to  a  datum  temperature  of 
32°  F.  As  this  is  the  melting  temperature  of  ice  under  ordi- 
nary conditions,  it  is  readily  checked  and  is  hence  a  very  satis- 
factory standard. 

To  make  the  results  of  the  process  under  consideration  con- 
form to  the  engineering  reality,  the  liquid  beneath  the  piston, 
in  Fig.  30,  will  be  assumed  at  32°  F. 

61.  Heat  of  the  Liquid,  (a)  If  heat  is  added  to  the  liquid 
beneath  the  piston  in  Fig.  30,  the  temperature  will  rise  and,  in 
the  case  of  water,  at  the  approximate  rate  of  i°  F.  for  each  B.t.u., 
since  the  specific  heat  of  water  at  constant  pressure  is  approxi- 
mately i.  In  any  case  the  rise  will  take  place  at  the  rate  of 


VAPORS  105 

i°  F.  for  each  addition  of  heat  equal  to  Cp,  the  constant-pressure 
specific  heat  of  the  liquid  dealt  with.  This  will  continue  until  a 
temperature  is  reached  at  which  vaporization  begins.  This  tem- 
perature will  depend  upon  the  value  of  the  pressure,  and  in 
any  case  has  to  be  determined  by  experiment.  Thus  with 
water  at  atmospheric  pressure  (equal  to  14.7  pounds  per  square 
inch,  or  14.7  X  144  =  2116.8  pounds  per  square  foot),  the  tem- 
perature will  be  212°  F.;  while  for  a  pressure  of  100  pounds  per 
square  inch  (equal  to  100  X  144  =  14,400  pounds  per  square 
foot)  the  temperature  will  be  about  327°  F.  These  various  tem- 
peratures are  called  the  Temperatures  of  Vaporization  and  will 
be  designated  by  the  symbols  tv  and  Tv  respectively  for  Fahr. 
and  Absolute  temperatures.  When  it  is  necessary  to  indicate  a 
particular  temperature,  the  corresponding  pressure  in  pounds 
per  square  inch  will  follow  the  subscript  »;  thus,  the  tempera- 
ture Fahr.  of  vaporization  at  atmospheric  pressure  would  be 
tvu.7  or  temperature  absolute  Tvu.7. 

(b)  The  heat  added  during  the  process  of  raising  the  tempera- 
ture from  32°,  or  other  datum  level,  to  the  temperature  of  vapor- 
ization is  called  the  Heat  of  the  Liquid  and  is  designated  by  q. 
Obviously  it  has  a  different  value  for  every  different  pressure 
and  it  is  customary  to  tabulate  these  values  with  others  in  so- 
called  Vapor  Tables.     In  general 

q  =  j*CpdT, (92) 

the  integration  being  performed  between  the  datum  tempera- 
ture as  the  lower  limit  and  the  temperature  corresponding  to  the 
pressure  in  question  as  the  upper  limit. 

If  the  specific  heat  of  water  were  exactly  equal  to  unity  at  all 
temperatures,  the  value  of  g  for  this  material  for  any  temperature 
or  pressure  of  vaporization  could  be  found  from  the  equation 

2  =  ^-32; (93) 

and  since  these  values  vary  but  slightly  from  those  determined 
by  experiment,  this  equation  is  often  used  by  engineers.  For 
accurate  work  the  experimentally  determined  values  given  in  the 
steam  tables  should  be  used. 

(c)  Eq.   (93)  could  not  be  used,  even  as  an  approximation, 
with  any  liquid  other  than  water,  since  it  depends  upon  the 
assumption   that  the  specific  heat  of  the  liquid  is  invariably 


106  HEAT-POWER  ENGINEERING 

equal  to  unity.  If,  as  before,  the  specific  heats  of  liquids  at  con- 
stant pressure  are  designated  by  Cp,  and  if  they  are  assumed  con- 
stant over  the  ranges  of  temperature  considered,  the  equation 

<z  =  Cpfe-32)    .  ;- "•->  .-   •  -;>  (94) 

may  be  used  in  determining  the  heat  of  the  liquid  for  any  tem- 
perature or  pressure  of  vaporization.  Note  that  there  are  liquids 
which  vaporize  at  ordinary  pressures  below  the  temperature  of 
32°  F.  In  such  cases  a  datum  temperature  lower  than  32°  may 
be  taken  from  which  the  heat  of  the  liquid  is  calculated.  This 
necessitates  a  different  form  of  equation.  In  its  most  general 
expression  this  would  become 

q  =  C,(T.-  Tt),    .    ',-   ,    .     .••'.'    (95) 
where  T0  stands  for  any  arbitrarily  chosen  datum. 

62.  Latent  Heat  of  Vaporization,  (a)  Consider  now  the  pound 
of  liquid  which  has  been  raised  to  the  temperature  /„.  With 
further  addition  of  heat  vaporization  occurs.  The  marked  char- 
acteristics of  vaporization  under  the  assumed  conditions  are  (i) 
the  very  great  increase  of  volume  at  constant  temperature  and 
pressure,  (2)  the  change  of  the  physical  state  of  the  material  from 
liquid  to  vapor,  and  (3)  the  enormous  quantity  of  heat  absorbed. 

(b)  The  process  carried  out  in  the  apparatus  of  Fig.  30  would 
result  in  driving  up  the  piston  to  some  higher  position  in  the 
cylinder,  against  the  pressure  exerted  by  that  piston  on  the  upper 
surface  of  the  vapor.  Evidently,  here,  force  would  act  through 
distance  and  therefore  external  work  would  be  done.  This 
work  could  not  be  done  without  a  supply  of  energy,  and,  since 
heat  energy  is  the  only  form  supplied  during  the  process,  it 
follows  that  at  least  some  of  this  heat  must  have  been  used  for 
the  doing  of  the  external  work.  Let  F  be  used  to  designate  the 
area  of  the  piston  face  in  square  feet,  and  L  the  number  of  feet 
the  piston  is  moved  during  the  vaporization  of  the  entire  pound 
of  liquid  under  consideration. 

Then  the  foot-pounds  of  external  work  done  per  unit  weight 
are 

778  AE  =  (PF)  L, 

which,  rearranged,  becomes 

778  AE  =  P  (FL)  =  P  (V2  -  Fi),  (96) 


VAPORS 


107 


where  Vi  represents  the  volume  occupied  by  the  liquid  and  V2 
that  occupied  by  the  vapor.  It  is  customary  to  designate  the 
increase  of  volume  (Yz  —  Vi)  by  the  letter  u,  hence  the  external 
work  done,  in  foot-pounds,  is 

778  AE  =  Pu, (96a) 

and  its  value  in  thermal  units  can  be  found  by  dividing  Pu  by 

778.     Representing  —  —  by  A ,  the  expression  for  the  B.t.u.  of  heat 

770 

used  in  the  doing  of  external  work  becomes 

AE  =  APu (97) 

This  quantity  is  called  the  External  Latent  Heat  of  Vaporiza- 
tion. It  has  a  different  value  for  every  different  pressure  at 
which  vaporization  takes  place,  and  these  values  are  tabulated 
in  the  Vapor  Tables  already  mentioned. 

It  is  very  necessary  to  observe  that  the  term  external  "latent 
heat"  is  a  misnomer.  The  heat  used  for  the  doing  of  external 
work  does  not  exist  as  heat  energy  in  the  vapor,  for,  during  the 
process  of  vaporization,  it  is  changed  into  mechanical  energy 
which  is  extraneous  to  the  vapor  itself.  The  case  is  somewhat 
similar  to  isothermal  expansion  of  a  gas.  This  heat  is  con- 
verted into  mechanical  energy  as  rapidly  as  received.  Hence,  in 
a  piston  engine,  the  external  latent  heat  may  be  considered  as 
external  work  delivered  by  the  piston  rod.  If  the  energy  after 
reception  can  be  said  to  be  "  latent,"  it  must  be  latent  mechani- 
cal energy  and  not  latent  heat  energy.  It  is  stored,  if  stored  at 
all,  in  the  piston  or  other  similar  part  of  the  apparatus,  and  is 
in  no  sense  in  the  vapor. 

(c)  Experiment  shows  that  the  heat  used  during  the  process 
of  vaporization  is  not  all  accounted  for  by  the  external  latent 
heat.  Inspection  of  Eq.  (i), 

A<2  =  AS  +  A/  +  AE, 

suggests  the  reason.  In  this  case  A<2  represents  the  heat  added 
to  vaporize  the  liquid.  As  the  temperature  does  not  change 
during  vaporization,  no  heat  can  be  used  as  sensible  heat,  hence 
AS  =  o;  but  some  of  it  may  be  used  for  the  doing  of  internal 
work,  A/.  In  fact  the  striking  change  of  properties  during  this 
process  could  not  occur  without  a  very  great  readjustment 
within  the  material.  The  part  of  AQ  which  does  not  become 


108  HEAT-POWER  ENGINEERING 

external  latent  heat  is  supposed  to  be  used  for  doing  this  internal 
work,  and  is  therefore  called  the  Internal  Latent  Heat.  It  is 
designated  by  the  symbol  p  and  is  tabulated  in  the  Vapor  Tables. 

Recent  work  has  led  to  the  conclusion  that  liquid  water  is  a 
more  complex  material  than  was  originally  supposed.  It  seems 
probable  that  instead  of  being  simply  a  collection  of  molecules 
with  formula  H2O  it  is  really  a  mixture  of  at  least  three  different 
kinds  of  molecules,  H2O,  (H2O)2  and  (H2O)3.  It  also  seems  prob- 
able that  during  the  formation  of  vapor  some  of  the  more  com- 
plex molecules  break  up  into  simpler  form.  If  this  is  so,  a 
possible  use  of  at  least  "part  of  the  Internal  Latent  Heat  in  the 
case  of  water  becomes  evident  since  it  would  be  used  for  break- 
ing up  the  complex  molecules.  "  Internal "  latent  heat  would 
then  be  a  correct  name  to  apply  to  this  part  of  the  heat  as  it 
is  latent  within  the  substance,  though  there  is  room  for  argu- 
ment as  to  whether  it  is  latent  as  heat. 

(d)  The  sum  of  the  two  latent  heats,  p  and  APu,  is  called  the 
Total  Latent  Heat  of  Vaporization,  and  is  designated  in  the 
tables  by  r.  Thus  r  =  p  +  APu 

63.  Total  Heat  per  Pound  of  Vapor,  (a)  Using  symbols,  the 
total  heat,  above  the  arbitrarily  chosen  datum  temperature,  per 
pound  of  vapor  at  any  pressure  P,  is  the  sum  of  the  sensible 
heat,  the  internal  latent  heat,  and  the  external  latent  heat;  thus 
it  is 

&>  +  PP  +  (APu)p  =  qp  +  rp,    .     .     .     .     (98) 

and  calling  this  X  gives 

Xp  =  ffp  +  fp,     .     .     .     .     .     .     (99) 

which  is  also  given  in  the  tables. 

(b)  Had  the  addition  of  heat  in  the  process  under  considera- 
tion ceased  before  the  entire  pound  of  liquid  had  been  vapor- 
ized, the  cylinder  would  have  contained  both  vapor  and  liquid 
at  the  same  temperature.  Representing  by  y  the  fraction  of  the 
total  pound  vaporized,  the  "  heat  of  the  vapor  "  *  present  must 
be 

A<2'  =  yqP  +  ypP  +  y  (APu)p 

*  The  expression  "  heat  of  "  will  hereafter  be  used  to  designate  the  quantity 
necessary  to  bring  the  material  in  question  to  the  condition  under  consideration, 
either  from  liquid  at  datum  temperature  or  from  liquid  at  the  temperature  of 
vaporization.  The  context  will  indicate  which  is  referred  to  in  any  case. 


VAPORS 

and  that  of  the  remaining  liquid  must  be 
A<2"  -  (1  -  y)  &, 

hence  the  total  heat  of  the  material  in  the  cylinder  is 
Aftp  =  A<2'  +  A<2" 

=  qp  +  ypp  +  y(APu)p      ....       (100) 
=  aP  +  yrp (iooa) 

which  will  be  equal  to  Eq.   (98)  when  y  =  1,  that  is,  when  the 
entire  pound  has  been  vaporized. 

64.  Saturated  Vapor,  (a)  The  process  assumed  in  the  pre- 
vious sections  is  really  more  or  less  idealized.  In  real  cases, 
such  as  that  taking  place  in  the  steam  boiler,  the  vaporization 
does  not  progress  so  quiescently  that  the  vapor  separates  en- 
tirely from  the  liquid  and  collects  above  it  in  the  simple  fashion 
already  described.  Instead,  the  formation  of  vapor  is  gen- 
erally more  or  less  violent,  and,  in  separating  from  the  body  of 
the  liquid,  the  vapor  carries  with  it  small  drops  of  that  liquid 
still  unvaporized  but  mechanically  entrained.  These  may  often 
be  carried  great  distances  by  a  stream  of  vapor,  and  their  sepa- 
ration from  that  vapor  frequently  presents  considerable  diffi- 
culty. 

(b)  Such  mixtures  of  vapors  and  liquids  are  called  Wet  Vapors, 
to  indicate  the  presence  of  the  liquid;  and  when  the  entrained 
moisture  has  been  entirely  eliminated  the  material  is  called  Dry 
Vapor.  Since,  under  the  conditions  assumed  in  connection  with 
Fig.  30,  the  liquid  must  all  be  raised  to  the  temperature  of 
vaporization  before  any  of  it  can  be  converted  into  vapor  at  the 
same  temperature,  it  follows  that  the  vapor  and  liquid  in  such  a 
wet  mixture  are  in  thermal  equilibrium;  that  is,  if  there  is  any 
tendency  for  heat  transfer  from  liquid  to  vapor,  there  is  an  equal 
tendency  towards  transfer  in  the  opposite  direction.  With  no 
heat  lost  to  surrounding  materials,  such  a  mixture  would  main- 
tain a  constant  composition  indefinitely. 

Vapor  when  in  thermal  equilibrium  with  its  liquid  is  called 
Saturated  Vapor.  It  is  termed  Wet  Saturated  Vapor,  or  simply 
Wet  Vapor,  if  containing  entrained  liquid  and  Dry  and  Saturated 
Vapor,  or  simply  Dry  Saturated  Vapor,  if  free  from  moisture  in 
suspension. 


HO  HEAT-POWER  ENGINEERING. 

(c)  At  different  pressures  the  quantity  of  he^it  necessary  to 
maintain  material  in  the  condition  of  dry  saturated  vapor  has 
different  values,  being  greater  the  higher  the  pressure.  Abstrac- 
tion of  heat  without  change  of  pressure  (and  therefore  without 
change  of  temperature)  will  cause  partial  or  total  condensation, 
but  any  vapor  remaining  will  still  be  saturated  vapor  exactly 
like  that  which  existed  before  condensation  occurred.  There- 
fore saturated  vapor  may  be  described  as  vapor  so  near  the 
point  of  liquefaction  that  the  removal  of  the  slightest  quantity 
of  heat  will  produce  partial  condensation.  Or  (see  following 
paragraphs)  it  may  be  described  as  vapor  in  which  the  maximum 
number  of  molecules,  consistent  with  the  maintenance  of  a  vapo- 
rous state  at  the  given  pressure,  exist  in  a  given  space. 

65.  Quality,     (a)    Practically  all  saturated  vapors  in  actual 
use  contain  some  entrained  moisture,  and  it  is  often  necessary  to 
express  just  how  much  of  each  pound  of  such  a  mixture  is  liquid 
and  how  much  is  vapor.     This  is  done  by  using  the  fraction 
representing  the  proportion  of  mixture  which  is  really  saturated 
vapor.     This  fraction  is  denoted  by  x,  and  is  called  the  Quality 
Factor,  or  Quality  of  the  vapor  or  mixture. 

Thus  if  x  is  f,  or  75  per  cent,  it  means  that  three-quarters  of 
every  pound  of  mixture  is  vapor  and  the  other  quarter  is  liquid. 
The  quaHty  of  the  mixture  would  then  be  said  to  be  75  per  cent. 

(b)  The  heat  content  above  datum  temperature  of  such  a 
mixture  could  obviously  be  found  by  putting  x  in  place  of  y  in 
Eq.  (100),  since,  so  far  as  associated  heat  is  concerned,  it  makes 
no  difference  whether  the  vapor  and  liquid  are  separated  or 
intimately  mixed.  For  wet  vapor  of  quality  x,  the  total  heat 
above  datum  temperature  is  then 

&QxP  =  qp  4-  XPP  +  x  (APu)p  =  qp  -f  x  rp.      .     (101) 

66.  Superheated    Vapor,     (a)    Having    converted    an    entire 
pound  of  liquid  into  dry  and  saturated  vapor  in  the  apparatus 
of  Fig.  30,  its  condition  may  be  further  modified  if  the  addition 
of  heat  is  still  continued.     Experiment  shows  that  this  further 
addition  causes  the  temperature  of  the  vapor  to  rise  above  that 
which  existed  during  vaporization.     This  process  is  known  as 
superheating,  that  is,  raising  above  the  saturation  temperature 
corresponding  to  the  existing  pressure.     The  material  formed  is 


VAPORS  m 

called  Superheated  Vapor,  and  it  becomes  more  and  more  like 
an  ideal  gas  as  its  temperature  is  raised  at  constant  pressure. 
Thus  it  increases  in  volume  with  the  addition  of  heat,  and  a  given 
space  must  hold  fewer  and  fewer  molecules  as  the  rise  of  temper- 
ature continues. 

(b)  To  make  the  meaning  of  the  term  "  saturated  "  clearer, 
imagine  a  superheated  vapor  to  be  cooled,  at  constant  pressure, 
by  the  removal  of  heat.  As  temperature  decreases  the  vol- 
ume also  becomes  less,  and  any  given  space  holds  more  and 
more  molecules  until  the  temperature  of  vaporization  is  reached, 
at  which  point  the  material  is  reduced  to  the  saturated  condi- 
tion. There  is  then,  in  a  given  space,  the  maximum  number  of 
molecules  which  can  exist  as  vapor  under  the  conditions  obtain- 
ing; and  further  removal  of  heat  would  allow  some  of  these  to 
collect  and  form  molecules  of  liquid,  —  that  is,  it  would  cause 
partial  condensation.  The  material  remaining  uncondensed 
would  still  be  saturated  vapor,  and  with  further  removal  of  heat 
more  and  more  of  it  would  condense  until'  finally  all  would  be- 
come liquid,  if  the  removal  of  heat  were  continued  sufficiently  far. 

67.  Heat  per  Pound  of  Superheated  Vapor.  The  amount  of 
heat  added  during  superheating  at  constant  pressure,  to  any 
temperature  TS1  as  described  above,  depends  upon  two  things,  — 
on  the  degree  of  superheat,  which  will  be  called  D  and  equals 
(Ta  —  Tv),  and  on  the  specific  heat  Cp  of  the  vapor.  Then  the 
heat  added  during  superheating  would  be  given  by  the  following 
equation  if  Cp  happened  to  be  a  constant: 

A(?z>  =  CPD.       . (102) 

The  total  heat  (above  datum  temperature)  of  one  pound  of 
superheated  *  vapor  would  be 

&Q*=gp  +  Pp  +  (APu)p  +  CpD    .     .     .     (103) 
=  qp  +  rp  +  CPD  =  \p  +  CPD.     .     .  (iO3a) 

*  Recent  experiment  has  shown  that  liquid  water  can  exist  for  a  considerable 
length  of  time  within  a  mass  of  superheated  steam,  despite  the  fact  that  the  two 
are  not  in  thermal  equilibrium.  This  fact  must  sometimes  be  taken  into  account 
in  dealing  with  superheated  steam  in  practical  problems,  when  sufficient  time  does 
not  elapse  to  establish  thermal  equilibrium.  The  heat  per  pound  of  such  a  mixture 
would  be 

Qxs  =  qp  +  xrp  4-  xCpD. 


112 


HEAT-POWER  ENGINEERING 


68.  Diagram  of  Heat  Changes  during  Vaporization,  (a)  The 
heat  changes  associated  with  the  process  of  vaporization  can  all 
be  graphically  represented,  as  in  Fig.  31,  by  plotting  temperature 
as  ordinates  and  heat  added  as  abscissas.  The  figure  is  for 
water,  but  a  similar  diagram  could  be  drawn  for  any  material 
whose  physical  constants  are  sufficiently  well  known. 


600 

c 

Temperatures  °!F. 
_ea  8  1  1  i 

<.  

XTSO  — 

-> 

p. 

7 

h  / 

150  Lbs. 

Sq.  In. 

C3i 

di 

6 
/ 

2 

70    » 

J>     >> 

"1 

I 

r 

30    » 

"     " 

7 

f"$ 





10   •» 

Xnr—  • 



-J| 

// 

200           400           600           800          1000         1200          14 

Heat.Added-  B.T.U. 

Fig.  31-  — TQ-Diagram  for  Vapor  Phenomena. 

The  line  abed  shows  the  relation  of  temperature  to  heat  added 
while  one  pound  of  water  under  10  pounds  pressure  is  first 
heated  from  32°  F.  to  vaporization  temperature  (line  ab) ,  is  then 
completely  vaporized  (line  be),  and  finally  is  superheated  through 
a  limited  range  (line  cd).  The  lines  abiddi,  abfadz,  etc.,  show 
the  same  things  for  the  other  pressures  indicated. 

(b)  A  diagram  drawn  to  a  sufficiently  large  scale  would  show 
the  line  abb3,  and  lines  cd,  c\d\,  etc.,  as  slightly  curved  because  of 
the  variation  in  the  value  of  the  specific  heat  of  liquid  water  and 
of  the  specific  heat,  CPJ  of  superheated  water  vapor.     In  draw- 
ing Fig.  31  an  average  specific  heat  was  used  for  the  liquid  and 
an  average  over  each  temperature  range  cd,  cidi,  etc.,  for  the 
superheated  vapor.     The  latter  accounts  for  the  slight  differ- 
ences in  slope  of  the  superheating  lines. 

(c)  The  diagram   shows   how   great   an    amount  of   heat  is 
absorbed  during  the  process  of  vaporization  as  compared  with 
that  used  in  bringing  the  liquid  to  the  temperature  of  vaporiza- 
tion, or  with  that  used  in  superheating.     This  is  of  great  im- 
portance in  heat  engineering  and  will  be  fully  considered  later. 

Two  other  facts  of  importance  are  made  evident  by  the  dia- 


VAPORS 

gram:  One  is  the  small  change  of  total  heat,  X,  for  a  wide 
pressure  range,  as  is  seen  by  comparing  the  abscissas  of  c,  c\, 
etc.;  and  the  other  is  the  decrease  of  the  total  latent  heat  of 
vaporization,  r,  as  the  pressure  rises. 

(d)  This  figure  also  shows  the  temperature  changes  and  heat 
given  up  when  superheated  vapor  at  any  of  the  given  pressures 
is  cooled  to  the  saturated  condition,  then  is  condensed;  and  the 
resulting  liquid  cooled  to  32°  F.  The  engineer  must  often  con- 
sider changes  in  this  direction. 

69.  Vapor  Tables.     Since  the  various  values  of  g,  p,  APu,  r, 
and  X  are  very  frequently  used  by  engineers  and  scientists,  they 
are    recorded,    as    already    intimated,    in    the    so-called    Vapor 
Tables.     There  is  of  course  a  table  for  each  material  dealt  with, 
so  that  it  is  customary  to  speak  of  "  Steam  Tables,"  "  Ammonia 
Tables,"  "  Carbon  Dioxide  Tables,"  etc. 

The  various  values  of  each  quantity  are  usually  tabulated  in 
vertical  columns,  the  first  two  columns  giving  pressures  and 
corresponding  temperatures  of  vaporization,  and  the  succeeding 
columns  giving  the  corresponding  values  of  the  various  heat 
quantities.  Certain  other  columns  are  usually  added  containing 
such  values  as  the  volume  occupied  by  a  pound  of  liquid  and  by 
a  pound  of  dry  and  saturated  vapor.  See  tables  in  Appendix. 

70.  Saturation   Curve,     (a)    Experiment  shows  that  just  as 
the  saturated  vapor  of  a  given  material  at  any  particular  tem- 
perature always  exerts  the  same  definite  pressure,  so  also  does 
one  pound  of  dry  saturated  vapor  at  any  temperature  always 
occupy  a  definite  volume.     This  latter  is  called   the  Specific 
Volume  and  is  tabulated  in  the  vapor  tables.     If  the  specific 
volumes   are   plotted   against  the  corresponding   pressures,    the 
locus  of  the  points  is  a  PV-diagram  similar  to  Fig.  32,  which 
like  the  last  is  drawn  for  water  vapor. 

(b)  This  curve,  called  the  Saturation  Curve,  may  be  very  useful. 
If  one  pound  of  material  at  a  given  pressure  has  a  volume  rep- 
resented by  a  point  which  falls  to  the  left  of  the  saturation 
curve,  the  material  must  be  wet  vapor;  but  if  the  point  falls  to 
the  right  of  that  curve,  the  material  must  be  superheated  vapor. 

In  the  case  of  most  engineering  materials,  the  volume  occupied 
by  one  pound  of  liquid  is  negligible  as  compared  with  that  of 
one  pound  of  vapor.  In  the  case  of  water,  the  volume  increases 


114  HEAT-POWER  ENGINEERING 

nearly  1700  times  when  changing  from  liquid  to  dry  saturated 
vapor  under  atmospheric  pressure.  If  the  volume  of  the  liquid 
present  be  neglected,  steam  of  50  per  cent  quality  would  occupy 
0.5  the  volume  it  would  if  dry  and  saturated,  and  steam  of  75  per 
cent  quality  would  have  0.75  of  the  volume  of  dry  saturated 
steam,  and  so  on. 

It  follows  that,  if  one  pound  of  mixture  is  found  to  occupy  a 
volume  ab,  Fig.  32,  at  the  pressure  indicated,  it  must  have  a 


\ 

a 

37 

\ 

.  °S 

Wet 

Region 

^ 

% 

^  . 

Specific  Volumes 
Fig.  32.  —  Saturation  Curve  for  Water  Vapor. 

quality  of  x  =  — ,  if  the  volume  of  the  water  present  is  neglected. 

The  case  of  superheated  steam  will  be  considered  later,  after  the 
discussion  of  the  experimental  results. 

The  area  to  the  left  of  the  saturation  curve  might  be  called 
the  region  of  wet  saturated  vapor;  and  the  area  to  the  right,  the 
region  of  superheated  vapor.  The  curve  itself  would  then  repre- 
sent the  boundary  between  the  two,  thus  emphasizing  the  fact 
that  dry  saturated  vapor  is  a  unique  condition  at  each  pressure. 

(c)  Because  of  the  resemblance  of  the  saturation  curve  to 
an  expansion  curve  there  is  a  tendency  to  regard  it  as  represent- 
ing a  possible  expansion  of  vapor,  that  is,  as  an  increase  of 
volume  during  which  the  vapor  remains  dry  and  saturated 
throughout  the  entire  process.  Such  an  expansion  might  be 
obtained  under  very  forced  conditions,  but  normally  no  such 
process  could  be  made  to  occur.  It  is  then  best  to  regard  this 


VAPORS 

curve  only  as  a  boundary  line  between  two  fields  and  not  as  the 
graph  of  a  process. 

71.  Defining  Conditions  for  Saturated  Vapors.     In  dealing 
with  ideal  gases  the  variables   to   be  considered  are   pressure, 
temperature,  and  volume.     They  are  so  interrelated  that  fixing 
any  two  determines  the  third. 

In  the  case  of  dry  saturated  vapors,  however,  the  pressure, 
temperature,  and  volume  are  so  related  that  the  fixing  of  one 
determines  the  other  two.  This  is  not  true  of  wet  saturated 
vapors  nor  of  superheated  vapors. 

In  the  case  of  wet  saturated  vapors,  the  fixing  of  temperature 
determines  the  pressure,  and  vice  versa,  but  the  quality  must  be 
known  in  order  to  determine  the  volume  occupied. 

Superheated  vapors  are  more  or  less  like  gases,  and  in  general 
the  fixing  of  any  two  of  the  variables  determines  the  third. 

72.  Evaporation,    (a)    There  is  sometimes  difficulty  in  harmo- 
nizing the  phenomena  of  vaporization,  just  described,  with  what 
is  commonly  known  as  evaporation.     There  is  no  real  difference 
in  the  phenomena,  vaporization  as  so  far  considered  being  only  a 
limiting  case  of  evaporation. 

(b)  In  what  follows  it  will  be  of  material  assistance  if  it  is 
remembered  that  the  so-called  temperature  of   vaporization  at 
any  pressure  is  really  the  temperature  of  saturated  vapor  (wet 
or  dry)  at  that  pressure. 

Thus  the  pressure  exerted  by  a  saturated  vapor  is  determined 
by  the  temperature  of  the  space  the  vapor  occupies,  and  the 
pressure  corresponding  to  any  temperature  can  be  found  in  the 
vapor  table  for  the  material. 

(c)  Experiment  shows  that  when  the  surface  of  a  liquid  is  ex- 
posed to  a  space  which  is  not  already  filled  with  the  saturated  vapor 
of  that  liquid,  vapor  is  generated  until  the  space  is  filled  with  such 
saturated  vapor,  unless  the  liquid  present  is  insufficient  in  amount. 
Of  course  vaporization  ceases  if  the  liquid  is  exhausted. 

If  the  condition  of  equilibrium  is  reached,  the  saturated  vapor 
must  exert  the  pressure  corresponding  to  the  temperature  of  the 
space  occupied.  Until  this  equilibrium  is  attained,  any  vapor 
present  must  be  superheated  vapor  because  the  number  of  mole- 
cules in  a  given  space  is  less  than  would  be  the  case  if  the  space 
were  filled  with  saturated  vapor.  Superheated  vapor,  however. 


1X6  HEAT-POWER  ENGINEERING 

exerts  a  pressure  less  than  that  exerted  by  saturated  vapor  at 
the  same  temperature. 

It  follows  that  the  pressure  under  which  the  liquid  changes  to 
vapor  must  constantly  increase  until  a  maximum  is  reached, 
when  the  space  becomes  filled  with  saturated  vapor.  After  that, 
there  can  be  no  further  change  in  the  relative  quantities  of 
liquid  and  vapor  present  unless  temperature  changes. 

(d)  Since  heat  is  required  to  change  a  liquid  to  a  vapor,  a 
supply  of  heat  must  be  obtained  from  some  source  to  cause 
"  evaporation."     If  heat  is  not  supplied  from  external  sources, 
it  is  taken  from  the  liquid  and  surrounding  matter;  hence  the 
sensation  of  cold  when  alcohol,  or  other  volatile  liquid,  is  quickly 
evaporated  from  the  skin. 

The  actual  amount  of  heat  necessary  for  evaporation  may  be 
found  by  considering  the  process  after  equilibrium  is  attained. 
Every  pound  of  dry  saturated  vapor  must  have  associated  with 
it  the  total  heat  X  corresponding  to  the  existing  pressure  and 
temperature. 

(e)  Usually  the  space  into  which  the  vapor  passes  contains 
other  material  beside  the  vapor;  for  example,  some  air  is  almost 
always  present.     Dalton's  law  states   that   each  constituent  of 
such  mixtures  behaves  as  though  the  others  were  not  present.     There- 
fore, the  phenomenon  is  not  in  any  way  complicated  by  the 
presence  of  any  number  of  other  vapors  and  gases.     The  evapo- 
ration goes  on  until  the  space  is  filled  with  the  saturated  vapor 
of  the  liquid  in  question,  and  only  then  is  equilibrium  reached. 
The  vapor  will  then  have  all  the  properties  given  numerically 
in  its  vapor  table  opposite  the  existing  temperature. 

The  reason  for  calling  vaporization  as  first  considered  a  limit- 
ing case  of  what  is  generally  known  as  evaporation  should  now 
be  evident.  The  apparatus  used  in  explanation  was  so  arranged 
that  the  space  available  automatically  increased  as  saturated 
vapor  became  available  to  fill  it.  This  was  done  for  simplicity 
and  because  of  the  close  resemblance  to  the  process  taking  place 
in  the  steam  boiler,  from  which  the  vapor  is  withdrawn  as 
rapidly  as  it  is  generated. 

Note  that  the  final  conditions  are  the  same  in  either  case.  A 
certain  space  is  filled  with  saturated  vapor  of  a  given  material, 
and  what  is  true  of  that  vapor  in  one  case  is  true  in  the  other. 

When  a  space  is  thus  filled  with  the  saturated  vapor  of  a 


VAPORS 


117 


material,  it  is  said  to  be  saturated  with  that  vapor  or  with  respect 
to  that  vapor.  Because  of  a  peculiar  construction  of  this  ex- 
pression an  incorrect  idea  has  become  fixed  in  engineering 
language.  It  is  usual  to  speak  of  air  saturated  with  water  vapor, 
whereas  the  real  meaning  is  that  a  space  occupied  by  air  is  also 
occupied  by  saturated  water  vapor. 

(f)  Dalton's  law  is  sometimes  called  the  Law  of  Partial  Pres- 
sures. From  the  previous  statement  of  this  law  it  is  evident 
(i)  that  when  several  gases  and  vapors  occupy  a  space  in  common, 
each  behaves  as  though  the  others  were  absent,  and  (2)  the  pressures 
upon  the  walls  enclosing  the  space,  or  at  any  point  within  the  space, 
must  be  the  sum  of  the  pressures  exerted  by  all  the  constituents  of 
the  mixture.  This  pressure  is  called  the  total  pressure  of  the 
mixture,  while  the  pressures  due  to  each  of  the  constituents  are 
called  partial  pressures. 

If  each  constituent  may  be  considered  as  obeying  the  laws  of 
ideal  gases,  the  same  is  true  of  the  mixture.  The  pressure  in  the 
vessel,  then,  would  be  the  total  pressure,  the  volume  would  be 
that  occupied  by  the  mixture,  and  the  temperature  would  be 
that  of  the  mixture,  which  temperature  must  be  the  same  for  all 
constituents. 

When  some  of  the  constituents  of  such  a  mixture  are  satu- 
rated vapors,  the  perfect  gas  laws  cannot  ordinarily  be  used  if 
great  accuracy  is  desired.  When,  however,  the  quantity  of 
such  vapors  is  small  as  compared  with  that  of  the  gases  present, 
the  error  resulting  from  the  use  of  the  gas  laws  is  small,  and  for 
the  sake  of  simplicity  those  laws  are  generally  used  and  the  error 
is  neglected. 

73.  Boiling.  Heat  is  often  added  to  a  liquid  at  such  a  rate 
and  in  such  a  way  that  the  temperature  of  one  part  becomes 
higher  than  the  temperature  of  adjacent  parts;  that  is,  local 
heating  takes  place.  This  is  the  result  when  the  local  addition 
of  heat  exceeds  the  rate  of  heat  conduction  through  the  material. 
Such  heating  raises  the  temperature  locally  to  that  of  vaporiza- 
tion corresponding  to  the  pressure,  after  which  further  addi- 
tion of  heat  would  cause  local  vaporization;  that  is,  a  small 
amount  of  the  liquid  inclosed  within  the  rest  would  be  converted 
into  vapor  and  appear  as  a  bubble. 

The  pressure  at  any  point  within  a  liquid  at  rest  must  be  that 


Il8  HEAT-POWER  ENGINEERING 

due  to  the  static  head  of  the  liquid  above  that  point  plus  the 
pressure  due  to  any  material  resting  upon  the  surface.  Therefore, 
the  bubble  of  vapor  would  be  formed  under  that  pressure  and, 
during  formation,  would  have  to  displace  the  column,  or 
"  piston,"  of  water  above  it  against  that  pressure. 

The  bubble,  being  less  dense  than  the  surrounding  liquid, 
would  rise,  but  if  the  temperature  of  the  liquid  encountered  was 
lower  than  its  own  it  might  entirely  condense  before  reaching 
the  surface.  This  process  continued  long  enough  would  bring 
all  the  liquid  approximately  to  the  same  temperature,  after  which 
the  vapor  bubbles  could  travel  upward  through  the  liquid  and 
escape  as  vapor  from  the  surface. 

Liquid  is  said  to  be  in  a  state  of  ebullition  or  to  be  boiling 
when  it  is  in  such  a  state  that  bubbles  of  vapor  formed  within 
its  mass  pass  up  and  out  through  its  surface. 

From  what  has  preceded  it  can  be  seen  that  this  process  will 
occur  when  the  body  of  water  is  at  such  a  temperature  that  the 
pressure  of  its  saturated  vapor  is  equal  to  that  upon  its  surface. 
This  is  sometimes  given  as  a  definition  of  boiling  temperature. 

74.  Temperature-Entropy  Changes  of  Vapors,  (a)  All  the 
processes  described  in  connection  with  the  formation  of  vapor 
are  thermodynamically  reversible;  hence  for  vapors,  just  as  was 
done  for  gases  in  Section  38  (a),  dE  may  be  substituted  for  APdV 
in  the  general  Eq.  (53)  defining  an  infinitesimal  entropy  change. 
Then  for  such  a  change  in  a  unit  weight  of  vapor  the  expression 
becomes 

,  ,       dS  +  dl  +  dE 

d*  =  ~yr-      -,      .....      (104) 

or 


and  for  a  finite  change 


These  expressions  may  be  used  for  determining  the  entropy 
changes  for  unit  weight  of  any  vapor  when  undergoing  any 
reversible  processes. 

(b)  The  reversible  temperature-entropy  changes  occurring 
during  the  vaporization  of  water  at  several  different  pressures 
are  shown  graphically  in  the  T0-diagram  given  in  Fig.  33. 


VAPORS 


119 


During  the  heating  of  the  liquid  at  constant  pressure  the 
specific  heat  Cp,  or  heat  required  per  pound  per  degree,  may  be 
either  variable  or  constant.  The  equation  for  the  lines  ab, 
abi,  abz,  etc.,  for  the  entropy  change  experienced  by  the  liquid, 


u 

S 


S 


7 


byt- 


150  Lbs 


30  Lbs 


0  0:2          0.1         0.0          0.8          1.0          1.2          1.1         1.6          1.8 

.Entropy 
Fig-  33-  —  T<£-Diagram  for  Water  and  Water  Vapor. 

called  briefly  the  entropy  of  the  liquid,  must  be  the  same  as 
Eq.  (61)  and  is  /**  c  dT 


or 


A0,  = 


(108) 


This  last  equation  can  be_used  even  if  the  specific  heat  is  not 
a  constant,  by  interpreting  Cp  as  the  mean  value  over  the  given 
temperature  range. 

(c)  The  process  of  vaporization  is  a  constant-temperature  or 
isothermal  one;  here,  following  Eq.  (65),  the  entropy  change 
experienced  by  the  material  during  vaporization,  called  briefly 
the  entropy  of  vaporization,  is  evidently 


(109) 


— f»  rp  rf     • 

1  V  J-  v 

where  Tv  is  the  temperature  of  vaporization. 

(d)  During  superheating  of  the  vapor  at  constant  pressure 
the  specific  heat  may  be  either  variable  or  constant,  and,  parallel- 
ing Eq.  (61),  the  entropy  change,  called  briefly  entropy  of  super- 
heating, is  rT*  C  dT 

A0/>  =    /      -r=fH,        (IIQ) 

jTv  1 

*  It  is  usually  more  convenient  to  usejpgio  instead  of  loge.  Since  loge  = 
2.302  logw, Eq.  (108)  maybe  written  A<&  =  Cp  X  2.302  logw  (Tt/Ti).  The  other 
logarithmic  equations  which  are  to  follow  may  be  similarly  transformed 


I20  HEAT-POWER  ENGINEERING 


=  C,loge        =  Cp  log*      vr 

./   U  -I   V 

v/here  Cp  is  the  mean  specific  heat,  D  is  the  temperature  in- 
crease above  the  saturation  temperature,  Tv,  and  T,  =  Tv  +  D. 
(e)  Summing  up  these  results  gives  the  total  entropy  change 
experienced  by  the  material  when  transformed  at  constant 
pressure  from  liquid  at  datum  temperature  to  superheated 
vapor  at  temperature  (/,  -f  D).  This,  which  is  briefly  called 
the  total  entropy  of  superheated  vapor,  is 

A0.  =  A0j  +  A0V  +  A0/>  .....     (ill) 


Then  ^-r     Sp+jr+J       *&     •     •     ("2) 

=  Cp  log,  =r  +  T=-  4 


f 

•*  t> 

in  which  T0  is  the  datum  temperature,  Tv  is  the  temperature  of 
saturation,  and  T,(  =  Tv  +  D)  is  that  of  the  superheated  steam 
when  the  amount  of  superheat  is  D  degrees. 

(f)  If  vaporization  ceases  before  the  entire  pound  of  material 
has  been  vaporized,  only  a  part,  xr,  of  the  total  latent  heat  of 
vaporization,  r,  will  have  been  added.  The  entropy  change 
experienced  by  the  material  in  coming  to  the  condition  of  wet 
saturated  vapor  with  quality  x  would  then  be 

.....     (113) 


(114) 


• 

When  x  becomes  unity,  —  that  is,  when  vaporization  is  just 
complete,  —  there  is  dry  saturated  vapor,  and  this  equation 
becomes 

A0aa  =  A0i  +  A0V    .     .     ..    .     .     .     (115) 


(116) 


The  points  e,  e\,  e^,  etc.,  in  Fig.  33,  show  the  entropy  change 
for  different  pressures  as  determined  by  Eq.  (114)  when  x  =  0.75. 
Obviously  the  distances  be,  btfi,  etc.,  must  be  0.75  of  the  dis- 
tances be,  bid,  etc.  This  diagram  then  furnishes  a  means  of 
determining  quality  in  a  manner  similar  to  that  used  in  the  case 
of  the  saturation  curve,  Fig.  32,  but  is  not  subject  to  the  ap- 
proximation there  necessary. 


VAPORS 


121 


75.  Continuity  of  the  Liquid  and  Gaseous  States,  (a)  It  has 
been  stated,  in  Chapter  IV,  that  no  real  gases  obey  exactly  the 
laws  of  ideal  ones,  but  that  it  may  be  assumed  without  great 
error  that  those  real  gases  which  are  farthest  removed  from  the 
conditions  of  liquefaction  do  obey  these  laws.  This  assumption, 
however,  is  not  justified  at 
very  low  temperatures  or 
very  high  pressures. 

The  study  of  materials  in 
the  liquid  and  gaseous  spates 
shows  clearly  that  these 
states  are  in  the  nature 
of  limiting  conditions  to 
gradual  physical  changes. 
This  may  be  presented  by 
means  of  Fig.  34.  It  should 
be  clearly  understood  how- 
ever that  this  figure  is 
qualitatively  but  not  quanti- 
tatively correct ;  that  is,  it  is 
not  drawn  to  scale,  nor  does 
it  exactly  represent  the  be- 
havior of  any  real  material. 
It  does,  however,  show  the  specific  volumes 

nature  of  the  changes  under     Fig.  34.—  Isothermals  of  Material  in  Liquid, 
consideration  for  all  known  Vaporous  and  Gaseous  States, 

materials. 

(b)  The  diagram  is  for  unit  weight  of  material  on  pressure- 
volume  coordinates,  and  each  of  the  heavy  lines  is  an  isothermal. 
Starting  with  the  lowest  line  of  the  series,  the  point  a  represents 
the  volume  occupied  by  unit  weight  of  liquid  at  temperature  T 
and  at  the  pressure  shown.  If  the  pressure  is  decreased  while 
the  temperature  is  maintained  constant,  the  volume  of  the 
liquid  will  increase  until  the  point  b  is  reached.*  At  this  point 
the  pressure,  volume,  and  temperature  are  such  that  any  further 
change  can  only  be  a  progressive  vaporization  at  constant  pres- 
sure, as  shown  by  line  be  (since  the  temperature  is  constant)  with 
increase  of  volume  from  b  to  c\  that  is,  the  material  is  at  the 


*  The  increase  of  volume  has  been  much  magnified  in  the  figure  to  emphasize 
the  phenomenon. 


HEAT-POWER  ENGINEERING 

point  of  vaporization  for  temperature  T.  At  c  the  material  has 
become  fully  vaporized,  and  hence  is  dry  saturated  vapor.  A 
further  decrease  of  pressure  at  constant  temperature  will  cause 
it  to  become  superheated  and  to  behave  somewhat  like  an  ideal 
gas.  The  volume  will  then  increase  almost  inversely  with  the 
pressure,  bringing  the  material  to  the  conditions  d  along  the 
curve  cd. 

Starting  from  alf  with  the  material  in  liquid  form  at  a  tem- 
perature Ti  >  2",  a  similar  process  carries  the  material  iso ther- 
mally to  di.  The  same  statements  can  be  made  for  all  other 
starting  points  at  different  temperatures  up  to  some  such  value 
as  r3,  when  the  process  will  be  that  shown  by  the  curve  a3Ms. 
In  this  case  the  points  63  and  c3  have  become  coincident,  the 
liquid,  if  it  is  such,  having  the  same  volume  at  pressure  P&3  as 
does  its  vapor. 

At  higher  temperatures,  such  as  T4  and  T5,  the  material  begins 
as  a  gas  and  the  isothermals  become  more  and  more  nearly 
rectangular  hyperbolas  (PV  =  const),  as  they  are  drawn  for 
higher  and  higher  temperatures. 

Reversing  the  process,  a  gaseous  material  compressed  iso- 
thermally  from  d$  conditions  will  remain  gaseous  no  matter  how 
high  the  pressure  is  carried.  A  gaseous  material  compressed 
iso  thermally  from  d\  will,  however,  begin  to  condense  at  c\  and 
will  continue  to  liquefy  with  further  compression  until  it  all 
becomes  liquid  at  b\. 

(c)  If  d$  is  chosen  as  the  point  to  begin  isothermal  compression, 
it  is  obvious  that  the  material  after  passing  63  must  be  on  the 
boundary  between  the  liquid  and  gaseous  states;  that  is,  the 
pressure,  volume,  and  temperature  conditions  for  the  two  states 
are  the  same  and  the  material  may  be  considered  a  liquid  or  a 
gas,  or  both. 

The  conditions  at  63  are  called  critical  conditions,  that  is, 
critical  volume,  critical  pressure,  and  critical  temperature.  The 
critical  temperature  of  gaseous  material  is  usually  defined  as  the 
temperature  above  which  liquefaction  is  impossible  by  any 
increase  of  pressure.  The  truth  of  this  definition  is  evident  from 
the  diagram;  no  isothermal  of  higher  temperature  than  a3W3 
could  cross  the  latter  and  so  enter  the  liquid  region. 

(d)  In  the  figure  the  hatched  area  with  the  lines  running 
upward  from  left  to  right  represents  the  region  in  which  the 


VAPORS 


123 


material  must  be  liquid.  That  is,  when  any  point  representing 
the  pressure  and  volume  of  the  substance  falls  within  this  region, 
the  material  must  be  in  the  liquid  state.  Similarly,  the  part 
hatched  downward  from  left  to  right  represents  the  region  of 
superheated  vapor,  and  that  crosshatched  in  both  directions 
represents  the  region  of  liquid  mixed  with  its  saturated  vapor. 

The  part  not  hatched  represents  the  region  in  which  the 
material  cannot  be  liquefied  by  change  of  pressure.  This  is 
now  commonly  called  the  region  of  the  gaseous  state.  A  gas 
may  then  be  defined  as  a  material  above  the  critical  temperature, 
and  a  vapor  as  material  which,  while  resembling  a  gas,  is  below 
the  critical  temperature. 

It  must  not  be  inferred  that  material  above  its  critical  tem- 
perature sensibly  obeys  the  laws  of  ideal  gases.  It  must  be  far 
removed  on  the  temperature  scale  before  this  occurs.  The 
isothermal  T5  shows  this. 

Note  in  the  figure  that  the  curve  bse  is  the  saturation  curve,  a 
part  of  which  was  drawn  for  water  vapor  in  Fig.  32. 

(e)  This  diagram,  Fig.  34,  is  useful  for  determining  the  be- 
havior of  material  when   subjected   to  volume,    pressure,  and 
temperature  changes.     Material  in  the  gas  state,  as  at  /  for  in- 
stance, can  be  liquefied  by  lowering  temperature  and  decreasing 
volume  while  the  pressure  is  maintained  constant,  as  along  the 
line  fg.     Or  it  can  be  brought  to  the  condition  of  wet  vapor  by 
lowering  pressure,  volume,  and  temperature  according  to  some 
curve  fh.     Similarly,  increasing  the  temperature  and  pressure  of 
a  superheated   vapor  at  constant  volume   (line  kl)   results  in 
carrying  it  into  the  gas  field. 

(f)  At  the  critical  temperature  the  latent  heat  of  vaporiza- 
tion, r,  becomes  zero;  that  is,  no  internal  and  no  external  work 
of  measurable  magnitude  is  done,  as  the  material  passes  from 
just  above  to  just  below  the  point  &3  on  the  isothermal  TV     In- 
spection of  the  Steam  Tables  in  the  Appendix  will  show  the  way 
in  which  the  latent  heat  of  vaporization  of  water  vapor  gradually 
decreases  from  large  values  at  low  temperatures  to  a  value  of 
zero  at  the  critical  temperature. 

76.  Van  der  Waals'  Equation  for  Real  Gases,  (a)  Obviously 
any  gas  is  really  only  a  very  attenuated  liquid,  differing  in  its 
properties  from  the  liquid  because  its  molecules  are  much  farther 


124  HEAT-POWER  ENGINEERING 

apart,  and  possibly  of  simpler  structure.  If  this  is  true,  it  ought 
to  be  possible  to  write  laws  of  condition  which  would  fit  the 
same  material  in  either  the  liquid  or  the  gaseous  form.  Several 
attempts  have  been  made  to  do  this,  and  one  in  particular  is  of 
great  interest.  It  is  due  to  Van  der  Waals  and  was  developed 
by  modifying  Boyle's  law  to  take  account  of  two  assumed  facts. 
These  are: 

(1)  The  space  filled  by  a  gas  is  partly  occupied  by  the  mole- 
cules of  that  gas,  and  it  is  only  the  space  between  the  molecules 
which  obeys  Boyle's  law. 

(2)  In  no  real  gas  are  the  molecules  far  enough  apart  to  be 
absolutely  independent  of  one  another;  certain  intermolecular 
forces  still  exist.     These  decrease  the  total  volume  occupied  or 
make  the  gas  behave  as  though  subjected  to  a  pressure  greater 
than  the  real  external  pressure. 

The  law  in  mathematical  form  is 

+  £)  (V  -  b)  =  Constant, 
or 


in  which  a  and  b  are  constants,  differing  with  the  kind  of  gas. 
(b)    This  equation  can  be  rearranged  to  read 


a  cubic  equation  in  terms  of  the  specific  volume  V.  Then  for  a 
given  temperature  and  pressure  there  must  be  three  values  of  V 
which  satisfy  the  equation. 

If  the  curves  obtained  by  substituting  in  the  equation  are 
drawn  for  constant  temperatures,  they  resemble  the  lines  abed, 
etc.,  in  Fig.  34,  except  that  the  horizontal  lines  be,  etc.,  are  re- 
placed by  the  dotted  curves  shown.  If  the  equation  is  really 
true,  the  process  of  vaporization  must  be  more  complicated  than 
at  first  appears.  The  fact  that  the  phenomena  corresponding 
to  part  of  the  curve  from  b  downward  and  from  c  upward  can 
be  realized  experimentally  gives  evidence  in  support  of  this  law. 
The  condition  of  the  material  thus  carried  into  the  dotted 
position  of  the  curve  is,  however,  very  unstable,  and  the  sub- 


VAPORS  125 

stance  suddenly  assumes  the  condition  shown  by  the  horizontal 
line  if  disturbed. 

(c)  The  critical  point  may  now  be  said  to  be  the  point  at 
which  all  three  roots  of  the  equation  coincide  or  at  which  one-  is 
real  and  two  are  imaginary. 

(d)  The  equation  of  Van  der  Waals,  though  better  than  that 
of  Boyle,  does  not  [fully  express  the  truth.     If  it  did;  it  would 
hold  for  material  in  the  solid  as  well  as  in  the  liquid  state.     It 
really  recognizes  no  such  condition  as  solid.     If  it  did,  its  graph, 
continued  far  enough  back  in  the  direction  dcba,  would  show 
another  jog  similar  to  but  shorter  than  cb,  representing  the  con- 
stant-pressure, constant- temperature  change  from  liquid  to  solid. 
This  it  does  not  do,  and  hence  it  is  imperfect. 

(e)  The  phenomenon  of  zero  volume  at  absolute  zero  tem- 
perature can   now  be  explained.      According  to  the  simplest 
kinetic  theory  of  gases,  the  temperature  is  supposed  to  be  a 
measure  of  the  translational  energy  of  the  molecules,  and  the 
pressure  is  the  result  of  the  bombardment  of  containing  walls  by 
the  rapidly  moving  molecules. 

Assuming,  with  Van  der  Waals,  that  the  volume  to  which  the 
ideal  laws  refer  is  not  the  total  volume  occupied  by  the  gas,  but 
equals  that  volume  corrected  for  the  volume  of  the  molecules 
present,  the  limiting  case  of  the  ideal  laws  is  easily  explained. 
When  absolute  zero  of  temperature  is  reached  the  molecules  of  a 
gas  must  be  assumed  to  be  devoid  of  translational  motion  and 
in  such  positions  that  the  volume  referred  to  above  has  become 
zero.  Then  as  the  molecules  at  rest  could  not  bombard  sur- 
rounding surfaces  the  pressure  would  also  be  zero. 

This  equation  of  Van  der  Waals  is  in  general  only  of  theoretical 
interest  to  the  engineer.  Seldom  does  the  accuracy  required  in 
engineering  calculations  warrant  the  use  of  such  refinement.  It 
is  introduced  here  only  to  give  a  possible  simple  explanation, 
though  an  incomplete  one,  of  what  otherwise  seems  very  in- 
definite, and  to  furnish  a  more  complete  view  of  the  continuity 
of  the  liquid  and  gaseous  states. 


CHAPTER   X. 

PROPERTIES    OF    STEAM. 

77.  Steam  or  Water  Vapor.  (a)  All  that  has  just  been 
said  about  the  formation  and  the  properties  of  vapors  in  general 
applies,  of  course,  to  the  case  of  water  vapor  or  steam. 

This  vapor  is  usually  generated  in  a  boiler  in  which  the  pres- 
sure is  maintained  substantially  constant  by  the  withdrawal  of 
some  of  the  steam  as  rapidly  as  more  vapor  is  generated.  This 
withdrawal  occurs  ordinarily  through  the  steam  pipe,  at  other 
times  through  the  safety  valve.  The  water  when  pumped  into 
the  boiler  is  under  the  pressure  existing  in  that  vessel.  Thus 
the  application  of  heat  causes  the  temperature  of  the  liquid 
to  rise  under  constant-pressure  conditions.  This  increase  of 
course  ceases  when  the  temperature  of  vaporization,  correspond- 
ing to  the  pressure,  is  reached.  Since  the  heat  is  added  at  con- 
stant pressure,  q  would  be  computed  from  Eq.  (94),  using  the 
mean  specific  heat  at  constant  pressure  for  Cp. 

(b)  The  further  addition  of  heat  to  this  water  causes  the 
formation  of  vapor,  or  steam.  Associated  with  this  process  there 
is  great  increase  in  volume  and  the  absorption  of  large  amounts 
of  heat.  In  discussing  the  general  case,  in  connection  with 
Fig-  30,  it  was  considered  that  the  external  latent  heat  expended 
in  connection  with  the  volume-increase  was  utilized  in  lifting  a 
weight,  thus  doing  work  in  overcoming  the  action  of  gravity. 
In  the  case  under  consideration,  when  steam  is  supplied  to  a 
piston  engine,  the  external  latent  heat  is  expended  in  displacing 
the  piston  against  resistance,  thus  doing  external  work  equal  to 
APu  per  pound  of  material  and  making  available  increased 
volume  of  steam  space  in  the  cylinder  as  rapidly  as  the  vapor  is 
generated.  It  is  true  that  engines  of  this  type  ordinarily  take 
steam  intermittently  from  the  boiler,  hence  the  steam  pressure 
within  that  vessel  would  fluctuate  slightly  on  this  account,  even 
if  other  causes  of  fluctuation  could  be  eliminated.  In  such  cases 
the  mean  pressure  is  the  one  commonly  used. 

126 


PROPERTIES  OF  STEAM 


I27 


It  is  not  only  true  in  the  case  of  the  piston  engine  but  also  in 
all  other  cases,  that  the  withdrawal  of  steam  from  the  boiler  is 
accompanied  by  the  doing  of  external  work,  equal  to  APu  per 
pound  of  material,  although  just  how  this  energy  is  expended  is 
not  always  clear  to  the  beginner. 

The  rest  of  the  heat  utilized  in  the  process  of  vaporization  is 
the  "  internal  latent  heat,"  p,  expended  in  causing  the  molecular 
rearrangement  accompanying  the  change  from  water  to  steam. 

(c)  In  many  instances  a  portion  of  the-  steam  pipe  is  modified 
in  form  and  subjected  to  heat  in  such  manner  that  it  becomes 
what  is  termed  a  "  Superheater,"  in  which  the  steam  becomes 
superheated  by  the  reception  of  more  heat,  as  it  passes  through, 
on  its  way  to  the  engine  or  other  device  which  is  being  supplied. 
During  this  superheating  the  steam  is  under  constant  pressure, 
hence  in  using  Eq.  (102)  to  determine  the  heat  added  the  mean 
specific  heat  at  constant  pressure  Cp  should  be  introduced. 

78.  Sources  of  Data.  The  different  related  properties  of  dry 
saturated  steam  are  tabulated  in  Steam  Tables  such  as  that 
given  in  the  Appendix.  Some  of  the  properties  are  determined 
directly  by  experiment  and  others  are  derived  quantities  which 
are  found  by  computations  involving  the  experimentally  de- 
termined data. 

Many  different  Steam  Tables  have  appeared,  and  all  except 
the  most  recent  ones  were  based  on  Regnault's  experiments, 
published  in  1847.  These  older  tables,  while  thus  based  on  the 
same  data,  depart  somewhat  from  one  another  in  the  values 
tabulated,  the  disagreement  arising  from  'differences  in  inter- 
preting the  data  and  in  choosing  values  of  Joule's  equivalent, 
absolute  zero,  specific  heat  of  liquid,  etc. 

In  spite  of  their  differences  and  errors,  these  steam  tables  are 
still  sufficiently  accurate  for  most  engineering  calculations;  and 
ordinarily  the  results  of  investigation  which  involved  their  use 
may  be  compared  with  those  based  on  the  later  tables,  without 
introducing  serious  errors. 

The  recent  rapid  increase  in  the  use  of  superheated  steam  has 
led  to  many  attempts  to  determine  accurately  the  different 
values  of  the  specific  heats  of  this  material  under  various  con- 
ditions. This  has  revived  interest  in  the  properties  of  saturated 
steam,  with  the  result  that  in  1909  new  and  more  accurate  Steam 


I28  HEAT-POWER  ENGINEERING 

Tables  appeared  in  book-form,  one  by  Peabody,  and  another  by 
Marks  and  Davis.  Both  books,  besides  giving  tables  for  the 
properties  of  dry  saturated  steam,  contain  elaborate  tables  giving 
the  entropy  and  other  properties  of  superheated  steam,  and  other 
auxiliary  tables,  together  with  certain  charts  which  are  useful  to 
the  engineer. 

For  the  mechanical  equivalent  of  I  B.t.u.,  Peabody  uses  778 
foot-pounds  and  M.  &  D.  use  777.52.  For  the  absolute  zero  the 
former  uses  491.5°  F.  below  freezing;  the  latter  491.64.  Peabody 
uses  for  the  B.t.u.  the  heat  required  to  raise  one  pound  of  water 
from  62°  to  63°  F.;  whereas  M.  &  D.  use  the  "mean  B.t.u." 
defined  in  Section  3.*  The  values  chosen  for  the  specific  heats 
of  water  also  vary  slightly.  However,  the  differences  mentioned 
are  so  small  as  to  be  negligible  for  engineering  purposes. 

The  discussion  of  how  tables  may  be  made  will  now  be  taken  up 
very  briefly.  For  a  more  thorough  treatment  and  for  references 
to  the  sources  of  data  the  student  is  referred  to  the  books  just 
mentioned. f 

79.  Properties  of  Dry  Saturated  Steam.  The  properties 
given  in  the  Steam  Table  in  the  Appendix  are  the  corresponding 
values  of  (a)  Pressure  and  Temperature;  (b)  Heat  of  the  Liquid; 
(c)  Total  Heat  of  Steam;  (d)  Latent  Heat  of  Vaporization;  (e) 
External  Latent  Heat;  (f)  Internal  Latent  Heat;  (g)  Entropies 
of  Water,  Vaporization,  and  Total;  and  (h)  Specific  Volumes. 

The  properties  are  tabulated  for  one  pound  of  material,  the 
pressures  are  in  pounds  per  square  inch  absolute,  and  the  heat 
quantities  and  entropies  (excepting  those  for  vaporization)  are 
measured  above  32°  F. 

Temperatures  and  Pressures. 

(a)  It  has  been  seen  that  saturated  vapor  has  a  definite  tem- 
perature corresponding  to  each  pressure  at  which  the  vaporiza- 
tion occurs.  The  variation  of  temperature  with  pressure  of 
water  vapor  has  been  determined  experimentally  and  is  shown 
graphically  in  Fig.  35,  to  two  different  pressure  scales.  It  is 
important  to  note  the  shape  of  this  curve,  especially  the  rapid  rise 

*  The  mean  B.t.u.  is  about  g$s  larger  than  that  measured  at  62°. 
t  Also  see  Trans.  A.  S.  M.  E.,  Vols.  29  to  33,  for  papers-  discussions,  and  refer- 
ences to  sources. 


PROPERTIES  OF  STEAM 


129 


of  pressure,  or  increase  in  the  slope  -^  with  elevation  of  tem- 
perature in  the  upper  region.     The   TP  relations  can  also  be 


100    200    300    400    600    600    700 

Temperatures  Deg.Eahr. 
Fig.  35-  —  PT  Relations  for  Steam. 

expressed  algebraically  by  formulas*  which  are  rather  compli- 
cated.    These  need  not  be  given  here,  however. 

Heat  of  Liquid  (g). 

(b)  The  heat  of  the  liquid  is  the  amount  added  to  water  at 
32  degrees  in  order  to  bring  it  to  the  temperature  of  vaporiza- 
tion. Its  amount  is  computed  by  using  Eq.  (92)  and  integrating 
between  the  temperatures  of  freezing  and  of  vaporization,  thus: 


=    ftvCpdt  =    CT' 

t/32  «/492 


(119) 


where  Cp  is  the  constant-pressure  specific  heat  of  the  liquid, 
which  in  the  case  of  water  varies  with  the  temperature.  The 
progressive  values  of  Cp  have  been  found  by  several  experimenters 
with  results  that  are  not  absolutely  in  accord.  The  curve  in 
Fig.  36  represents  an  interpolation  between  the  several  data. 

The  right  member  of  Eq.  (119)  will  be  recognized  as  the  ex- 
pression for  the  area  below  the  Cp  curve,  and  lying  between  the 
ordinates  at  32  degrees  and  /„.  This  area  can  be  found  by 
planimeter  or  other  method  of  integration. 

*See  "The  Pressure-Temperature  Relations  of  Saturated  Steam,"  by  Prof. 
Lionel  .S.  Marks.  Trans.  A.  S.  M.  E.,  Vol.  33. 


130 


HEAT-POWER  ENGINEERING 


If  Cp  is  the  Mean  Specific  Heat  for  the  temperature  range 
d  =  (tv  —  32),  between  limits  32  degrees  and  tv,  then 

g.  =  Cp  (t  -  32)  =  Cp  X  d (120) 

"Cp  is  obviously  the  mean  height  of  the  part  of  the  Cp-curve 
lying  between  the  temperature  limits  under  consideration. 


Ul 

1.16 
1.11 

1.12 
1.10 
1.08 
1.06 
1.01 

1.02 
1.01 
1.00 
.99 

y 

f 

/ 

Water 

/ 

/ 

/ 

7 

/ 

/ 

/ 

/ 

V 

jr 

*v 

^ 

' 

^^_ 

r^r^1^ 

0  32       100  200          300  100          500 

Temperatures  Deg.  Fahr. 


600 


700 


Fig-  36.  —  Progressive  Values  of  Specific  Heat,  Cp,  of  Water. 

Hereafter  the  instantaneous,  or  the  progressive,  values  of  Cp 
(that  is,  those  corresponding  to  one  degree  rise  at  different  tem- 
peratures) will  be  called  the  progressive  specific  heats  to  dis- 
tinguish them  from  the  mean  values. 

For  many  purposes,  especially  at  low  temperature,  it  is 
sufficiently  accurate  to  assume  Cp  =  I,  then  q  =  (/  —  32).  In 
computing  the  values  of  q  for  the  steam  tables,  however,  it  is 
necessary  to  employ  the  greatest  accuracy. 

In  Fig.  31^  the  curve  a&3  shows  approximately  how  q  varies 
with  /„.  If  Cp  is  taken  as  unity,  this  curve  becomes  a  straight 
line. 

Total  Heat  of  Steam  (X). 

(c)  This  is  the  amount  of  heat  required  to  raise  one  pound  of 
water  from  32  degrees  to  the  temperature  of  vaporization,  then 
to  separate  the  constituent  particles  during  the  formation  of 


PROPERTIES  OF  STEAM  131 

steam,  and  to  do  the  external  work  accompanying  the  increase  in 
volume. 

The  values  of  X  have  been  determined  for  a  number  of  pressures 
by  various  experimenters.  By  plotting  the  most  trustworthy 
data  on  cross-section  paper,  with  X  and  temperature  as  coordi- 
nates, Dr.  H.  N.  Davis  obtained  a  curve  which  is  generally 
regarded  as  giving  the  most  reliable  values  of  this  quantity. 
The  portion  of  the  curve  lying  between  212  degrees  and  400 
degrees  is  represented  by  the  equation 

X  -  1150.3  +  0.3745  (/,-  212)  -  0.00055  (*•-  2I2)2.     (121) 

Regnault's  formula  for  total  heat,  which  was  generally  em- 
ployed before  1909,  is  accurate  enough  for  ordinary  engineering 
purposes  and  is  much  simpler  than  Davis'.  It  is 

X  =  1091.7  +  0.305  (/„-  32).       ...     (122) 

Note  that  this  quantity  increases  with  the  temperature,  but  at 
a  very  slow  rate.  This  is  shown  in  Fig.  31,  by  the  abscissas  ot 
points  c,  ci,  €2,  etc.  The  higher  the  pressure  the  less  rapid  is 
the  rate  of  increase. 

Latent  Heat  of  Vaporization  (r). 

(d)  Having  obtained  the  total  heat  X  and  the  heat  of  the 
liquid  q,  the  latent  heat  of  vaporization  may  be  found  from 

r  =  X  -  q (123) 

If  the  specific  heat  of  water  is  taken  as  unity,  q  =  (tv  —  32)  ; 
and  if  this  is  subtracted  from  Eq.  (122),  Regnault's  approxi- 
mate equation  for  the  latent  heat  of  vaporization  is  obtained. 
This  is 

r  =  1091.7  —  0.695  (k  —  32) (I24) 

In  Fig.  31,  the  values  of  r  for  different  temperatures  and  pres- 
sures are  shown  by  the  distances  be,  b^c^  bsC3,  etc.  The  latent 
heat  decreases  with  rise  in  temperature,  and  becomes  zero  at  the 
critical  temperature.  At  atmospheric  pressure  r  is  970,*  and 
this  figure  should  be  remembered,  as  it  is  used  frequently  in 
engineering  computations. 

*  The  old  value  is  966. 


132  HEAT-POWER  ENGINEERING 

The  External  Latent  Heat  (AE).' 

(e)   The  external  latent  heat  AE  expended  in  displacing  the 
surrounding  media  can  be  computed  from  the  equation 

.     .     .     (125) 


in  which  A  =  --$>  p  is  the  pressure  in  pounds  per  square  inch, 

778 

P  is  the  pressure  in  pounds  per  square  foot,  and  u  is  the  increase 
in  volume  during  vaporization.  How  u  may  be  determined  will 
be  explained  in  (h)  of  this  section.  The  value  of  APu  is  rela- 
tively small  and  varies  from  about  61  B.t.u.  at  one  pound 
pressure  to  about  85  B.t.u.  at  400  pounds. 

The  Internal  Latent  Heat  (p). 

(f)  The  internal  latent  heat  expended  in  producing  the  molec- 
ular rearrangement  may  be  obtained  by  subtracting  the  external 
latent  heat  from  the  total.     Thus 

p  =  r  -APu  ........     (126) 

Entropies  (A0). 

(g)  The   values   tabulated    are    per    pound   of   steam.     The 
entropy  of  the  liquid  may  be  found  from 


As  the  heat  of  the  liquid,  Cp  I  dT,  is  measured  above  the  freez- 

ing point  of  water,  it  follows  that  the  corresponding  entropy 
must  also  be  calculated  above  the  same  datum,  that  is,  492°  F. 
absolute.  The  integration  of  Eq.  (127)  gives  for  the  entropy  of 
water, 

.....     (128) 


in  which  Tv  is  the  saturation  temperature  for  the  pressure  under 
consideration  and  Cp  is  the  mean  specific  heat  of  water  for  the 
temperature  range  from  32  degrees  to  /„,  as  found  from  Fig.  36 
in  the  manner  described  in  Section  79  (b). 

The  entropy  of  vaporization   (A0B)   may  be  found  from  Eq. 


PROPERTIES  OF  STEAM 


(109)  by  substituting  the  values  of    Tv  and  r  corresponding  to 
the  pressure  under  consideration. 

The  total  entropy  (A0sa)  of  one  pound  of  dry  saturated  steam 
above  32  degrees  is  A<£8a  = 


Specific  Volume  (V). 

(h)  This  is  the  number  of  cubic  feet  occupied  by  one  pound  of 
steam.  It  varies  with  the  pressure  and  is  equal  to  the  sum  of 
the  original  volume  of  the  pound  of  water  (0.017  =t  cu.  ft.)* 
and  u,  the  increase  in  volume  during  vaporization.  Thus, 

V  =  u  +  0.017  ±cu.  ft (129) 

The  value  of  u  can  be  obtained  from  what  is  known  as  Clapey- 
ron's equation, 

JL    778 
"  r." 
dt 


cu.  ft. 


(130) 


fdP\   . 

(tr 


Here  (-77)   is   the  slope   of   the  pressure-temperature  curve 


see  Fig.  35,  in  which -^ 


.*r\ 


and   may  be  found  either 


144  dTl' 

graphically  or  mathematically. 

The  following  is  a  rather  crude  way  of  deriving  Clapeyron's 
equation:  On  a  PV-diagram,   Fig.  37,  starting  at  A  with  one 


Fig.  37- 


Fig.  38- 


pound  of  water  already  at  the  boiling  point  (pressure  P,  and 
absolute  temperature  T),  let  sufficient  heat  be  added  to  cause 
complete  vaporization,  the  increase  in  volume  being  u]  then  let 
there  be  a  slight  drop  in  pressure  dP,  next  let  there  be  a  de- 

*  The  volume  of  a  pound  of  water  varies  from  0.016  to  0.018  cubic  feet  within 
the  ordinary  range  of  temperatures. 


HEAT-POWER  ENGINEERING 

crease  in  volume  at  the  uniform  pressure  (P  —  dP)  until  all  of 
the  steam  is  condensed  to  water  at  the  corresponding  boiling 
point;  and  finally  bring  the  water  up  to  its  original  temperature 
to  complete  the  cycle.  Evidently  the  work  done,  as  shown  by 
the  area  of  the  figure,  is  u  .  dP  foot-pounds,  which  in  B.t.u.  is 


AE= 


On  the  T0-diagram,  Fig.  38,  let  the  same  cycle  be  shown. 
Starting  at  A  with  water  at  the  boiling  temperature  T,  let  heat, 
r,  be  added  to  vaporize  the  water.  This  is  accompanied  by  an 

increase  in  entropy  of  amount  -^.     Next  let  there  be  a  temper- 

ature drop  dT  (corresponding  to  dP),  and  then  let  the  steam 
be  condensed  at  constant  temperature  (T  —  dT),  corresponding 
to  (P  —  dP),  to  water  at  the  boiling  point.  Upon  returning  the 
water  to  its  original  condition  the  cycle  is  completed  and  the 
work  done  in  B.t.u.,  as  shown  by  the  area  surrounded,  is 


(b) 


Evidently  equations  (a)  and  (b)  both  represent  the  same 
amount  of  work.  Hence,  —  ^-  =(-^]dT,  solving  which  for  u 
results  in  Clapeyron's  equation. 

The  Specific  Density. 

(i)  The  specific  density  or  weight  of  one  cubic  foot  of  steam  is 
equal  to  (~J  .  As  this  is  merely  the  reciprocal  of  the  specific 
volume,  it  is  not  given  in  the  Steam  Table  in  the  Appendix. 

Properties  of  Steam  at  High  Pressures. 

(j)  Above  250  pounds  per  square  inch  (400°  F.)  the  properties 
of  steam  have  not  been  determined  with  great  accuracy,  so  that 
the  values  given  in  the  tables  above  this  pressure  are  not  very 
trustworthy.  More  accurate  values  are,  however,  not  available 
at  present. 

It  will  be  noticed  that  the  latent  heat  decreases  as  the  tem- 
perature increases  until  it  becomes  zero  at  the  critical  tempera- 


PROPERTIES  OF  STEAM  135 

ture  of  about  706°  F.,*  corresponding  to  a  pressure  of  about 
3200  pounds  per  square  inch. 

80.  Properties  of  Superheated  Steam,  (a)  Specific  Heat  at 
Constant  Pressure.  In  dealing  with  superheated  steam  the 
engineer  ordinarily  uses  only  the  specific  heat  at  constant  pres- 
sure. For  ideal  gases  it  has  been  shown  that  Cp  is  independent 
of  temperature  and  pressure,  and  that  it  is  sensibly  so  for  most 
real  gases  within  ordinary  ranges.  For  superheated  steam, 
however,  it  cannot  be  considered  constant  at  the  temperatures 
used  in  engineering,  for  the  material  is  always  far  below  the 
critical  conditions,  and  though  approximating  the  behavior  of 
a  gas  it  varies  greatly  from  the  laws  for  perfect  gases. 

Several  experimenters  have  recently  determined  values  of  Cp 
for  steam  over  wide  temperature  and  pressure  ranges.  Among 
these  the  results  of  Knoblauch  and  Jakob  are  generally  con- 
sidered the  most  trustworthy,  and  were  used  both  by  Peabody 


Temperatures  Deg.  Fahr. 
Figt  29.  —  Progressive  Values  of  Specific  Heat  Cp  of  Superheated  Steam. 

and  by  Marks  and  Davis  in  computing  their  tables.  M.  and  D. 
made  slight  modifications  to  better  coordinate  the  Knoblauch 
and  Jakob  results  with  those  of  other  authoritative  researches. 
The  variation  of  the  progressive  specific  heat  Cp  with  tempera- 
ture, for  different  constant  pressures,  is  shown  in  Fig.  39.  Be- 
*  Prof.  L.  S.  Marks.  Trans.  A.  S.  M.  E.,  Vol.  33. 


136 


HEAT-POWER  ENGINEERING 


cause  of  the  comparatively  rapid  variation  from  degree  to  degree, 
the  progressive  values  can  be  used  in  ordinary  arithmetical  cal- 
culations for  a  temperature  rise  of  one  degree  only. 

For  greater  ranges,  the  mean  specific  heat  must  be  used,  and 
this  can  be  found  from  Fig.  39  in  a  manner  similar  to  that 
described  in  79  (b)  for  the  mean  specific  heat  of  water.  As  most 
problems  connected  with  superheated  steam  involve  a  tem- 
perature range  D  measured  from  the  saturation  temperature,  Tv, 
for  the  pressure  under  consideration,  it  is  convenient  to  have 


s 


.40 


0  50  100  150  200  250  300 

Temperatures  above  Saturation  °F. 

Fig.  40. — Variation  of  Mean  Specific  Heat  Cp  of  Superheated  Steam. 


curves  giving  the  constant-pressure  mean  specific  heat  Cp 
measured  above  saturation  temperature.  The  values  plotted  in 
Fig.  40  may  be  used  pending  the  appearance  of  more  accurate 
ones. 

Superheat. 

(b)   The  heat  added  during  superheating  D  degrees  is  evidently 

A<2/>=  CPI>,    .' (131). 

where  D  =  (rsup  -  T,). 


PROPERTIES  OF  STEAM  137 

The  Total  Heat  of  Superheated  Steam  (Aft). 

(c)  This  quantity  is  the  total  heat  above  32°  F.  per  pound  of 
steam  which  is  superheated   D  degrees  above  saturation  tem- 
perature.    Representing  this  by  Aft,  it  is  given  by  the  equation 

Aft  =  X  +  Aft)  =  X  +  Cp£>  .....     (132) 

The  Entropy  of  Superheated  Steam. 

(d)  The  entropy  above  saturation  temperature  Tv  is  A0z>  and 
is  given  by  Eq.  (no). 

The  total  entropy  of  steam  superheated  D  degrees  is  obtained 
from  Eq.  (in)  or  (112). 

Specific  Volume  of  Superheated  Steam  .(V.). 

(e)  The  volume  of  one  pound  of  superheated  steam  may  be 
computed  from  Linde's  empirical  formula 


T 

V,  =  0.5962-  -  (i  +  0.0014  p) 


(133) 


in  which  V,  is  in  cubic  feet,  T  is  the  absolute  temperature  of  the 
superheated  steam  in  Fahr.  degrees,  and  p  is  in  pounds  per 
square  inch. 

A  simpler  formula  and  one  that  is  nearly  as  accurate  is  given 
by  Tumlirz.     It  is,  for  p  in  pounds  per  square  inch, 

V8  =  0.5962  j  -  0.256,  .....     (134) 
and  for  P  in  pounds  per  square  foot, 

V,  =  85.86-^-0.256  ......     (135) 

81.  Temperature-Entropy    Chart    for    Water    and    Steam. 

(a)  Diagrams  drawn  with  T<£-coordinates  are  of  great  con- 
venience in  solving  many  problems  involving  the  use  of  steam. 
Especially  are  they  valuable  when  reversible  adiabatic  changes 
and  associated  heat  changes  are  considered,  for  with  these  co- 
ordinates, the  former  are  straight  lines  and  the  latter  are  areas. 

The  T0-chart  may  be  constructed  for  any  weight  of  working 
substance;  but  it  is  customary  and  more  convenient  to  base  it  on 


138 


HEAT-POWER  ENGINEERING 


unit  weight.  The  chart  in  Plate  I  in  the  Appendix  is  for  one 
pound  and  the  entropies  are  measured  above  32°  F.  to  corre- 
spond with  the  steam  tables. 

The  value  of  a  T<£-chart  is  greatly  increased  by  the  addition 
of  certain  lines  of  reference  which  aid  in  reading  directly  many 
of  the  quantities  sought.  The  construction  of  these  lines  will 
now  be  considered. 

Water  Curve,  or  W-curve. 

(b)  Eq.  (128)  expresses  algebraically  the  law  by  which  the 
entropy  of  the  liquid  varies  with  the  absolute  temperature. 

From  it  can  be  obtained  simul- 
taneous values  of  Tv  and  A0*  and 
these  can  be  used  in  plotting 
points  on  a  J\£-chart  to  show 
graphically  the  relation  between 
the  two  variables.  The  Water 
Curve  is  the  locus  of  these  points 
and  therefore  is  the  graph  of  Eq. 
(128).  In  Fig.  41,  AB  is  the 
W-curve. 

If  a  steam  table  is  available  the 
values  of  A<£j  and  tv  used  in  plot- 
ting the  W-curve  can  be  obtained 


Fig.  41.— T0-Diagram  for  Water 
Vapor. 

directly  from  it. 

In  general  the  heat  used  during  a  reversible  process  to  pro- 
duce a  7>-change  is 


jf 


The  right  side  of  this  equation  is  of  the  form  iy  dx,  which  is  the 

mathematical  expression  for  an  area,  and  which  here  represents 
the  heat  quantities  A@.  As  dx  in  this  case  is  d<l>,  which  is 
measured  above  32°  F.,  the  heat  represented  by  the  area  must  be 
that  above  32°  F.  also;  and  as  y  =  T  (abs)  these  areas  must 
extend  down  to  absolute  zero  of  temperature,  that  is,  to  the  0-axis. 
From  this  it  is  seen  that  the  heat  of  the  liquid  above  32°  F.  is 
represented  by  the  area  under  the  W-curve,  extending  to  the 
T  and  <t>  axes,  such  as  area  OABfa,  in  Fig.  41. 


PROPERTIES  OF  STEAM  139 

The  W-curve  has  little  curvature.  If  it  is  considered  straight 
(involving  small  error  for  ordinary  ranges) ,  it  is  seen  that  the  area 
under  that  line  is  the  product  of  A<£*  by  the  mean  temperature 

-;  that  is, 

r  +  49; 


Substituting  g  =  (T  —  492),  which  would  be  its  value  when 
C  =  1,  gives  the  following  approximate  equation  for  the  entropy 
of  water: 


which   is   convenient   for  rough   computations,  as  it  does   not 
involve  the  use  of  tables. 

Saturation  Curve,  or  S-curve. 

(c)  The  entropy  of  dry  saturated  steam  is,  from  Eq.  (115), 
A080  =  A</>j  +  A<£w  =  A<£j  +  r/Tj  the  values  of  all  quantities  in 
which  are  given  in  the  steam  tables.  In  Fig.  41,  the  abscissa 
TB  is  A<fo  for  the  temperature  T\  so  if  BC  is  made  equal  to 
the  corresponding  value  of  A<£v,  the  point  C  must  fall  on  the 
Saturation  Curve.  The  locus  of  a  series  of  points  plotted  in 
this  manner  for  different  temperatures  is  the  S-curve.  Evi- 
dently this  curve  is  the  graph  of  Eq.  (115). 

The  area  of  the  rectangle  below  the  line  BC  is 


and  hence  is  the  latent  heat  of  vaporization.  Then  the  total 
heat  of  the  steam,  X,  is  given  by  the  area  below  ABC,  since  this 
latter  represents  r  +  q. 

Constant-Quality  Curves,  or  X-curves. 

(d)    The  equation  of  these  curves  is  A</>x  =  A<£j  -f-  ^  ,  in  which 

x  is  constant  for  each  curve  and  is  equal  to  the  quality  under  con- 
sideration. Taking  various  corresponding  values  of  r  and  T  from 

the  steam  tables,  the  quantities  f  ^H  may  be  computed,  and  add- 


140 


HEAT-POWER  ENGINEERING 


ing  these  to  the  values  of  A<fo  for  the  corresponding  tempera- 
tures gives  Ac^c.     In  Fig.  42,  TB  as  before  equals  A$j  and  BD  is 


Fig.  42.  —  T0-Diagram  Showing  X-Curves. 


laid  off  equal  to     ^;),  thus  locating  the  state  point  at  D  for 

the  temperature  T.  The  locus  of  points  similarly  plotted  for 
different  temperatures  is  the  Curve  of  Constant  Quality.  A 
series  of  such  curves  is  shown  in  Fig.  42  (a). 

BD  =         it    follows    that 


Since 


BC  =  -^    and 

1 


-L>C 


x. 


This  relation  suggests  another  and  simpler  method  of  plotting 
points  to  determine  the  X-curve:  In  the  figure  draw  the  hori- 
zontal intercepts  BC,  B\C\,  etc.,  between  the  W-curve  and  the 
S-curve,  and  on  them  locate  the  points  D,  Dlt  etc.,  in  such 

73  D        7?  D 

positions  that  -=r~  =     *    *  =  etc.  =  x.     Then  the  locus  of  these 
£>L       JJiCi 

points,  D,  DI,  etc.,  is  the  curve  desired. 

The  heat  used  in  vaporizing  x  parts  of  a  pound  of  steam  at 
temperature  T  is  shown  by  the  area  below  BD,  Fig.  42,  since 

this  area  =  f  yr)  X  T  =  xr.     The  total  heat  in  the  mixture  of 

steam  and  water  is  given  by  the  area  below  ABD,  for  this  area 
equals  xr  +  g. 

Constant-Volume  Curves,  or  V-curves. 

(e)   At  any  temperature   T,  Fig.  43,  the  change  in  entropy 
from  B  to  C  during  complete  vaporization  is  accompanied  by 
an  increase,  equal  to  u,  in  the  volume  of  the  working  substance. 
If  at  the  same  temperature  only  part  of  the  unit  weight  - 
occupying  the  volume  V—  is  in  the  vaporous  form,  it  is  evident 


PROPERTIES  OF  STEAM 


that  the  quality  of  the  steam  must  be  x  = 


By 


maintaining  V  constant  in  this  equation  and  substituting  values 
of  u  corresponding  to  different  temperatures,  the  way  x  varies 
with  T  during  an  isovolumic  change  can  be  determined.  Then 
the  V-curve  can  be  plotted  either  by  using  the  quality  or  by 
making 

BD  _  (V  -  0.017)          ffiA       (V  -  0.017) 
T> /~i  >          T?  /-i  >  etc. 

J3C  u  -OiCi  u\ 

The  same  curve  can  be  obtained  by  graphical  construction  in 
the  following  manner:  In  Fig.  43  lay  off  a  V-axis  opposite  to 
the  T-axis,  thus  forming  a  V0-quadrant 
in  which  volumes  are  laid  off  downward. 
Directly  below  B  drop  an  ordinate  ab 
for  the  corresponding  volume  of  the 
material.  This  is  the  volume  of  the 
water  at  temperature  71,  or  0.017  ± 
cubic  feet.  Directly  below  C  lay  off 
the  volume  corresponding  to  that  point, 
thus  locating  c.  The  value  in  this  case 
is  V,  the  specific  volume  of  the  steam. 
Then  the  straight  line  be  joining  these 
points  shows  the  uniform  increase  of  the 
volume  and  entropy  during  the  process 
of  vaporization  of  one  pound  of  working 
substance  at  the  temperature  T.  In 
like  manner  similar  V$-lines,  such  as 
62£2,  etc,  can  be  drawn  for  other 


T^Diagram  Show. 

temperatures  of  vaporization.     If  any        ing  Method  of  Constructing 
isovolumic  line  V  is  then  drawn,  it  inter-        v-Curves. 
sects  be,  biCi,  etc,  at  points  v,  v\,  v%,  etc, 

whence  projecting  upward  to  the  corresponding  isothermals  de- 
termines points  D,  A,  etc,  on  the  V-curve  with  T<f>  coordinates. 
In  the  case  shown  in  this  figure,  V  =  Vi,  so  vi  would  coincide 
with  ci,  and  DI  with  C\. 

Constant-Heat  Curves,  or  Q-curves. 

(f)  For  wet  saturated  steam  the  equation  of  this  curve  is 
xr  +  q=  const.  =  A().  For  any  given  A<2,  the  variation  of  x 
with  T  can  be  found  by  substituting  the  values  of  r  and  q  corre- 


142 


HEAT-POWER  ENGINEERING 


spending  to  the  different  temperatures  used.'    Several  of  these 
curves  for  different  values  of  AQ  are  shown  in  Fig.  44.     Referring 

to  curve  E  EiEz,  etc.,  it  is  evident 
that  the  areas  under  A  BE,  ABiEi, 
etc.,  must  all  be  the  same  and 
equal  to  the  value  of  AQ  for  that 
curve.  Note  particularly  that 
these  curves  represent  xr  +  q  and 
not  xp  +  2- 

(g)  For  superheated  steam  the 
Q-curve  is  found  in  the  following 
manner :  For  any  assumed  pressure 
p,  the  corresponding  values  of  X 
and  Tv  are  obtained  from  the 
Steam  Tables.  Then  if  AQ  is  the 


Fig.  44.  —  T0-Diagram  Showing 
P-Curves,  and  Q-Curves. 


onstant-heat  quantity  under  consideration,  the  temperature  rise 

during  superheating  at  pressure  p  is  D  =  = — .      The  ordin- 

Cp 

ates  of  the  Q-curve  are  T  —  Tv  -\-  D,  and  the  abscissas   are 


Cp  loge 


(138) 


in  which   Tv,  D  and  Cp  are  known  and  A$sa  can  be   obtained 
from  the  tables. 

A  difficulty  arises  in  selecting  the  proper  value  of  Cp,  because 
the  mean  specific  heat  is  dependent  on  D,  which  is  initially 
unknown.  Hence  it  is  necessary  to  adopt  the  "  cut  and  try 
method."  That  is,  a  trial_value  of  Cp  is  assumed  and  D  is  com- 
puted; then  the  value  of  Cp  corresponding  to  the  pressure  and 
to  D  is  obtained  from  the  curves,  and  if  it  is  the  same  as  the 
trial  value  the  assumption  was  correct;  but  if  there  is  much 
difference,  a  new  value  must  be  assumed  and  the  process  must 
be  repeated. 


Constant-Pressure  Curves,  or  P-curves. 

(h)  For  saturated  steam  the  P-curves  are  isothermals;  for 
superheated  steam  they  are  not.  In  the  latter  case,  the  rela- 
tion between  A<£.  and  (Tv  +  D),  the  temperature  after  super- 
heating, is  given  by  the  Eq.  (138).  If  this  is  solved  for  any 


PROPERTIES  OF  STEAM  143 

fixed  pressure,  Tv  and  A</>sa  become  constants,  and  the  variables 
are  A<£a  and  (Tv  +  D)  with  related  values  of  Cp.  Correspond- 
ing values  of  these  variables  would  be  used  in  plotting  the 
P-curves,  several  of  which  are  shown  in  Fig.  44. 

The  temperature  of  saturation  Tv  for  any  pressure  can  be 
found  by  using  these  curves,  for  it  is  given  by  the  ordinate  of 
the  point  of  intersection  between  the  corresponding  P-curve  and 
the  Saturation  Curve. 


The  Final  T<|>-chart. 

(i)  The  final  T$-chart,  Plate  I  in  the  Appendix,*  contains  all 
the  curves  described  in  this  section,  and  to  it  has  been  added  a 
scale  for  the  absolute  pressures  corresponding  to  the  tempera- 
tures of  saturation. 

For  a  point  anywhere  on  it  in  the  Saturation  Region  there  can 
be  read  directly  the  corresponding  values  of  Tv,  A<j>x,  x,  V,  p, 
and  AQ.  The  latter  is  given  either  by  the  Q-curve  or  by  area; 
the  values  of  q  and  xr  are  given  by  areas;  and  the  pressures  can 
be  read  either  on  the  scale  at  the  left  or  by  extending  the  isother- 
mal to  intersect  the  S-curve,  thus  finding  the  corresponding 
P-curve  in  the  superheated  region. 

If  the  point  is  on  the  W-curve,  Tv,  A<f>i,  and  p  can  be  read 
directly,  while  q  is  given  by  the  area  below  the  curve. 

For  a  point  on  the  saturation  line  the  values  of  Tv,  A$,a,  X,  V, 
and  p  can  be  read  at  once. 

If  the  point  is  in  the  Region  of  Superheat,  T,  A<£s,  A$8a,  p,  and 
A<2  can  be  read  directly;  the  increase  in  temperature  above 
saturation  is  D  =  T  —  Tv\  the  B.t.u.  superheat,  AQD,  is  given 
either  by  an  area,  or  by  (AQ  —  X) ;  and  the  entropy  of  super- 
heat A<t>D  is  (A08  —  A<£ao). 

If  any  expansion  line  is  drawn  on  the  chart,  all  of  the  above- 
mentioned  quantities  can  be  read  for  each  point  on  the  line.  If 
the  lines  inclosing  a  cycle  are  drawn,  the  work  done  per  cycle  is 
of  course  given  by  the  area  surrounded. 

It  is  important  to  note  that  the  quantities  given  by  the 
Q-curves  are  values  of  (xr  +  q),  not  (xp  +  q),  and  contain  the 
external  work  of  vaporization  (xAPu). 

*  A  larger  and  more  accurate  l>-chart  is  contained  in  Peabody's  Steam  and 
Entropy  Tables,  published  by  Wiley  &  Sons. 


144 


HEAT-POWER  ENGINEERING 


82.  The  Mollier  Chart,  or  Q0-Chart.  (a)  This  chart,  Fig.  45,  is 
constructed  with  (^-coordinates.  On  it  are  drawn  lines  for 
constant  pressure  (P-curves);  for  constant  qualities  (X-curves) 

1400 1300       1200       1100       1QOO       900       800 


1.5 


1400 


1300 


1200  1100  1000  900 

Fig.  45.  —  Mollier  or  Heat-Entropy  Chart. 

for  wet  steam;  and  for  constant  temperatures  (T-curves)  for 
superheated  steam.  The  boundary  line  between  the  Regions  of 
Saturation  and  Superheat  is  the  Saturation  Line  (S-curve). 

(b)  For   wet    steam    Aft  =  xr  +  g   and    A<£x  =  A<£z  +  xA(f>v. 
If  the  pressure  is  constant,  x,  Aft,  and  A$x  are  the  only  variables. 
Then  by  substituting  different  qualities,  related  values  of  Aft 
and  A<£x  may  be  found  and  these  can  be  used  in  plotting  the 
P-curve.     A  series  of  such  curves  is  shown  in  the  figure. 

(c)  Lines  joining  points  of  the  same  quality  on  the  different 
P-curves  constitute  the  X-curves. 

(d)  For  superheated  steam 

Ti          I         7~\ 

Aft  =  X  +  CPD  and  A<£8  =  A<£aa  +  Cp  \oge 


Tv 

If  the  pressure  is  constant,  Aft,  A<£8,  and  (Tv  -f-  D)  are  the 
variables.  By  substituting  different  values  of  D  in  these 
equations,  the  Aft  and  A<£a  coordinates  of  points  on  the  P-curve 
may  be  found. 

(e)  Lines  through  points  of  like  temperatures  are  the  T-curves, 
and  as  drawn  these  give  the  temperatures  in  degrees  Fahr.,  not 
absolute.     Lines  through  points  representing  the  same  increase 
of  temperatures  above  saturation  constitute  D-curves. 

(f)  The  final  Q<£-chart  is  given  in  Plate  II  in  the  Appendix. 
This  has  all  the  curves  just  discussed,  except  the  D-curves. 


PROPERTIES  OF  STEAM 


145 


For  any  point  on  it  there  can  be  read  at  once  the  values  of 
A0,  p,  and  x  (or  /). 

82A.   The  Ellenwood  QV-Chart.     (a)  In  this  chart,  Fig. 
the  coordinates  are  total  heat  (A@)  and  volumes  (xV  or  V.)  per 
pound.     Oblique    lines    are    given 
respectively  for  constant  values  of 
pressure  (p),  quality  (#),  superheat 
(D)  and  entropy  (</>). 

(b)  For  any  state  point  on  the 
chart   one   may  read  directly  the 
values  of  p,  x  or  D,  xV  or  Va,  A0 
and  AQ.     From  the  intersection  of 
the  pressure  line  with  the  q-curve 
the  corresponding  value  of  q  may 
be  read  and  from  the  temperature 
scale  along  this  curve  the  vaporiza- 
tion temperature  /„  may  be  deter- 
mined.    Hence  in  addition  to  the 
values  given  by  the  Mollier  Chart, 
this  one  gives  volumes  per  pound, 

g,  and  /„,  which  greatly  increases        Fig.  45a.- Ellenwood  Chart, 
its  field  of  application. 

(c)  Plate  IV  in  the  Appendix  is  a  small  two-page  Ellenwood 
Chart  *  in  which  the  volume  scale  changes  progressively,  which 
accounts  for  the  scolloped  appearance  of  the  curves. 

826.  The  Constant-Pressure  External-Work  Chart  (Ellen- 
wood),  (a)  In  Plate  III  (Appendix)*  the  abscissas  are  volumes 
and  the  ordinates  give  the  external  work  of  formation  of  steam, 
under  constant  pressure,  from  one  pound  of  water  at  32°  F. 
For  any  point  on  the  chart  one  may  read  the  external  work,  the 
volume  per  pound,  the  pressure,  and  the  quality  (or  superheat). 

(b)  The  T0,  Mollier,  and  Ellenwood  Charts  give  total  heat. 
To  obtain  the  intrinsic  heat  necessitates  subtracting  the  ex- 
ternal work  (computed  or  obtained  from  Plate  III). 

*  Redrawn  to  greatly  reduce  scale  from  "Steam  Charts  "  by  F.  O.  Ellenwood, 
published  by  John  Wiley  &  Sons,  Inc. 


CHAPTER   XI. 

VOLUME    CHANGES    OF    VAPORS. 

83.  General.     Saturated  and  superheated  vapors,  like  gases, 
may  be  made  to  change  volume  in  many  different  ways,  but  the 
general  study  of  such  transformations  may  be  based  on  a  few 
simple  cases.     The  laws  governing  these  changes  are  different 
from  those  for  similar  gas  processes,  and  this  is  because  of  the 
different  properties  of  the  materials  dealt  with.      For  conven- 
ience the  order  of  treatment  in  this  chapter  is  different  from 
that  of  Chapter  V. 

84.  Constant-Pressure  and  Isothermal  Volume -Changes  for 
Saturated    Vapors,     (a)    Fixing    the    pressure    of    a    saturated 
vapor,  wet  or  dry,   fixes  the  temperature;   hence  a  constant- 
pressure  change  of  such  material  must  also  be  a  constant-tem- 
perature, or  isothermal  one. 

The  line  ab  in  the  PV-diagram,  Fig.  46,  and  in  the  T</>-diagram, 
Fig.  47,  is  the  graph  of  an  isobaric  or  isothermal  change  for  dry 
saturated  vapor.  In  Fig.  46,  the  abscissa  of  point  a  represents 
the  volume  of  unit  weight  of  the  liquid  at  the  temperature  of 
vaporization  corresponding  to  the  pressure  PI.  By  the  addi- 
tion of  heat  the  liquid  can  be  vaporized  to  any  desired  extent 
until  finally  it  has  all  become  dry  saturated  vapor.  This  is  an 
expansion  at  constant  pressure  and  at  constant  temperature  and 
is  the  only  isothermal  expansion  possible  with  saturated  vapor. 
It  follows  that  isobaric  and  isothermal  volume  changes  of  satu- 
rated vapors  can  only  occur  during  vaporization  or  condensa- 
tion of  the  material.  This  is  equivalent  to  saying  that  such 
transformations  are  always  accompanied  by  quality  changes. 

Such  volume  changes  cannot  be  carried  beyond  a  quality  of 
100  per  cent,  because  then  the  material  will  all  be  saturated 
steam,  with  the  specific  volume  corresponding  to  the  existing 
pressure,  and  because  further  addition  of  heat  at  constant  pres- 
sure must  increase  the  volume  of  unit  weight  above  the  value  at 
saturation,  hence,  must  superheat  the  vapor. 

146 


VOLUME  CHANGES  OF   VAPORS 


Equation  for   Isobaric  and  Isothermal    Changes  of   Saturated 

Vapors. 

(b)  The  equation  of  such  changes  in  terms  of  P  and  V  must 
be  the  same  as  that  for  the  constant-pressure  change  of  gases; 

that  is, 

P  70  =  p  =  Constant. 

There  is,  however,  a  real  difference  in  the  two  cases.  When 
dealing  with  gases  it  is  possible,  in  imagination  at  least,  to  carry 
the  isobaric  expansion  to  any  desired  volume,  while  in  the  case 


Volume 

Fig.  46.  —  PV-DIagram  for  Vapor. 

of  saturated  vapors  expansion  per  pound  cannot  be  carried  be- 
yond the  specific  volume  corresponding  to  the  existing  pressure 
without  changing  the  nature  of  the  material  and  its  behavior. 

The  volume  occupied  by  one  pound  of  material  depends  on  the 
quality  x,  and  can  be  computed  for  water  and  its  vapor  from 

V  =  0.017  +  xu  =  xV  (approx.). 

This  is  true,  no  matter  what  process  the  material  has  under- 
gone, and  a  similar  equation  can  be  found  for  each  material. 

Heat  Changes  during  Isobaric  or  Isothermal  Changes  of  Satu- 
rated Vapors. 

(c)  If  the  expansion  starts  with  all  the  material  as  liquid  at 
the  temperature  of  vaporization,  that  is,  with  an  initial  vapor 
volume  equal  to  zero,  the  heat  change  is  merely  that  accompany- 


i48 


HEAT-POWER  ENGINEERING 


ing  vaporization,  and  must  equal  the  latent  heat  of  vaporiza- 
tion per  pound  of  material  if  the  condition  of  dry  saturation  is 
reached.  Hence  the  heat  added  is 

AQ  =  r=  (p  +  APu),    .....     (139) 

where  u  is  the  volume  change  represented  by  the  distance  ab 
in  Fig.  46  and  A(?  is  the  area  below  ab  in  Fig.  47.  In  the  case 
of  water  vapor,  the  values  of  all  the  quantities  occurring  in  this 
equation  may  be  obtained  from  the  Steam  Table  given  in  the 
Appendix.* 

If  the  pound  of  material  is  not  completely  vaporized  but  has 
a  quality  equal  to  x,  then 

AQ  =  xr  =  xp  +  xAPu,     ....     (140) 

in  which  xu  is  the  volume  change,  which  is  shown  by  the  distance 
ab'  in  Fig.  46  and  AQ  is  the  area  below  abi  in  Fig.  47. 


Entropy  Change  A  p 

Fig.  47. — T<£-Diagram  for  Vapor. 

If  the  expansion  is  from  quality  xi  to  Xz,  with  corresponding 
volume  change  from  xiu  to  x2u  (not  shown  in  the  figure),  the 
case  is  general,  and  the  change  in  associated  heat  is 

A(?  =  x2r  -  xir 

=  (xz  -  #1)  (P  +  ^4Pw) 

*  For  steam,  u 
Tables. 


(V  —  0.017  ±).  in  which  V  may  be  obtained  from  the  Steam 


VOLUME  CHANGES  OF   VAPORS 


I49 


Work  during  Isobaric   or   Isothermal   Changes    of   Saturated 

Vapors. 

(d)  The  External  Latent  Heat  of  vaporization  is  that  part  of 
the  total  heat  which  does  the  external  work  accompanying  the 
increase  of  volume;  it  must  therefore  be  equivalent  to  the  ex- 
ternal work  done.  Hence  in  vaporizing  to  quality  x,  per  pound 
of  material, 

AE  =  x  •  APu  B.t.u (142) 

and 

778  AE  =  x  •  Pu  ft.-lbs.     .     .     ...     (143) 

This  work  is  shown  in  Fig.  46  by  the  area  below  ab' '.     For  the 
case  in  which  x  =  i.oo,  it  is  the  area  below  ab. 

With  change  of  quality  from  xi  to  x2  the  work  done  is, 

AE  =  fa-  x'i)  APu  B.t.u.      .     .     .     (144) 
and 

778  AE  =  fa-xi)  Pu  ft.-lbs (145) 

85.  Constant-Pressure  Volume  Changes  of  Superheated 
Vapors,  (a)  Starting  from  the  point  b  in  Figs.  46  and  47,  the 
dry  and  saturated  vapor  may  be  made  to  still  further  expand  at 
constant  pressure  to  some  point  c\  by  superheating,  that  is,  by 
raising  the  temperature  above  that  corresponding  to  saturation 
at  that  pressure.  The  further  this  expansion  continues  the 
more  nearly  the  behavior  resembles  that  of  a  gas,  and  there  is 
no  theoretical  limit  to  such  expansion,  as  there  was  in  the  case  of 
the  saturated  vapor. 

Equation  of  Isobaric  Change  of  Superheated  Vapor. 

(b)  The  equation  in  terms  of  P  and  V  must  be  the  same  as 
that  already  developed  for  gases  and  saturated  vapors,  namely, 

p  V°  =  P  =  Constant. 
Heat  Change  during  Isobaric  Changes  of  Superheated  Vapor. 

(c)  As  the  temperature  must  be  raised  at  constant  pressure 
in  order  to  increase  the  volume,  or  lowered  at  constant  pressure 
to  reduce  the  volume,  it  follows  that  a  quantity  of  heat  equal 
to  the  specific  heat  at  constant  pressure,   Cp,  must   be  added 
or  abstracted  per  degree  change.     Then  for  heat  added  above 
saturation 


I5o  HEAT-POWER  ENGINEERING 

or,  using  the  mean  specific  heat  Cp  for  the  temperature  range  D 
measured  from  the  temperature  of  saturation, 

AQD  =  CPD.   '-.-.     .     .     .     ,     (146) 

In  Fig.  47  this  is  shown  by  the  area  below  bci  for  a  case  in  which 
tha  heat  change  is  reversible. 

For  an  isobaric  change  from  superheat  temperature  DI  to  Z>2 


(147) 


This  is  equivalent  to  A<2  =  C'p  (A  -  DI)  =  C'P  (T2  -  Ti),  where 
C'p  is  the  mean  specific  heat  for  the  temperature  range  involved. 
In  Fig.  47  this  heat  change  is  shown  for  reversible  conditions  by 
the  area  below  C\C<L. 

The  foregoing  equations  giving  the  heat  change  are  not 
sufficient  for  use  in  engineering  problems  as  they  generally 
occur.  It  is  usually  not  only  necessary  to  know  the  range  of 
superheat,  but  also  the  volume  change  accompanying  it.  In 
the  case  of  gases,  this  can  be  found  from  the  Law  of  Charles, 
but  superheated  vapors  as  generally  treated  in  engineering  are 
not  far  enough  removed  from  the  condition  of  saturation  to  even 
sensibly  obey  that  law. 

It  is  possible  to  find  this  volume  change  for  superheated 
water  vapor  by  using  the  approximate  equation  of  Tumlirz  pre- 
viously given  as  Eq.  (134).  Writing  this  for  volumes  Vi  and  V2 
and  then  dividing  gives,  for  pressures  in  pounds  per  square  inch, 

Vi  _  T!  -  0.4293  P! 

V2~r2-  0.4293  p*  .....   *   (I4) 

Since  pz  =  pi  during  an  isobaric  change,  this  equation  reduces 
to  the  form 

Vi  _  TI  —  Constant  (       , 

V2  ~  T2  -  Constant'  ' 

in  which  the  constant  has  a  different  value  for  every  pressure. 

The  effect  of  this  corrective  constant  becomes  less  with  in- 
crease of  temperature  or  decrease  of  pressure,  and  there  is  an 
accompanying  closer  approach  of  the  equation  to  that  of  Charles' 
Law  and  a  closer  resemblance  of  the  superheated  vapor  to  an 
ideal  gas. 


VOLUME  CHANGES  OF   VAPORS  151 

Work  during  Isobaric  Changes  of  Superheated  Vapor. 

(d)    During  an  isobaric  change  with  one  pound  of  any  work- 
ing material  the  work  is 

778  AE  =  P  (V2  -  Vi)  ft.-lbs.,      .     ,     .     (150) 

which  was  first  developed  in  the  case  of  gases  as  Eq.  (24).  If,  in 
Fig.  46,  the  expansion  is  from  c\  to  c2,  the  work  done  is  given 
by  the  area  below  c\c^. 

86.   Isothermal-Volume    Changes    of    Superheated    Vapors. 

(a)  These  must  in  a  general  way  resemble  the  isothermal 
changes  of  gases,  since  superheated  vapors  approximate  the 
gaseous  conditions.  The  exact  behavior  of  any  particular  vapor 
under  these  conditions  must,  however,  be  determined  by  experi- 
ment. For  superheated  water  vapor  the  necessary  information 
can  be  obtained  from  the  approximate  equation  of  Tumlirz. 

Equation  of  Isothermal  Change  of  Superheated  Water  Vapor. 

(b)  Rearranging  the  Tumlirz  equation  (134)  and  maintaining 
T  constant  gives  the  following  for  isothermal  changes  for  this 
material,  for  p  in  pounds  per  square  inch, 

pV  +  0.256  p  =  0.5962  T  =  Constant,     .     .     (151) 
and  from  Eq.  (135),  for  P  in  pounds  per  square  foot, 

PV  +  0.256  P  =  85.86  T  =  Constant.       .     .     (152) 
Comparing  this  latter  with   the  Eq.  (14)  for  gases,  namely, 

PV  =  RT, 

it  is  evident  that  it  differs  only  in  the  addition  of  a  second 
term  (0.256  P)  in  the  first  member.  Obviously  the  smaller  the 
numerical  value  of  the  pressure  the  smaller  will  be  this  cor- 
rective factor  and  the  more  nearly  will  the  vapor  obey  the  ideal 
gas  law.  If  Eqs.  (151)  and  (152)  be  divided  by  T,  it  becomes 
apparent  that  the  greater  the  numerical  value  of  T  the  smaller 
will  be  the  effect  of  the  corrective  factor  and  therefore  the  more 
nearly  will  the  material  approach  the  condition  of  an  ideal  gas. 

Work  during  Isothermal  Changes  of  Superheated  Vapor. 

(c)  The  work  done  by  an  expanding  vapor,  as  well  as  gas,  is 
given  in  all  cases  by  the  expression  first  developed  as  Eq.  (41), 

778  AE  =    fV*PdV ft.-lbs. 

i/  Vi 


152 


HEAT-POWER  ENGINEERING 


However,  in  order  to  perform  the  integration  in'  any  case,  it  is 
necessary  to  know  the  relation  between  P  and  F,  and  this  is  a 
matter  for  experimental  determination.  The  relation  given  by 
the  equation  of  Tumlirz,  Eq.  (135),  may  be  used  for  superheated 
water  vapor.  From  this  equation, 

85.86  T 
V  +  0.256' 

which  value  may  be  substituted  in  the  type  integral,  and  the 
integration  performed,  giving  per  pound  of  water  vapor 

dV 


778  AE  =  85.86  T  C 

t/Fi 


V  +  0.256 


=  85.86  riog  ft.-lbs.      (153) 


Eq.  (43b),  for  work  during  isothermal  changes  of  gases,  may  be 
written 

778  AE  = 

Comparing  Eq.  (153)  with^his,  it  again  appears  that  the  higher 
the  temperature  and  the  lower  the  pressure  the  more  nearly  do 
the  equations  developed  for  superheated  water  vapor  approach 
those  for  the  behavior  of  gases,  and  by  analogy  the  same  must 
be  true  of  the  behavior  of  all  superheated  vapors. 

If,  in  Fig.  46,  the  isothermal  expansion  is  from  cz  to  d,  the 
work  is  represented  by  the  area  below  ca/d. 

Heat  Change  during  Isothermal  Changes  of  Superheated  Vapors. 

(d)   Applying  Eq.  (i), 

A<2  =  AS  +  A  I  +  AE, 

to  this  case,  it  is  evident  that  the  term  AS  must  be  zero,  since 
temperature  does  not  change;  but  A/  must  have  some  value 
other  than  zero,  since  the  materials  cannot  be  said  to  even 
sensibly  approach  the  condition  of  ideal  gases.  The  term  AE 
must  also  have  a  value  other  than  zero  if  work  is  to  be  done  by 
or  upon  the  superheated  vapor.  For  any  case  AE  can  be  readily 
found,  but  A/  is  more  difficult  to  evaluate,  and  any  equation  for 
the  value  of  AQ  which  could  be  developed  would  necessarily  be 
a  very  cumbersome  one. 


VOLUME  CHANGES  OF   VAPORS  153 

(e)  Fortunately  the  T<£-diagram  offers  a  simple  means  of  deter- 
mining A<2,  since  this  quantity  is  represented  by  an  area  on  that 
diagram,  when  the  change  is  reversible. 

Assume  for  instance  that  it  is  desired  to  find  the  heat  required 
when  one  pound  of  water  vapor  is  expanded  isothermally  and 
reversibly  from  a  pressure  PI  and  a  temperature  T2  above  satu- 
ration temperature  TVl,  to  a  lower  pressure  P3.  It  is  only 
necessary  to  draw  the  horizontal  line  c2d  in  Fig.  47,  between  the 
two  pressure  lines  and  at  the  desired  temperature,  and  then 
determine  the  area  under  c-id. 

Fig.  47  is  only  a  special  case  of  Plate  I  of  the  Appendix,  and 
in  practice  the  latter  would  be  used. 

(f)  Note  that  the  heat  added  to,  or  subtracted  from,  super- 
heated   steam    isothermally  is    not   equal   to  the  difference   in 
total  heats,  since  the  isothermal  of  superheated  vapors  is  not 
a  constant-pressure  line.     In  the  case  of   reversible  isothermal 
expansion  this  heat  is  equal  to   T  X  A<£,  both  of  which  quan- 
tities can  be  obtained  from  the  Mollier  or  Ellenwood  Charts 
given  in  the  Appendix. 

87.  Adiabatic  Changes  of  Saturated  Vapors,  (a)  With  the 
exception  of  problems  involving  the  flow  of  vapors  in  which  the 
material  is  accelerated  as  a  whole,  the  adiabatic  changes  of  vapors 
which  are  considered  by  the  engineer  are  thermodynamically 
reversible  in  the  ideal  case.  In  the  following  paragraphs  only 
these  reversible  processes  will  be  considered,  leaving  the  more 
complicated  irreversible  processes  for  later  development. 

Since  reversible  adiabatic  changes  are  also  isentropic  ones, 
their  graph  on  the  T0-diagram  must  be  a  vertical  line.  This 
offers  a  very  easy  means  of  studying  these  changes  in  every  case 
where  there  are  sufficient  experimental  data  for  the  drawing  of 
this  diagram. 

(b)  The  diagram  in  Fig.  48  is  developed  from  the  T0-dia- 
gram  for  water  vapor  with  the  lines  of  constant  quality  shown  — 
originally  given  in  Fig.  42  (a)  and  Plate  I.  To  this  have  been 
added  vertical  lines  representing  reversible  adiabatic  expansions 
starting  at  each  20  per  cent  of  quality  at  the  pressure  Pi.  The 
diagram  shows  that  when  the  initial  quality  is  high  (point  a  in 
Fig.  48)  the  quality  of  water  vapor  must  decrease  as  the  expansion 
progresses,  and  when  the  initial  quality  is  low  (point  b)  it  must  in 


154 


HEAT-POWER  ENGINEERING 


crease  during  expansion.     Near  the  middle  of  tlie  diagram,  that 
is,  with  initial  quality  near  50  per  cent,  x  remains  nearly  con- 


60  i>    80*  1005$  Quality 
I 


50*    60* 


80  %  Quafily 


Entropy 
Fig:  48. — T0-Diagram  for  Water  Vapor. 

stant  during  the  entire  expansion.  This  is  not  necessarily  a 
property  of  all  vapors,  as  it  depends  on  the  relation  between  the 
various  heat  quantities  and  is  thus  a  matter  for  experimental 
determination. 

This  is  well  shown  by  considering  the  case  of  Ether   Vapor. 
The  T<£-diagram  for  this  material  is  given  in  Fig'.  49,     As  in  the 


Ether 


20*       40*       60*        80?      100* 


Entropy 

Fig.  49.  —  T0-Diagram  for  Ether  Vapor. 

last  case,  the  constant-quality  lines  and  isentropic  lines  for  every 
20  per  cent  initial  quality  are  drawn.  It  is  evident  from  the 
figure  that  during  reversible  adiabatic  expansion  of  ether  vapor 


VOLUME  CHANGES  OF   VAPORS  155 

the  quality  must  continually  increase,  whatever  its  initial  value 
may  be. 

(c)  At  any  initial  quality  between  o  per  cent  and  100  per  cent 
the  quality  changes  will  be  governed  by  the  relative  quantities  of 
liquid  and  vapor  present,  as  can  be  seen  for  the  case  of  water  by 
referring  to  Fig.  48.     In  this  case  large  quantities  of  liquid  make 
available  so  much  heat  with  decrease  of  pressure  or  temperature 
that  evaporation  (or  "quality  increase")  must  occur  as  expansion 
progresses  ;  large  quantities  of  vapormake  available  so  small  a  quan- 
tity of  heat  by  pressure  drop  alone  that  condensation  must  occur. 

With  initial  qualities  of  about  50  per  cent,  the  two  effects 
approximately  balance  and  the  quality  remains  almost  constant. 

(d)  The  case  of  ether  as  already  shown   is   very  different. 
Referring  to  Fig.  49,  it  is  seen  that  with  expansion  starting  at 
any  quality  between  o  per  cent  and  100  per  cent  the  heat  liber- 
ated due  to  pressure  drop  alone  is  more  than  sufficient  to  do  the 
necessary  external  work,  and  the  expanding  material  must  ab- 
sorb part  of  the  liberated  heat.     When  the  quality  is  less  than 
100  per  cent,  this  is  done  by  vaporization,  with  possible  super- 
heating toward  the  end  of  the  process;  and  when  the  quality 
is  equal  to  or  greater  than  100  per  cent,  superheating  occurs 
throughout  the  expansion. 

Comparison  of  Figs.  48  and  49  shows  that  because  the  heat 
of  the  liquid  varies  much  more  rapidly  and  is  much  greater  in 
quantity  in  the  case  of  ether  vapor,  the  quality  lines  for  that 
vapor  all  slope  in  the  same  direction,  thus  accounting  for  the 
difference  in  phenomena  occurring  during  adiabatic  expansion. 

Equation  of  Reversible  Adiabatic  Changes  of  Saturated  Vapors. 

(e)  Since  these  changes  are  generally  studied  by  means  of  the 
T0-diagram,  the  most  useful  equation  is 

A</>  =  Constant,  or 


This  equation  gives  no  direct  means  of  plotting  the  curves  rep- 
resenting adiabatic  expansion  to  PV-coordinates,  but  may  be 
used  indirectly  for  that  purpose. 

First,  the  quality  at  the  end  of  adiabatic  expansion,  from 
pressure  pi  and  quality  xi  to  pressure  fa,  may  be  computed  by 
solving  for  x%  in  the  following  equation: 

-f  x  A0r)i  =  (A0z  +  x  A<£w)2.    •     •     •     (J54) 


!56  HEAT-POWER  ENGINEERING 

Then,  the  volume  occupied  by  unit  weight  of  the  substance, 
at  the  end  of  the  expansion,  is  found  by  multiplying  the  specific 
volume  by  x2. 

As  already  shown,  the  isentropic  line  corresponding  to  Eq. 
(154)  gives  a  means  of  reading  directly  the  quality  of  the  expand- 
ing material  on  the  T</>,  Mollier,  and  Ellenwood  Charts. 

(f)  For  water  vapor  at  common  operating  pressures  and  with 
initial  quality  between  100  and  70  per  cent,  the  relations  be- 
tween pressure  and  volume  during  adiabatic  expansion  are  given 
approximately,  but  very  accurately,  by  the  equation 

P  F"  =  Constant,  ......     (155) 

in  which  the  value  of  n  is  given  by  the  following  equation, 

«  =  I-o$5  +  o.i  x,       .....     (156) 

where  x  is  the  initial  quality  expressed  as  a  decimal  fraction. 

The  PV  relations  can  also  be  obtained  from  the  Ellenwood 
and  T<£  Charts. 

Work  Done  during  Adiabatic  Changes  of  Saturated  Vapors. 

(g)  Since  all  the  work  done  during  such  an  expansion  must 
be  obtained  at  the  expense  of  intrinsic  heat  energy,  and  since 
no  heat  energy  is  used  for  other  purposes,  it  follows  that  if 
(xr  +  2  —  xAPu)i  =  (xp  +  g)i    represent     the     intrinsic    heat 
energy  before  an  adiabatic  change  and   (xr  +  g  —  xAPu*)2  = 
(xp  +  2)2,   the  intrinsic  heat  energy  after  such  a  change,   the 
External  Work  Done  is 

AE  =  (xr  +  g  -  xAPu)i  -  (xr  +  q  -  xAPu}2  .     (157) 


In  using  this  equation  the  initial  conditions  are  known:  x2  is 
obtained  from  Eq.  154,  and  p2  and  g2  are  found  from  the  Vapor 
Tables  for  pressure  p2. 

(h)  If  the  PV-diagram,  Fig.  50,  be  for  one  pound  of  steam, 
then  when  the  point  b  is  reached  the  heat-energy  (xAPu)i  has 
been  abstracted  from  the  steam  and  absorbed  by  displacing  a 
piston  or  surrounding  media  against  resistance.  Thus  there  re- 
main (xp  +  g)i  heat  units  with  which  to  begin  the  adiabatic  ex- 
pansion. At  point  c,  there  are  (xp  +  q\  heat  units  left  in  the 
steam,  and  the  quantity  (xAPu)2  would  not  appear  unless 
either  by  compression  or  some  equivalent  process  the  volume  of 
the  steam  is  contracted  isobarically  an  amount  X2uz  to  the 
volume  of  the  liquid,  as  shown  at  d, 


VOLUME  CHANGES  OF    VAPORS 


157 


The  area  below  ab  is  (xAPu)i  B.t.u.;   the  area  below  be  shows 
the  work  done,  or  heat  utilized  during  adiabatic  expansion  alone, 


Volumes 
Fig.  50,  —  PV-Diagram. 


Entropy 

Fig.  51. — T0-Diagram. 


and  is  [(#p  +  ff)i  —  (xp  +  q)z]  B.t.u.;  the  area  below  cd  is 
(xAPu)*  B.t.u. 

(i)  On  the  T0-diagram,  Fig.  51,  the  areas  below  lines  such  as 
oab  represent  (xr  +  q)  quantities  which  include  the  external 
latent  heat  of  vaporization.  From  these  quantities  must  be  de- 
ducted the  appropriate  values  of  xAPu*  to  obtain  the  heat  in  the 
steam  during  an  isentropic  process.  (Note  that  in  the  T0-chart, 
Plate  I,  the  xAPu  quantities  are  also  included  in  the  values 
given  by  the  Q-curves.) 

(j)  On  the  Mollier  diagram  and  on  the  Ellenwood  Chart  the 
abscissas  (AQ)  also  include  the  external  work,  and  this  latter  * 
must  be  deducted  when  considering  the  heat  utilized  during 
adiabatic  expansion  alone  (see  (g)  above). 

88.  Adiabatic  Changes  of  Superheated  Vapors,  (a)  These 
changes,  like  those  for  saturated  vapors,  are  best  studied  by 
means  of  the  T0-diagram.  Vertical  lines,  such  as  that  through 
e  in  Fig.  48,  drawn  to  represent  reversible  adiabatic  expansion  or 
superheated  water  vapor,  show  that  as  the  expansion  is  carried 
to  lower  pressures  the  material  approaches  the  saturated  con- 
dition and  may  indeed  attain  a  quality  less  than  unity.  On  the 
other  hand,  similar  lines  on  the  T</>-diagram  for  ether,  Fig.  49, 
show  that  if  such  un  expansion  starts  with  superheated  vapor  the 
superheat  increases  as  the  expansion  continues. 

*  The  constant-pressure  external  work  of  formation  of  steam  from  one  pound  of 
water  can  be  obtained  from  the  External  Work  Chart,  Plate  III,  in  the  Appendix. 


I58  HEAT-POWER  ENGINEERING 

Equation    of    Reversible    Adiabatic    Changes    of    Superheated 

Vapors. 

(b)'  As  in  the  case  of  saturated  vapors,  the  general  equation 
for  reversible  adiabatic  changes  of  superheated  vapor  is 

A<£  =  Constant,   or   (A<£s)i  =  (A</>)2. 

If  the  steam  is  expanded  to  wetness,  the  quality  may  be  found 
by  solving  for  x%  in  the  following  equation  : 

(159) 


can  be  computed  from  Eq.  138,  (A<^)2  and  (A0V)2,  in  the 
case  of  water  vapor,  can  be  obtained  directly  from  the  Steam 
Tables. 

If  the  expansion  takes  place  entirely  in  the  Region  of  Super- 
heat, the  final  temperature  T%  =  (Tv  -f  Z>)2  can  be  found  from 

C9  loge  Tv    T  ^     •        .     .      (160) 


Here  Cp  is  the  mean  specific  heat  for  the  temperature  range 
DZ  =  (T  —  Tv)2  and  TVi  is  the  temperature  of  vaporization  at 
the  terminal  pressure. 

External  Work  Done  during  Adiabatic  Changes  of  Superheated 

Vapors. 

(c)  As  in  other  cases  of  adiabatic  changes,  the  external  work 
done  during  this  reversible  adiabatic  change  is  equal  to  the 
intrinsic  heat  change.  During  a  constant-pressure  change  from 
liquid  at  the  temperature  of  vaporization  to  superheated  vapor, 
the  external  work  per  pound  is 

AEP  =  AP(Va  -  0.017)  B.t.u.,       .     .     .     (161) 

where  V,  is  the  specific  volume  of  the  superheated  steam  from 
Eq.  (134)  ;  hence  the  external  work  done,  if  the  steam  remains  in 
the  superheated  state  throughout  the  isentropic  expansion,  is 

AE.  =    X  +  fJCpdT  -  AEP]    T\  +  fj  CpdT  -  A£pj  (162) 


=  [X  +  CPD  -  AEj!  -  [X  +  C9D  -AEJ,,     ....     (163) 
in  which  A  is  found  from  Eq.  (160) 


VOLUME  CHANGES  OF   VAPORS  159 

If  vapor  initially  superheated  is  expanded  to  wetness  with 
quality  #2,  the  external  work  done  is 

AESX  =  [X  +  "CPD  -  AEJi  -  [xp  +  g]2,   .     .     .     (164) 

in  which  x%  is  found  from  Eq.  (159). 

On  the  PV-diagram  this  work  is  represented  by  the  area  below 
the  expansion  line.  In  using  either  the  T<£,  Mollier,  or  Ellen- 
wood  diagrams,  to  obtain  the  work  done  during  isentropic  ex- 
pansion alone,  it  is  necessary  to  deduct  the  &EP  quantities 
(and  the  APu  quantities  if  entering  the  saturation  region)  from 
the  heat  values  found. 

89.  Constant- Volume  Changes  of  Saturated  Vapors,     (a)    If 
a  saturated  vapor  is  to  change  pressure  at  constant  volume,  there 
must  be  a  quality  change,  because  the  same  weight  of  material 
in  the  form  of  vapor  cannot  occupy  a  given  space  at  two  differ- 
ent temperatures.     During  a  pressure  drop  there  is  a  tendency 
for  saturated  vapor  to  increase  in  volume,  hence  if  the  volume 
is  maintained  constant  there  must  be  a  decrease  of  quality ;  that 
is,  condensation  must  take  place.     The  reverse  is  of  course  true 
for  a  pressure  rise. 

Equation  of  Constant-Volume  Change  of  Saturated  Vapor. 

(b)  As  in  previous  cases,  the  equation  of  a  constant-volume 
change  is,  in  terms  of  pressure  and  volume, 

V  =  Constant. 

Heat  Change  during   Constant-Volume   Change  of    Saturated 

Vapor. 

(c)  It  was  shown  in  Section  70  that  the  quality  of  saturated 
vapor  could  be  found  by  dividing  the  volume  occupied  per  pound 
of  mixed  vapor  and  liquid  by  the  specific  volume  corresponding  to 
the  pressure  existing.     By  using  this  method  the  quality  changes 
which  occur  during  a  constant- volume  change  of  saturated  vapor 
may  be  found,  and  when  the  quality  at  any  pressure  is  known 
the  intrinsic  heat  for  that  state  may  be  determined. 

90.  Constant-Volume     Changes     of     Superheated     Vapors. 
(a)  When  a  superheated  vapor  changes  pressure  at  a  constant 
volume,  there  must  be  a  temperature  change  similar,  but  not 
equal,  to  that  occurring  in  the  case  of  an  ideal  gas  undergoing 


160  HEAT-POWER  ENGINEERING 

the  same  sort  of  change.  The  equation  of  Tumlirz,  Eq.  (134)5 
may  be  used  to  find  the  temperature  of  water  vapor  correspond^ 
ing  to  any  pressure  and  volume,  and  hence  such  changes  (01 
their  equivalents,  if  irreversible)  can  be  plotted  to  PV  or  Ttf 
coordinates. 

Equation  of  Constant- Volume  Changes  of  Superheated  Vapors. 

(b)  As  in  all  other  cases,  the  equation  in  terms  of  PV  coordi- 
nates is 

V  =  Constant. 

Heat  Change  during  Constant-Volume  Change  of  Superheated 

Vapor. 

(c)  Since  the  temperature  and  pressure  can  be  found  for  any 
point   in   a   constant-volume   pressure   change   of   superheated 
vapor,  the  intrinsic  heat  can  also  be  found  for  every  point.     The 
difference  between  the  intrinsic  heats  at  beginning  and  end  of 
the  constant  volume  change  must  be  the  amount  of  heat  added 
to,  or  subtracted  from,  the  steam. 


CHAPTER  XII. 

VAPOR    CYCLES. 

91.  Carnot  Cycle  with  Dry  Saturated  Steam,  (a)  The  Carnot 
cycle  may  be  carried  out  with  a  saturated  vapor  of  any  kind  in 
the  same  apparatus  as  was  assumed  in  Section  49  and  shown 
in  Fig.  17.  For  simplicity  assume  the  cylinder  to  contain  unit 
weight  of  water  at  the  temperature  7\.  Then  the  volume  occu- 
pied by  the  liquid,  inclosed  by  the  cylinder  head,  cylinder  walls, 
and  piston,  will  be  that  of  unit  weight  of  water  at  temperature 
T\  and  corresponding  pressure.  This  is  plotted  as  the  point  a 
on  the  PV-diagram,  in  Fig.  52,  with  volume  greatly  exaggerated. 

If  heat  is  added  to  the  liquid  from  the  hot  body  U  and 
the  piston  is  allowed  to  move  out  at  just  the  proper  rate 
to  maintain  a  constant  pressure  on  the  working  substance, 
vaporization  will  occur  at  constant  pressure  and  therefore  at 
constant  temperature.  The  volume  would  consequently  in- 
crease isothermally,  or  the  process  would  be  an  isothermal  ex- 
pansion. 

When  vaporization  is  complete  the  volume  attained  will  be 
the  specific  volume,  V&,  of  water  vapor  at  temperature  TI  and 
corresponding  pressure.  The  isothermal  expansion  will  then  be 
represented  by  the  constant  pressure  line  ab. 

If  now  the  nonconducting  cylinder  cover  Z  is  applied  and  the 
piston  allowed  to  continue  its  outward  motion,  the  expansion  of 
the  vapor  must  be  adiabatic.  The  actual  shape  of  the  line 
representing  such  expansion  will  be  given  approximately  by 
p  Vn  =  Constant,  and  is  represented  by  the  curve  be,  on  which 
c  is  a  point  where  the  temperature  has  reached  that  of  the  cold 
body,  T2. 

If  now  Z  is  replaced  by  the  cold  body  and  the  piston  is  forced 
inward,  condensation  must  occur,  the  heat  liberated  being  ab- 
sorbed by  the  cold  body.  Condensation,  like  evaporation,  is  a 
change  at  constant  temperature  and  constant  pressure,  and  hence 
is  represented  by  a  horizontal  line  from  c  toward  the  left. 

161 


162 


HEAT-POWER  ENGINEERING 


To  complete  a  Carnot  cycle,  it  is  necessary  to 'stop  the  process 
of  condensation  when  the  volume  has  decreased  to  some  value 
Vd,  so  chosen  that  the  final  adiabatic  compression  will  bring  the 
material  back  to  the  liquid  form  with  conditions  7\,  P0,  and  Va. 


Volumes 
Fig.  52.  — PV-Diagram  for  Carnot  Cycle  with  Dry  Saturated  Water  Vapor  at  &. 

.  (b)  The  T<£-diagram  of  the  cycle  is  drawn  in  Fig.  53,  on  which 
the  water  curve  and  saturation  curve  are  indicated  by  dotted  lines. 
This  diagram  is  lettered  to  correspond  with  Fig.  52.  It  shows 
how  the  quality  of  the  steam  must  decrease  during  the  adiabatic 
expansion  be,  and  how  by  stopping  the  condensation,  or  iso- 
thermal compression,  at  the  proper  point,  d,  it  is  possible  to 
return  the  material  to  the  liquid  condition  at  temperature  T±  by 
adiabatic  compression  da. 

Note  that  the  T<£-diagrams  for  the  Carnot  cycle  for  vapor  and 
gas  are  identical,  but  that  this  is  not  true  for  the  PV-diagrams 
because  of  the  difference  in  the  properties  of  the  materials. 

Work  per  Pound  of  Dry  Saturated  Water  Vapor  Operating  in 

Carnot  Cycle. 

(c)  The  work  done  per  cycle  can  be  obtained  in  several  ways, 
two  of  which  will  be  considered.     They  are  practically  the  same 
as  those  previously  used  for  gas  cycles. 

(d)  The  first  method  is  to  take  the  algebraic  sum  of  the  quan- 
tities of  work  done  during  the  several  processes  of  the  cycle. 


VAPOR  CYCLES 


I63 

D 

(i)  The  work  during  the  isothermal  expansion  equals  —  ^  (Vb  —  Va) 


778 


B.t.u.,  and  (2)  that  during  the  isothermal  compression  similarly 
equals  — |  (Ve  —  Vd)  B.t.u.  (3)  The  work  during  adiabatic  ex- 
pansion must  be,  as  shown  in  Eq.  (158),  the  difference  between 
the  quantities  of  intrinsic  heat  energy  above  32°  F.  at  the  be- 
ginning and  end  of  the  process;  that  is,  (qb  +  p6)  —  (qc  +  xcpc}. 
(4)  Similarly,  the  work  during  adiabatic  compression  is 
Q.a  —  (&  +  Xdpd)-  The  values  of  the  qualities  xc  and  x*  can  be 
found  from  the  constant-entropy  equation  (154)  or  from  either 


a 

Ti 

\b 

$' 

1 
I 

I 

Car 

not 

\£ 
$ 

'9 

\ 

9 

*£/ 
I 
1 

I  d 

T2 

£ 

\" 

c 

Entropy  Changes 
Fig.  S3-  —  T0-Diagram  for  Carnot  Cycle  with  Dry  Saturated  Water  Vapor  at  b. 

of  the  entropy  diagrams;  hence  in  any  problem  all  the  terms  are 
known  and  the  total  work  done  during  the  cycle  equals  the 
algebraic  sum  of  the  four  expressions. 

(e)  The  second  method  and  more  direct  one  is  to  subtract 
from  the  total  heat  supplied  the  total  heat  rejected;  the  differ- 
ence must  be  the  heat  converted  into  work,  and  must  be  rep- 
resented by  the  area  within  the  four  lines  of  the  cycle. 

The  heat  supplied  during  the  isothermal  expansion  is  ft,  the 
latent  heat  of  vaporization  of  the  material  at  the  temperature 
TI.  The  heat  rejected  is  the  part  of  the  latent  heat  liberated 
during  the  partial  condensation  and  is  (xcr^  —  xtfz)  =  r%  (xc  —  x<i), 
in  which  xc  and  Xd  are  determined  from  the  constant-entropy 
equation*  (154)  or  from  either  of  the  entropy  diagrams.  The 

*  Just  as  xc  is  the  quality  at  the  end  of  adiabatic  expansion  be,  so  xd  may  be 
considered  as  the  quality  at  the  end  of  an  adiabatic  expansion  ad.  The  constant- 
entropy  equation  is  applied  to  the  line  be  to  find  xc  and  to  the  line  ad  to  find  x#. 


1  64  HEAT-POWER  ENGINEERING 

external  work  done  must  then  be,  when  the  steam  is  dry  and 
saturated  at  the  beginning  of  expansion, 

AE  =  Aft  -  A(?2  =  n  -  r2  (xe  -  xd)  B.t.u.  .     .     (165) 
and 

778  A£  =  778  [ri  ~  r*  (xc  -  xd)]  ft.-lbs.    ....     (166) 

The  expression  numbered    (165)   is  really  obvious  from  the 
T^-diagram  drawn  in  Fig.  53. 

(f)   From  Fig.  53  it  is  also  seen  that 

AE=  (7\-  r2)A0v   =  (T,-  r2).  .     .     (167) 


The  last  form  is  the  simpler  in  use.     In  it  the  expression 

_  T  \ 
*          -  is  the  efficiency  Efc  of  the  cycle,  as  will  be  shown 


next,  hence 

AE  =  n  XEfc.     .     .     .  V-Y    .     (i 68) 

Efficiency  of  the   Carnot  Cycle  Using  Dry   Saturated  Water 
Vapor  as  a  Working  Substance. 

(g)    The  efficiency  must  of  course  equal  the  ratio  of  the  work 
done  per  cycle  to  the  heat  supplied  per  cycle;  hence  from  Eq. 

(165) 

—  r2  (xc  —  Xd) 


P/. 
Efe- 


A  more  convenient  expression  can  be  found  directly  from  the 
T0-diagram. 

(h)  Remembering  that  area  under  the  line  ab  in  Fig.  53  repre- 
sents heat  supplied  from  the  hot  body,  and  that  the  area  of  the 
cycle  represents  heat  converted  into  work,  it  is  evident  that 

7\-  T2 


which  is  the  same  as  the  expression  for  efficiency  of  the  Carnot 
engine  using  gas  as  a  working  substance. 

(i)  The  Carnot  cycle,  consisting  as  it  does  of  two  reversible 
isothermals  crossed  by  two  reversible  adiabatics,  must  have 
identical  T</>-diagrams  for  all  working  substances.  Since  the 
development  just  given  depends  only  on  this  diagram  and  not 


VAPOR  CYCLES 


upon  the  properties  of  the  material,  it  follows  that  the  expression 

^—^ — -must  give  the  efficiency  of  the  Carnot  cycle  operating 

1\ 
with  any  working  substance. 

92.  The  Carnot  Cycle  with  Any  Vapor,  (a)  The  case  just  con- 
sidered, in  which  the  working  vapor  is  brought  to  the  dry  satu- 
rated condition  before  adiabatic  expansion  begins,  is  the  simplest 
possible  case  as  far  as  the  expressions  for  heat  and  work  are  con- 
cerned. But  adiabatic  expansion  might  begin  with  the  liquid 
only  partly  vaporized  by  isothermal  expansion;  that  is,  with  a 
quality,  Xb,  at  the  top  of  the  adiabatic.  Or,  the  vapor  might  be 
superheated  before  adiabatic  expansion  begins.  Further,  a  mate- 
rial like  ether,  with  properties  markedly  different  from  steam,  and 
with  different  behavior  during  adiabatic  expansion,  might  be  used. 

In  any  case  j-  _  y 

Efc=     *        2, (170) 


and 


(170 


where  A<2i  is  the  heat  added  at  constant  temperature  7\  to  the 

liquid  previously  raised  to  that  temperature. 

For  steam  initially  dry  and  saturated,  A(?i  =  n  .     .     .     (172) 
For  steam  initially  wet,  Aft  =  xtfi     .     .     (173) 


/                                  \          A 

-if                   Tl 

/ 

t 

Q 

\ 

\ 

/ 

o 

/ 

4                  T{, 

Q 

/ 

/ 

\ 

/ 
/ 

Carnot 

\ 
\ 
\ 

/ 

\ 

/ 

\ 

/  d 

T2 

\ 

>c 

\ 

i 

\ 

i 

;  ** 

« 

Entropies 
fpig>  S4>  —  T0-Diagram  for  Carnot  Cycle  with  Superheated  Steam. 

(b)    For  steam  at  pressure  P,  Fig.  54,  superheated  to  temper- 
ature TV  AQi  is  given  by  the  area  below  ab.    In  the  figure  PP 


i66 


HEAT-POWER  ENGINEERING 


is  the  constant-pressure  curve  through  b  and  A<£«a'  is  the  entropy 
of  saturation  at  this  pressure.     Evidently 

(174) 
(175) 


Cp'  loge  — 


where  the  subscript  1  refers  to  the  values  corresponding  to  TI 
and  the  primed  quantities  are  those  referring  to  the  pressure  at 
the  point  b:  hence  r\  does  not  correspond  to  pressure  P. 

(c)    In   Fig.   55  are  shown  PV-  and  T0-diagrams  of  Carnot 
cycles    illustrating   different    possibilities   when    saturated    and 


a  _  bL 


C 

/ 

d 

i            61       \ft 

T! 

> 

i\ 

To     Ci           C     N 

(ft)  Steam  Wet  at  61  and 


Dry  at  6 


1 

'   c 

-I              b     I 

Tl     N 

!\ 

?                T«        C     Co  < 

(c) 


Steam  Superheated  Through- 
out Expansion  from  bi  to  Ci 


d  T« 


1 

/ 

/ 

c 

1            b 

61 

TI            f»x 

1  \ 

To               C 

(6) 


Superheated  Steam  at  6] 
Expanded  to  Wetness  at  Cl 


CT  T« 


To     /Ci     C 


(d) 


Ether  Vapor-  Dry  at  b  becomes 
Superheated  during  Expansion  be 


Fig-  55-  —Carnot  Cycles  for  Vapors  —  Various  Possibilities. 

superheated  vapor  are  used  as  working  substances.  The  bold 
lines  represent  the  isothermal  reception  and  rejection  of  heat. 
In  the  PV-diagram  these  are  horizontal  only  when  the  vapor  is 
saturated.  Figs.  55  (a),  (6),  and  (c)  are  for  steam,  and  in  each 


VAPOR  CYCLES 


167 


case  abed  is  the  diagram  which  is  obtained  with  dry  saturated 
vapor  at  b.     Fig.  55  (d)  is  for  ether. 

93.  Clausius  Cycle  with  Dry  Saturated  Water  Vapor,  (a)  This 
cycle  is  often  called  the  Rankine  cycle,  but  as  another  cycle 
which  is  universally  known  by  this  latter  name  must  also  be 
considered,  the  name  of  Clausius  will  be  used  in  tmVbook  to 
designate  the  cycle  at  present  under  consideration.  As  shown 
in  the  PV-diagram,  Fig.  56,  it  consists  of  two  constant-pressure 


\ 


Claus  us 


Volumes 
Fig0  56.  —  PV-Diagram  for  Clausius  Cycle  with  Dry  Saturated  Water  Vapor  at  c. 

lines  be  and  da  joined  by  an  adiabatic  cd  and  what  is  practically 
a  constant- volume  line  ab.  The  apparatus  of  Fig.  17  used  in 
developing  the  Carnot  cycle  can  also  be  used  for  the  ideal 
Clausius  cycle. 

The  volume  plotted  at  b  is  that  of  unit  weight  of  water  just 
ready  to  vaporize,  corresponding  to  a  of  the  Carnot  cycle  shown 
in  Fig.  52.  The  addition  of  the  latent  heat  of  vaporization,  rit 
causes  the  material  to  expand  at  constant  pressure  until  it 
occupies  the  specific  volume  Vc  at  c.  This  quantity  of  heat,  as 
before,  comes  from  the  hot  body  at  temperature  7\. 

The  adiabatic  expansion  is  exactly  like  that  of  the  Carnot 
cycle  and  is  produced  in  exactly  the  same  way. 

The  constant-pressure  decrease  of  volume  starts  exactly  like 
the  similar  line  in  the  other  cycle,  but  condensation  is  carried  to 
completion  by  the  removal  of  heat  equal  to  xdrz.  The  voh»me 


i68 


HEAT-POWER  ENGINEERING 


Va  is  then  the  volume  of  unit  weight  of  water  at  the  temperature 
of  vaporization  corresponding  to  the  lower  pressure  Pa.  The 
heat  given  up  during  t(his  condensation  is  received  by  the  cold 
body  at  the  constant  temperature  T2. 

The  line  ab  which  takes  the  place  of  the  adiabatic  compression 
of  Carnot  represents  the  heating  of  the  liquid  from  temperature 
TZ  to  the  higher  value  7\,  while  the  pressure  rises  from  Pa  to  Pb. 
There  will  be  a  very  small  volume  change  in  the  liquid  during  this 
process,  but  it  is  so  small  in  comparison  with  the  other  volume 
changes  in  the  cycle  that  it  may  be  neglected  and  the  process 
considered  as  a  constant-volume  pressure  rise. 

(b)  The  T0-diagram  correspondingly  lettered  is  shown  in  Fig. 
57.  The  heat  used  to  raise  the  temperature  of  the  water  must 


Clausius 


Entropies 
Fig.  57-  —  T</>-Diagram  for  Clausius  Cycle  with  Dry  Saturated  Water  Vapor  at  c. 

come  from  the  hot  body  which  has  the  temperature  Ji,  and  during 
its  reception  the  temperature  of  the  water  will  vary  from  T2  to 
TV  Hence  the  cycle  does  not  fulfill  the  criterion  for  maximum 
efficiency  because  all  heat  is  not  received  when  the  working  sub- 
stance is  at  its  highest  temperature.  It  is  also  evident  that  the 
cycle  is  not  reversible,  because  the  addition  of  heat  to  the 
liquid  exemplifies  a  process  which  is  intrinsically  irreversible. 
Strictly  interpreted,  the  line  ab  in  Fig.  57  represents  a  reversible 
process  equivalent  to  the  irreversible  process  ab  of  the  Clausius 
cycle. 


VAPOR   CYCLES  169 

Work  per  Pound  of  Water  Vapor  Carried  through  Clausius 

Cycle  with  Dry  Saturated  Vapor  at  Beginning  of 

Adiabatic  Expansion. 

(c)  As  before,  AE  =  Aft  —  Aft,  from  which  the  value  of  the 
work  done  per  cycle  may  be  determined.  The  heat  Aft  consists 
of  two  parts,  (i)  that  added  to  raise  the  temperature  of  "the  water 
from  T2  to  TI,  and  (2)  the  heat  used  in  vaporizing  during  the 
volume  change  from  F&  to  Vc.  The  quantity  Aft  given  up 
during  the  condensation,  as  already  explained,  can  be  determined 
as  soon  as  the  quality  Xd  is  known.  This  is  easily  found  from 
Eq.  (154)  or  from  either  of  the  entropy  diagrams. 

Then, 


AE  =  Aft  -&Q2=l(qb-qa)  +  ril-lxdrdl  B.t.u.     .     (176) 
=  Xi  -  22  -  Xdri  .......     (177) 


From  inspection  of  the  T$-diagram  it  is  evident  that  the  work 
done  is  given  by  the  following  expression,  the  symbol  Cp  standing 
for  the  mean  specific  heat  of  the  liquid  over  the  temperature 
range: 

AE  =  Cp  (Ti  -  T2)  +  Ti  (A0C  -  A<fc) 

(178) 


Since  (A<£c  -  A<fe)  =  A<fc,,,  A<£d  =  A<£,0l,  and  A00  =  A0ia,  Eq.(i78) 
may  be  written 

AE  =\Cp(Ti-  r2)+r1A4s} 

}.     .     .     .     .     .     (179) 


A  more  useful  formula,  which  may  also  be  written  from  in- 
spection of  the  T<£-diagram,  is 


,    .     (180) 
J.\ 

all  quantities  in  which  may  be  obtained  directly  from  the  Steam 
Tables. 


170  HEAT-POWER  ENGINEERING 

Efficiency  of  the  Clausius  Cycle  with  Dry  Saturated  Water 
Vapor  at  the  Point  c. 

(d)    To  find  this  item,  it  is  only  necessary  to  divide  the  work 
done,  Eq.  (177),  by  the  heat  supplied;  then 

AE         Xl  ~  g2  ~ 


(182) 


(e)  This  form  is  not  readily  comparable  with  the  expression 
for  the  Carnot  efficiency,  and  although  the  fact  is  already  known 
that  the  Clausius  efficiency  must  be  lower  than  the  other  because 
of  the  addition  of  heat  below  maximum  temperature,  it  is  of 
interest  to  derive  an  expression  which  will  show  this  difference. 
This  can  be  done  by  using  Eq.  (178)  in  obtaining  the  efficiency 
expression,  thus, 

AE   =  CP(T!- 
J'      Aft  -  <_ 

T"1      f  \   -L  \    -L     \ 

•      •      •       (183) 


The  Carnot  efficiency  written  in  similar  form  is 

•  •  •  •  (I85) 

In  Eqs.  (184)  and  (185),  the  magnitude  of  the  last  term  deter- 
mines the  value  of  the  efficiency  in  each  case,  but  inspection  of 
the  expressions  as  they  stand  does  not  show  which  of  the  last 
terms  is  the  greater.  If  Fig.  57,  which  shows 'the  two  cycles 
superposed,  is  consulted,  the  interpretation  of  the  last  terms  is 
much  simplified.* 

It  is  evident  from  the  figure  that  the  heat  supplied  during  the 
Clausius  cycle,  equal  to  the  area  under  abcy  is  greater  than  that 

*  In  the  strict  interpretation  of  Fig.  57,  the  line  ab  is  not  the  irreversible  line 
of  the  Clausius  cycle,  but  represents  a  reversible  process  which  would  give  the 
same  P,  V,  T  conditions  as  the  other,  as  mentioned  before  in  connection  with 
Fig.  57- 


VAPOR  CYCLES 


171 


supplied  during  the  Carnot  cycle  by  the  triangular  area  abdi, 
plus  the  area  below  adi.  The  heat  rejected  is,  however,  greater 
by  the  area  below  adi.  Therefore  in  the  case  of  the  Clausius  cycle 
the  heat  rejected  is  increased  in  greater  proportion  than  the  heat 

received,  and  the  fraction^  for  this  cycle  must  be  greater  than 
for  the  Carnot,  and  hence  the  efficiency  is  less. 

94.   The  Clausius  Cycle  in  General,     (a)   As  in  the  case  of  the 
Carnot  cycle,  it  is  possible  to  imagine  a  Clausius  cycle  developed 


P  b    c\ 


di      d 


(n\  Steam  Wet  at  Ci  and 

^     }  Dry  atC 


P    6 


Steam  Superheated  Through- 
out Expansion.  fromCi  to  di 


C    Cl 


I 


d  di  \ 


Superheated  Steam  at  C 1 
Expanded  to  Wetness  at  dl 


di 


A 


)  Ether  Vaper- Dry  atC  Becomes 
Superheated  During  Expansion  cd 


Fig.  58. — Clausius  Cycles  —  Various  Possibilities. 

with  the  vapor  of  any  material  in  either  the  saturated  or  super- 
heated condition.  The  general  equations  for  the  Clausius  cycle 
will  be  given  in  the  latter  part  of  this  section.  Some  of  the 
possible  cases  are  shown  in  Fig.  58,  in  which  the  heavy  lines  in 
all  instances  represent  constant  pressures. 

A  word  of  explanation  will  probably  help  to  make  the  con- 
struction of  the  diagrams  in  Fig.  58  clearer.  In  the  Carnot  cycle 
the  upper  and  lower  lines  are  denned  as  isothermals,  while  in  the 


HEAT-POWER  ENGINEERING 

Clausius  cycle  they  are  lines  of  constant  pressure.  -  For  saturated 
vapors  the  two  are  the  same,  but  for  superheated  vapors  the  two 
cycles  present  very  different  phenomena.  The  isobars  give 
"  horns  "  (at  ci)  in  the  T>-diagrams  when  in  the  superheated 
region,  the  height  of  these  being  determined  directly  by  the  de- 
gree of  superheat. 

(b)  Another  interesting  difference  results  from  the  character- 
istics of  this  constant-pressure  line.     In  the  Clausius  cycle  the 
temperature  rises  during  superheating,  while  in  the  Carnot  it 
remains  constant  and  the  pressure  drops.     In  the  case  of  the 
former  cycle,  then,  the  hot  body  must  have  a  temperature  at  least 
equal  to  that  reached  at  the  end  of  the  superheating  process  and 
therefore  higher  than  that  of  the  working  substance  during  the 
entire  reception  of  heat.     For  this  case,  then,  all  the  heat  is 
received  irreversibly. 

(c)  It  thus  develops  that  for  all  Clausius  cycles  the  heat  re- 
ceived along  the  line  ab  is  received  irreversibly,  the  hot  body 
having  a  temperature  at  least  as  high  as  TCl,  and  for  Clausius 
cycles  in  which  superheating  takes  place,  all  the  heat  is  received 
irreversibly,  because  the  hot  body  must  have  a  temperature  at 
least  as  high  as  that  attained  by  superheating.     This  cycle  when 
using  superheated  vapor  therefore  departs  still  further  from  the 
criterion  for  maximum  efficiency,  and  must  have  a  theoretical 
efficiency  lower  than  that  of  the  same  cycle  with  saturated  vapor 
having  the  same  maximum  temperature.     This  conclusion  is  the 
more  interesting  because,  notwithstanding  the  lower  theoretical 
efficiency,  real  engines  operating  on  this  cycle  obtain  their  highest 
commercial  efficiency  with  superheated  vapor.     The  reason  for 
this  will  be  brought  out  in  a  later  chapter. 

(d)  For  the  Clausius  cycle  with  the  adiabatic  expansion  start- 
ing with  wet  steam,  with  quality  Xi, 


AE  =         (7\  -  ra)  +  ffl  -  22  -  T2  (A<^  -  A0z2),    (186) 


Ef.  =  -  -      -  .......     (187) 

+  qi  -  & 


and 


(e)  In  the  general  case  the  quality  (or  temperature  of  super- 
heat) at  the  end  of  the  adiabatic  expansion  must  first  be  found. 
This  can  be  done  by  solving  for  x*  (or  Dd)  from 

,     .     (188) 


VAPOR  CYCLES  173 

Of,  A^  +  *A&,  +  Cp  log,  ^)rf 

Cploga^±^^.    .     (189) 

If  the  steam  is  initially  superheated  xc  =  1 ;  if  wet,  the  entropy 
of  superheat  (A<^D)C  disappears.  Should  the  value  of  x*  found 
be  greater  than  i.oo,  it  indicates  that  the  steam  is  still  super- 
heated, then  Dd  should  be  determined,  using  Xd  =  1.* 

Having  determined  Xd  (or  Dd),  the  work  may  be  found  from 

AE  =  (q  +  xr  +  CPD)C  -  (q  +  xr  +  CpD)d.      .     (190) 
Also,  the  work  may  be  found  from 

AE  =  Aft  -  Aft, (191) 

in  which  the  values  of  Aft  and  Aft,  the  heat  supplied  and  the 
heat  rejected,  are  equal  respectively  to  the  heat  above  32°  F., 
at  the  beginning  and  end  of  the  isen tropic  expansion,  and  may  be 
read  directly  from  the  Q-curves  on  the  T0-chart  (Plate  I,  Ap- 
pendix) or  from  the  Q-scales  on  the  Mollier  or  Ellenwood  Charts 
(Plates  II  and  IV  in  the  Appendix). 
The  efficiency  is 

(q  +  xr  +  CpD)c  —  g2 

*"^£ <«* 

This  last  form  is  the  most  convenient  when  the  charts  are  used 
for  obtaining  Aft  and  Aft.  These  heat  quantities  are  of  course 
measured  above  32°  F. 

95.  The  Rankine  Cycle,  (a)  This  cycle  is  very  similar  to 
that  last  described,  being  obtained  from  it  by  a  simple  modifica- 
tion, the  reason  for  which  will  be  considered  in  a  later  chapter. 
The  Rankine  cycle,  shown  in  Figs.  59  and  60  for  dry  steam  at  the 
beginning  of  expansion  and  superposed  on  the  Clausius  cycle  for 
the  same  conditions,  is  seen  to  differ  from  the  latter  only  in  having 
the  adiabatic  expansion  cut  short  by  a  constant-volume  line  de. 

Since  the  adiabatic  line  is  not  continued  to  the  lowest  tempera- 

*  In  solving  for  Dd  it  is  necessary  to  assume  a  trial  value  of  Cp  and  use  tha 
"cut  and  try  method." 


174 


HE  A  T-POWER  ENGINEERING 


ture  in  the  cycle,  the  expansion  is  said  to  be  incomplete.     As  the 
figures  show,  the  area  of  this  cycle  is  less  than  that  of  the  one 


Rankine 


(xu)cl 


Volumes 
F»g.  59-  —  PV-Diagram  for  Rankine  Cycle  with  Dry  Saturated  Water  Vapor  at  c. 


Entropies 


Rar 


kine 


Fig.  60.  —  T<*>-Diagram  for  Rankine  Cycle  with  Dry  Saturated  Water  Vapor  at  c. 

having  complete  expansion,  while  the  heat  added  along  ab  and  be 
is  the  same  in  both.  It  therefore  follows  that  the  Rankine  cycle 
must  be  still  less  efficient  than  the  Clausius.  Despite  this  fact, 


VAPOR  CYCLES  175 

it  is  one  of  the  most  commonly  used  vapor  cycles,  being  that 
approximated  by  most  reciprocating  steam  engines. 

(b)  During  the  constant-volume   pressure  drop,  de,  heat  is 
given  up  irreversibly  by  the  working  material  because  the  cold 
body  receiving  that  heat  must  have  a  temperature  at  least  as  low 
as  Te.     Strictly  interpreted,  the  line  de  on  the  T<£-diagram  repre- 
sents an  equivalent  reversible  process. 

It  is  evident  that  all  the  heat  given  to  the  cold  body  is  not 
rejected  when  the  working  substance  has  the  same  temperature 
as  that  body,  and  hence  this  cycle  should  have  a  lower  efficiency 
than  a  similar  Clausius  cycle.  This  has  just  been  shown  to  be 
the  case. 

Work  per  Pound  of  Dry  Saturated  Steam  Used  in  Rankine  Cycle. 

(c)  With  vapor  dry  and  saturated  at  the  beginning  of  adia- 
batic  expansion,  the  work  per  pound  is 

AE=A(?i-Aft (194) 

AE=  Kfl6-ffa)J+riJ 

-  { (xdpd  +  ffd)  -  (xepe  +  2«)  +  xer2]  B.t.u.   .     .     (195) 

In  this  expression  the  difference  (xdpd  +  gd)  —  (%epe  +  2«)  '1S  tne 
difference  of  intrinsic  energy  possessed  by  the  vapor  at  the  points 
d  and  e.  It  is  obvious  that,  to  decrease  the  pressure  at  constant 
volume,  heat  must  be  abstracted,  and  since  no  external  work, 
positive  or  negative,  is  done,  all  heat  removed  must  come  from 
the  stock  of  intrinsic  heat  energy  possessed  by  the  material  at  d. 
To  use  Eq.  (195),  however,  the  two  qualities  xe  and  Xd  must  be 
determined  first. 

(d)  A  more  useful  expression  may  be  developed  as  follows: 
Reference  to  Fig.  60  shows  that  the  work  of  the  cycle  is  repre- 
sented by  the  sum  of  areas  fbcd  and  afde.     The  former  area  is 
the  same  as  that  of  a  Clausius  cycle  with  temperature  limits  T\ 
and   Td,  and  its  heat  value  can  be  computed  from  Eq.  (177). 
The  area  afde  corresponds  to  the  similarly  lettered  area  in  the 
PV-diagram,   Fig.  59,  and  hence  represents  A  (Pd  —  Pe)  •  (xu)d 
B.t.u.  of  work.     Hence  the  work  of  the  Rankine  cycle  for  steam 
initially  dry  and  saturated  is 

AE  =  f\!  -  &  -  (xr)d\  +A(Pd-  Pe)  •  (xu)d,  .  (196) 
and  all  quantities  in  this  expression  are  either  known  at  the 
outset  or  are  obtainable  directly  from  the  Steam  Table,  with  the 
exception  of  xd.,  which  can  be  obtained  from  Eq.  (188)  or  (189). 


176 


HEAT-POWER  ENGINEERING 


Efficiency  of  Rankine  Cycle  Using  Dry  Saturated  Steam. 

(e)   The  heat  received  in  this  cycle  is  the  same  as  that  in  the 
Clausius  cycle,  that  is, 

AQi  =  Xi  -  22- 
Hence  the  efficiency  is 

Aft  -Aft  =  AEfromEq.  (196) 
Qi  Xi  —  £2 


= 


96.   The  Rankine  Cycle  in  General,     (a)   Starting  with  steam 
initially  wet,  the  work  done  is 

AE  =  I  (Xln  +  21  -  2/)  -  xdrd]  +A(Pd-  P2)  xdud,  .     (198) 


e\     e, 


/  n  \          Steam  Wet  at  C  i  and 
V     '  Dry  at  C 


l(>\    Steam  Superheated  Through- 
out Expansion  from  Ci  to  ci\ 


/i,\     Superheated  Steam  at  Ci 
V          Expanded  to  Wetness  at  d  I 


t^  \  Ether  Vaper  Dry  at  C  Becomes 

Superheated  During  Expansion  C  d 


Fig.  61.  — Rankine  Cycles  —  Various  Cases. 

in  which  all  quantities  are  known  or  are  obtainable  from  the 
Steam  Tables  except  xd,  which  must  be  computed  by  using  Eq. 
(188)  or  (189). 

(b)    In  the  most  general  case,  having  first  determined  from 


VAPOR   CYCLES 


I77 


the  equation  last  mentioned  the  quality  xd  (or  superheat  Dd)  at 
the  end  of  the  adiabatic  expansion,  the  work  done  is 

AE  =  { (g  +  xr  +  CPD)C  -  q,  -  (xr  +  CpD)d  { 

+  ,4(Pd-P2)  Fd, (199) 

where  Fd  =  (#V  —  0.017)^  if   the  steam  is  wet  at  d,  or    Vd  = 
(V,  —  o.oi7)d  if  superheated.     Vs  can  be  found  from  Eq.  (134). 

=  (2+*r  +  C,Z>)e-fe'  *     *     (20< 

(c)  As  in  the  other  vapor  cycles,  there  are  a  number  of  different 
possibilities  as  regards  the  working  substance,  but  every  case  can 
be  worked  out  more  or  less  simply  by  means  of  the  expressions 
already   developed.     Various   cases   of   the   Rankine   cycle   are 
shown  in  Fig.  61. 

(d)  The  Rankine  cycle  can  be  solved  readily  by  the  use  of 
Ellenwood's  Charts  (Plates  III  and   IV,  Appendix),  since  these 
have  one  coordinate  representing  volumes.     Thus,  letting  Fig.  59 
represent  the  Rankine  cycle  in  general,  it  is  evident  that  this 
cycle  may  be  considered  as  composed  of  the   Clausius  cycle 
fbcd  and  the  rectangular  area  afde.     Then,  if  Aft  and  Aft  are 
respectively  the  total  heats  at  the  beginning  and  end  of  the 
isentropic  expansion,  as  obtained  from  Plate  IV,*  the 

Net  work  of  area  fbcd  =  Aft  —  Aft  B.t.u. 

and,  if  the  constant-pressure  external  work  represented  by  the 
area  below  fd  is  A  Ed,  per  pound,  and  if  that  below  ae  is  AEe, 
then 

Net  work  of  rectangle  afde  =  AEd  —  A Ee  B.t.u. 
in  which  the  values  of  A  Ed  and  AEe  can  be  obtained  directly 
from  Plate  III  for  the  volume  Vde  and  the  pressures  (or  qualities 
or  superheats)  already  given  or  determined  for  d  and  e. 
Then  for  the  Rankine  cycle  (per  Ib.  of  working  substance) 

Net  work  =  (Aft  -  Aft)  +  (AErf  -  AEe)  B.t.u. 
Ellenwood's  Charts  offer  an  easy  solution  for  this  cycle  re- 
gardless of  whether  it  is  the  pressure  or  the  volume  at  d  that  is 
initially  known.     Without  these  charts  a  laborious  cut-and-try 
process  must  be  used  if  only  the  volume  is  given. 

*  When  AQd  is  obtained  from  Plate  IV  the  values  of  the  volume  Vde  and  pressure 
at  d  should  be  noted  as  they  will  be  needed  later  in  obtaining  AEd  from  Plate  III. 


1 78 


HEAT-POWER  ENGINEERING 


97.   Cycle  with  Rectangular  PV-Diagram.     (a)  This  cycle  is 
the  least  efficient  of  all  the  vapor  cycles  in  practical  use.     It  is 


*     d 


Volumes 
Fig.  62.  —  Cycle  with  Rectangular  PV-Diagram. 

composed  of  two  constant-pressure  lines  joined  by  two  lines  of 
constant  volume,  as  shown  in  the  PV-diagram,  Fig.  62,  and  in 
the  T</>-diagram,  Fig.  63. 
The  diagrams  show  this  cycle  superimposed  upon  a  Clausius 


Entropies 
Fig.  63.  —  T0-Diagram  for  Rectangular  PV  Cycle. 

cycle  so  chosen  that  the  same  weight  of  working  substance  is 
used  in  each.  It  is  evident  that  the  Clausius  cycle  will  require 
a  much  larger  cylinder  than  the  cycle  under  consideration,  but 
the  work  per  cycle  will  also  be  much  greater  per  pound  of  vapor. 


VAPOR   CYCLES 


179 


The  T0-diagram  shows  that  the  heat  absorbed  is  the  same  with 
both  cycles,  namely,  the  area  beneath  the  line  abc.  The  work 
done  is,  however,  greater  with  the  Clausius  cycle  than  with  the 
rectangular  PV  cycle,  as  is  shown  by  the  inclosed  areas  of  the 
diagrams.  It  follows  that  the  efficiency  of  the  cycle  with  rec- 
tangular PV-diagram  must  be  less  than  that  of  the  Clausius 
cycle.  The  Rankine  cycle  for  the  same  heat  inpuf  evidently 
gives  an  amount  of  external  work  intermediate  between  that 
obtained  with  the  Clausius  cycle  and  that  obtained  with  the 
cycle  under  consideration,  and  must  therefore  have  an  inter- 
mediate efficiency.  The  rectangular  PV-diagram  may  be  looked 
upon  as  a  limiting  case  of  the  Rankine  cycle,  the  Clausius  cycle 
being  the  other  limit. 

Work  per  Pound  of  Dry  Saturated  Steam  Used. 

(b)  From  Fig.  62  it  is  apparent  that 

kE  =  A  (Pi  -  P2)  «  .....     (201) 
Efficiency  of  the  Cycle  Using  Dry  Saturated  Steam. 

(c)  The  heat  received  is  the  same  as  that  in  the  Clausius  cycle. 
Hence 

AE  _  A  (P.  -  P*)u 
Ef'  ~  Aft  ~       (Xi  -  a) 

98.   The  Rectangular  PV  Cycle  in  General.     In  any  case 

AE  =  A  (Pi  -  P2)  *cu,  .....     (203) 

where  xcu  =  (xV  —  o.oi7)c  if  the  steam  is  wet,  or  =  (V,  —  0.017)0 
if  superheated.  V8  can  be  found  from  Eq.  (134).  The  general 
expression  for  the  efficiency  is 


Ef.  =  -  --         -.       .     .     •     (204) 

(q  +  xr+  CPD)C  -  q, 

For  method  of  using  Ellenwood's  Charts  for  solving  the  Rec- 
tangular PV  cycle  see  the  middle  of  96  (d). 


CHAPTER   XIII. 

POWER,  EFFICIENCY,  AND  PERFORMANCE. 

CERTAIN  general  definitions  which  are  necessary  in  the  con- 
sideration of  real  engines  are  collected  in  this  chapter.  They 
will  be  discussed  here  very  briefly;  most  of  them  will  be  con- 
sidered more  fully  in  later  chapters  and  some  belong  more  prop- 
erly to  the  province  of  Experimental  Engineering. 

99.  Power,  (a)  In  English-speaking  countries,  the  foot- 
pound (ft.-lb.)  is  the  unit  of  work  generally  used  by  engineers. 
The  unit  of  power,  or  unit  of  the  "  rate  "  of  doing  work,  is  the 
horse  power  (h.p.)  ;  it  equals  the  power  equivalent  to  the  doing 
of  33,ooo  foot-pounds  of  work  per  minute. 

Then  the  horse  power  developed  by  any  apparatus  is 

,         _  Total  ft.-lbs.  of  work  developed  per  min.          ,      . 

(2°5) 


The  heat  equivalent  of  one  horse  power  is 

One  h.p.  =  33,000  -r-  778  =  42.42  B.t.u.  per  min.*      (206) 

(b)  If  work  is  done  for  one  hour  at  the  rate  of  one  horse  power, 
the  total  work  done  is  called  one  horse-power  hour  (h.p.  -hr.). 

Then,     oneh.p.-hr.  =  33,000  X  60  =  1,980,000  ft.-lbs.     .     (207) 
=  1,980,000  -T-  778  =  2545  B.t.u.*     .     (208) 

100.  Distinction  between  Real  and  Ideal  Engines.  In  con- 
sidering the  ideal  or  thermodynamic  engine  in  preceding  chap- 
ters, a  working  substance  was  assumed  to  pass  through  cycles 
within  a  closed  cylinder,  and  it  was  found  that  a  certain  amount 
of  work,  AE,  would  be  delivered  to  the  piston  during  each  cycle. 
The  material  of  the  cylinder  and  piston  was  assumed  to  have 
certain  properties  which  no  available  material  really  has.  The 
cylinder  and  piston  were  assumed  to  neither  absorb  nor  conduct 

"The  A.S.M.E.  Power  Test  Code  (1915)  uses  777.54  ft.-lb.  as  the  equivalent  of 
one  B.t.u.  Then  one  h.p.  =  42.44  B.t.u.  per  minute  or  2546.5  B.t.u.  per  hr. 

180 


POWER,  EFFICIENCY,  AND  PERFORMANCE 


181 


heat.  The  piston  was  supposed  to  be  without  leakage  and 
friction;  and  any  other  necessary  mechanism  of  the  engine  was 
assumed  frictionless.  These  conditions  cannot  be  realized  in 
practice.  Therefore,  the  action  of  a  real  engine  must  differ  con- 
siderably from  the  conceived  action  of  an  ideal  engine. 
Losses  in  real  heat  engines  may  be  classified  as  follows: 

(1)  Cycle  loss,  —  for  even  with  the  ideal  cycle  only  part  of  the 
heat  supplied  can  be  converted  into  work. 

(2)  Cylinder  losses,  or  those  which  occur  within  the  real 
cylinder  because  the  ideal  cycle  is  not  perfectly  produced.     These 
losses  reduce  the  work  actually  delivered  to  the  piston  by  the 
working  substance. 

(3)  Friction  losses,  occurring  in  the  mechanism  used  in  the 
transmission  of  work  between  the  piston  face  and  the  place  of 
utilization. 

101.  The  Indicator.  The  work  actually  performed  on  the 
piston  by  the  working  substance  in  the  cylinder  of  the  real 
engine  and  the  pressure- volume  changes  that  actually  occur 
within  the  cylinder  can  be 
determined  by  using  the  in- 
strument called  the  "  Indica- 
tor," which  can  be  made  to 
draw  the  PV-diagram  for  the 
changes  actually  occurring. 
The  comparison  of  such  a  dia- 
gram with  the  ideal  one  aids 
in  determining  the  cylinder 
losses. 

This  instrument  is  shown 
in  Fig.  64.  A  card  is  mounted 
on  the  outside  of  a  metallic 
cylinder  which  is  caused  to 
oscillate  in  unison  with  the 
motion  of  the  engine  piston. 
A  pencil,  which  may  be 
pressed  against  this  card,  is  actuated  by  a  small,  spring-balanced 
piston  subjected  to  the  same  pressure  as  the  engine  piston. 
Thus  the  card  movement  is  proportional  to  the  volume  dis- 
placed by  the  engine  piston,  while  the  pencil  movement  is  pro- 


Fig.  64. 


182 


HEAT-POWER  ENGINEERING 


portional  to  the  pressure  which  actuates  the  piston.  The  pencil 
movement  is  at  right  angles  to  the  card  movement,  and  hence 
a  pressure-volume  diagram  with  rectangular  coordinates,  such 
as  abcde  in  Fig.  65,  is  drawn.  If  the  card  cylinder  oscillates 
under  the  pencil  while  the  indicator  piston  is  disconnected  from 
the  engine  cylinder  and  subjected  to  atmospheric  pressure,  a 
horizontal  line,  called  the  atmospheric  line,  will  be  drawn. 

1 02.  The  Indicator  Diagram,  (a.)  In  the  pressure- volume 
diagram  drawn  by  the  indicator,  as  in  the  PV-diagrams  pre- 
viously considered,  the  inclosed  area  represents  the  work  done 
upon  the  engine  piston  by  the  working  substance  during  the 
cycle. 

(b)  The  Pressure  Scale,  Sp,  is  commonly  expressed  as  the 
number  of  pounds  per  square  inch  of  piston  area,  corresponding 

to  one  inch  of  ordinate.  This 
is  also  called  the  "  Spring 
Scale."  Obviously,  the  scale 
giving  pressure  per  square  foot 
of  piston  area  is  144  X  Sp. 

The  datum  of  absolute  pres- 
sures is  a  horizontal  line,  00 
in  Fig.  65,  drawn  at  a  distance 
below  the  atmospheric  line, 
A  A,  equal  to  the  atmospheric 
pressure  as  measured  on  the  pressure  scale.  Thus  for  any  point, 
the  absolute  intensity  of  pressure  per  square  inch  of  piston 
area  =  (ordinate  above  OO)  X  Sp;  similarly,  the  pressure  above 
atmospheric  =  (ordinate  above  A  A)  X  Sp.  The  latter  pressure 
is  usually  called  the  "  gauge  pressure." 

(c)  The  Volume  Scale,  Sv,  is  the  displacement,  in  cubic  feet, 
per  square  foot  of  piston,  represented  by  one  inch  of  abscissa. 

The  datum  of  total  volumes  is  a  vertical  line,  YY  in  Fig.  65, 
located  to  the  left  of  Aa  at  a  distance  representing,  to  scale,  the 
"  clearance  volume  "  or  space  in  the  cylinder  occupied  by  the 
working  substance  when  the  piston  is  at  the  beginning  of  its 
stroke.  Thus  for  any  point  on  the  diagram,  the  total  volume 
of  working  substance  in  the  cylinder  equals  Sv  X  (abscissa 
from  YY) ,  and  the  volume  displaced  by  the  piston  is  Sv  X  (ab- 
scissa from 


Fig.  65. 


POWER,   EFFICIENCY,  AND  PERFORMANCE  183 

(d)  The    Scale   of    Work,   Sw,  corresponding   to  one  square 
inch  of  area  of  the  diagram  =  Sw  =  Sp  X  Sv  foot-pounds  per 
square  inch  of  piston  area,  or  144  Sw  ft.-lbs.  per  square  foot. 

The  work  done  per  cycle  by  the  working  substance  acting  on 
the  total  piston  area,  as  represented  by  the  area  of  the  diagram, 
is  called  the  Indicated  Work.  Thus  the  i.w.  =  (area  of  diagram) 
X  (area  of  piston  in  sq.  in.)  X  Sw. 

The  corresponding  rate  of  doing  indicated  work  is  expressed 
in  terms  of  horse  power;  it  is  called  the  Indicated  Horse  Power 
(i.h.p.)  and  is  computed  by  using  Eq.  (205). 

(e)  Consider  Fig.  65  as  an  actual  diagram  taken  from  an  engine. 
From  the  point  a  the  engine  piston  moved  out  until  the  point 
c  was  reached.     By  virtue  of  the  property  of  the  PV-diagram, 
the  area  between  the  lines  abc  and  00  represents  the  work  done 
upon  the  piston  by  the  expanding  working  substance.     This 
work  may  be  computed  by  multiplying  the  average  pressure 
on  the  face  of  the  piston  of  the  engine  by  the  piston's  move- 
ment.    To  find  the  average  pressure  per  square  inch  of  piston, 
divide  the  square  inches  of  area  between  abc  and  the  pressure 
datum  00  by  the  length  A  A  in  inches  and  multiply  this  average 
height  by  Sp.     Multiplying  this  mean  intensity  of  pressure  by 
the  area  of  the  piston  in  square  inches  and  by  the  length  of 
stroke  of  the  piston  in  feet  gives  the  work  done  during  the  out 
stroke  of  the  piston. 

(f)  Similarly,  the  area  under  the  line  cde  represents  the  work 
done  by   the   piston   upon   the  working  substance  during  the 
return  stroke,  and  the  mean  ordinate  of  this  area  multiplied 
by  Sp  gives  the  average  intensity  of  pressure  against  which  the 
engine  piston  moved  during  this  stroke.     This,  multiplied  by 
the  area  of  the  piston  in  square  inches  and  by  the  stroke  of  the 
piston  in  feet,  gives  the  work  in  foot-pounds  done  by  the  piston 
on  the  working  substance  during  the  return  stroke. 

(g)  The  useful  work  delivered  to  the  piston  during  one  cycle 
equals  the  difference  between  the  work  done  upon  it  on  the  out 
stroke  and  that  done  by  it  on  the  working  substance  during  the 
return  stroke. 

The  amount  of  work  actually  accomplished  would  have  been 
the  same  if  the  difference  between  these  two  average  pressures 
had  acted  upon  the  piston  during  one  stroke  only.  The  value 
of  this  difference  is,  however,  given  by  dividing  the  area  abcde  by 


1  84  HEAT-POWER  ENGINEERING 

the  length  of  the  diagram  and  multiplying  by  Sp.  This  is 
known  as  the  mean  effective  pressure  (m.e.p.),  and  is  defined 
as  the  pressure  which,  operating  on  the  face  of  the  piston  during 
one  stroke,  would  do  the  same  amount  of  work  as  is  actually 
done  per  cycle  by  the  variable  pressure  really  acting. 

(h)  In  terms  of  the  mean  effective  pressure,  which  will  here- 
after be  designated  by  pm,  the  work  done  upon  the  piston  by 
the  working  substance,  per  cycle,  is 

Work  =  £m-a-L  ft.-lbs.,    ....     (209) 

in  which  a  represents  the  area  of  the  engine  piston  in  square 
inches  and  L  is  the  stroke  in  feet. 

If  there  are  n  cycles  per  minute,  the  work  per  minute  will  be 
n  times  the  work  per  cycle,  and  the  indicated  horse  power  of 

the  engine  will  be 

.  t  pmLan  ,       , 

i.h.p.  =—  --  .......     (210) 

33,000 

(i)  Eq.  (210)  can  be  used  to  determine  the  diameter  of  cylinder 
needed  to  develop  any  i.h.p.,  provided  the  m.e.p.,  the  length  of 
stroke,  and  the  number  of  cycles  per  minute  are  known.  Thus 
the  effective  area  of  the  piston  must  be 

33,ooo  i.h.p. 


pmLn 
from  which  the  piston  diameter  follows. 


103.  Methods  of  Determining  the  Area  of  an  Indicator 
Diagram,  (a)  The  area  of  an  indicator  diagram  can  be  deter- 
mined (i)  by  placing  transparent  "  cross-section  paper  "  over 
the  diagram  and  counting  the  squares  surrounded;  (2)  by  using 
some  such  form  of  mechanical  integrating  instrument  as  the 
"  planimeter;"  (3)  by  applying  the  "  method  of  ordinates;" 
or  (4)  by  using  some  integration  rule  such  as  the  "  Trapezoidal 
Rule  "  *  and  "  Simpson's  One-  third  Rule."  f 

(b)  One  form  of  planimeter  is  shown  in  Fig.  66.  It  consists 
of  two  arms  jointed  together,  one  terminating  in  a  "  fixed  point  " 
which  is  a  stationary  pivot,  while  the  other  carries  a  "  tracing 
point."  The  third  support  for  the  instrument  is  a  point  of  the 

*  For  this  rule  see  Kent's  "  Pocket  Book." 

t  See  Church's  "  Notes  on  Mechanics  "  or  Kent's  "  Pocket  Book,"  published 
by  John  Wiley  &  Sons. 


-Joint 


POWER,   EFFICIENCY,  AND  PERFORMANCE 

rim  of  a  graduated  wheel  or  "  record  roller."  If  the  record 
wheel  is  set  at  zero  and  the  tracing  point  is  moved  clockwise 
around  the  outline  of  the  diagram  and  is  re- 
turned to  its  original  position,  the  area  of  the 
figure  is  given  by  the  reading  of  the  record 
wheel.  The  theory  and  use  of  planimeters 
is  treated  in  books  on  Experimental  Engi- 
neering.* The  mean  ordinate  is  found  by 
dividing  the  area  by  the  length  of  dia- 
gram, and  the  m.e.p.  is  the  product  of  the 
mean  ordinate  and  the  pressure  scale. 

(c)  In  the  method  of  ordinates,  the  length 
of  the  diagram  is  divided  into  a  number  of 
equal  parts,  with  interval  Ax  as  in  Fig.  67, 
and  ordinates  are  drawn,  as  I,  2,  3,  etc.,  in 


^Fixed-Point 

Fig.    66. 


Tracing  Point 


the  figure.  Central  intermediate  ordinates  are  then  drawn  and  the 
intercepts  yi,  y2,  y3,  etc.,  are  scaled  and  used 
as  the  mean  heights  of  the  elementary  areas 
between  ordinates.  The  area  of  the  dia- 
gram is  approximately  A  =  2y  X  A*,  and 


Fig.  67. 


the  mean  ordinate  is  ym  =  7— 

(no.  of  ordinates) 

This  method  is  not  strictly  correct,  for 
the  middle  intercepts  are  not  necessarily  the  mean  heights  of  the 
elementary  areas.    These  mean  heights  can  be  found  quite  accu- 
rately by  the  method  shown  in  Fig.  68.     Here  lines 
AB  and    CD   (not  necessarily  horizontal)  are  so 
drawn  that  areas  a\  and  0%  are  equal  and  that  b\  =  62- 
Then  the  distance  y  between  the  centers  of  these 
lines  is  the  true  mean  height.     The  equality  be- 
tween areas  a\  and  az  and  between  b\  and  b%  can 
be  estimated  very  accurately  by  eye. 


104.   Delivered  Power,     (a)    In  Section  100  it       Fi     6g 
was  stated  that  only  a  part  of  the  net  work  done 
on  the  piston  by  the  working  substance  is  delivered  by  the  engine, 
as  there  is  a  friction  loss  in  the  moving  parts.    The  power  which 
actually  is  made  available  by  the  engine  is  variously  called  the 

*  See  Carpenter  and  Diederich's  "  Experimental   Engineering,"  published  by 
John  Wiley  &  Sons. 


!86  HEAT-POWER  ENGINEERING 

delivered  horse  power  (d.h.p.).  the  brake  horse  power  (b.h.p.), 
and  the  effective  horse  power  (e.h.p.). 

The  difference  between  the  indicated  horse  power  and  the 
delivered  horse  power  is  a  measure  of  the  power  lost  in  friction, 
and  is  called  the  friction  horse  power  (f.h.p.).  Then 

f.h.p.  =  i.h.p.  -  d.h.p.  ....     .'    .     (212) 

The  indicated  horse  power  can  be  determined  by  means  of  the 
indicator,  and  hence,  if  either  the  friction  horse  power  or  the 
delivered  horse  power  can  be  measured,  all  three  of  the  quanti- 
ties of  Eq.  (212)  become  known. 

(b)  The  direct  measurement  of  the  friction  horse  power  is 
usually  impossible,  but  several  approximate  methods  are  used. 
One  scheme  depends  upon  the  assumption  that  the  power  con- 
sumed in  engine  friction  is  constant  for  all  values  of  delivered 
power.  This  assumption  is  not  accurate,  but  may  be  used  for 
approximation.  Assuming  it  true,  the  indicated  horse  power 
obtained  when  the  engine  is  running  at  speed  with  no  external 
load,  that  is,  when  all  the  indicated  power  is  applied  to  overcome 
friction,  may  be  taken  as  a  measure  of  the  friction  horse  power. 

Sometimes  it  is  possible  to  drive  an  engine  at  its  normal  speed, 
from  some  external  source  of  power,  such  as  an  electric  motor  or 
a  shaft.  When  this  can  be  done,  and  when  the  power  thus  con- 
sumed can  be  measured,  it  furnishes  an  approximate  determina- 
tion of  the  friction  horse  power.  However,  it  is  necessary  to 
make  the  same  assumption  as  in  the  previous  case. 

The  usual  method  is  to  determine  the  delivered  horse  power 
experimentally  and  to  calculate  the  friction  horse  power  by 
Eq.  (212). 

The  delivered  horse  power  may  be  measured  by  the  use  of  a 
prony  brake  or  similar  absorption  or  transmission  dynamometer; 
hence  the  term  "  brake  horse  power."  For  large  engines  ab- 
sorption dynamometers  become  elaborate  and  expensive  and  are 
seldom  used  except  in  special  cases. 

105.  Efficiencies,  (a)  Efficiency  is  the  ratio  of  result  to 
effort.  For  the  heat  engine  there  are  several  such  ratios,  which 
depend  upon  the  meanings  given  to  the  terms  "  result  "  and 
"  effort."  They  are  useful  in  comparing  performances  of  dif- 
ferent engines,  in  locating  losses,  and  in  showing  opportunities  for 
improvement.  Unfortunately,  there  is  lack  of  uniformity  in  the 


POWER,   EFFICIENCY,  AND  PERFORMANCE 


I87 


names  applied  to  the  various  efficiencies,  and  in  some  cases  the 
same  term  has  been  used  for  entirely  different  ratios.  In  the  fol- 
lowing discussion  the  names  which  are  apparently  the  most  suit- 
able have  been  adopted. 

Fig.  69  is  a  diagram  showing  the  energy  stream.  Here,  as  in 
Fig.  3,  the  width  of  stream  shows  the  amount  of  energy  still 
available  for  doing  external  work.  As  the  stream  progresses 
losses  occur,  as  shown  by  the  offshoots,  and  less  energy  remains 


Fig.  69. 

available  for  doing  external  work.  The  several  efficiencies, 
which  will  now  be  considered,  may  be  studied  in  connection  with 
this  figure,  and  the  relation  between  the  various  ones  will  be 
made  clearer  by  referring  to  the  figure  as  the  discussion  pro- 
gresses. 

(b)  Carnot  Efficiency.  It  has  been  shown  that  the  efficiency 
of  the  Carnot  cycle,  and  of  all  other  reversible  cycles,  is  the 
theoretical  maximum  with  any  given  temperature  limits.  It  is 
an  ideal  efficiency,  but  is  impossible  of  attainment  in  any  real 
case.  Its  value  regardless  of  the  kind  of  working  substance  is 

T,-  T2 


Efc  = 


(213) 


In  Fig.  69,  XZ  represents  the  heat  supplied   and  XY  that 
which  would   be  delivered  as  external  work  if  the  Carnot  cycle 

XY 
were  followed ;  hence  the  Carnot  Efficiency  is  Efe  =  -       • 


188  HEAT-POWER  ENGINEERING 

(c)  Cycle  Efficiency.     In  all  real   engines  the  working  sub- 
stance in  its  action  approximates  one  of  the  theoretical  cycles 
already  developed.     Each  of  these  cycles  was  shown  to  have  in- 
herent thermodynamic  loss  and  a  theoretical  efficiency  less  than 
unity.     This  efficiency  will  hereafter  be  called  the  Cycle  Effi- 

ciency, CEf.     It  is  shown  in  Fig.  69  by  the  ratio  -77;-* 

A  C 

For  example,  if  a  steam  engine  is  assumed  to  follow  the  ideal 
Clausius  cycle,  the  Cycle  Efficiency  is  given  by  Eq.  (192),  and 
the  work,  AEi,  per  pound  of  material  by  Eqs.  (188)  to  (191). 
In  Fig.  69,  AB  represents  AEi. 

No  real  engine  actually  attains  the  efficiency  of  its  theoretical 
cycle  because  of  unpreventable  losses,  but  the  Cycle  Efficiency 
represents  the  best  result  attainable  with  the  cycle  in  an  engine 
having  no  extra-thermodynamic  losses. 

(d)  Relative  Efficiency.     It  would    seem   that    the  engineer 
should  be  able  to  design  and  construct  engines  to  operate  with 
the  Carnot  and  other  reversible  cycles,  and  thus  approximate  the 
ideal  efficiency.     However,  practical  reasons  generally  compel 
the  use  of  engines  approximating  theoretical  cycles  that  are 
thermodynamically    less    efficient.     This    reduces    the    possible 
efficiency  even  before  the  practical  losses  are  considered. 

A  measure  of  this  reduction  is  obtained  by  dividing  the  Cycle 
Efficiency  of  the  engine  considered  by  the  Carnot  Efficiency. 
The  quotient  will  be  called  the  Relative  Efficiency,  REf,  and  is 


Referring  to  Fig.  69,  it  is  evident  that 


_  Work  done  by  cycle  under  consideration 
Work  done  by  Carnot  cycle 

(e)  Indicated  or  Cylinder  Efficiency.  In  actual  engines,  as 
stated,  the  work  done  upon  the  piston  by  the  working  substance 
is  of  course  always  less  than  the  theoretical  quantity;  that  is, 

*  Note  that  any  engine  operating  on  a  cycle  which  is  theoretically  reversible  will 
have  a  Cycle  Efficiency  equal  to  the  Carnot  Efficiency  (as  in  (b)).  In  other  cases 
the  amount  by  which  the  CEf  falls  short  of  Efc  indicates  the  theoretical  disadvan- 
tage of  the  irreversible  cycle. 


POWER,  EFFICIENCY,   AND  PERFORMANCE  189 

it  is  less  than  the  product  of  the  Cycle  Efficiency  by  the  heat 
supplied. 

The  ratio  of  work  actually  done  to  work  theoretically  possible 
measures  the  perfection  of  design,  construction,  and  operation  of 
the  cylinder,  piston,  and  valves. 

This  ratio,  which  will  be  called  either  the  Indicated  or  the 
Cylinder  Efficiency,*  IE/,  can  be  expressed  in  several  ways  as 
follows : 

Area  of  actual  indicator  diagram 
Area  of  theoretical  PV-diagram 

Indicated  work  per  pound  of  working  substance  f         . 
778  AE  (for  corresponding  theoretical  cycle) 

Heat  utilized  per  pound  of  working  substance 
AE  (for  corresponding  theoretical  cycle) 

I.h.p. 


Theoretical  horse  power' 

In  the  energy  stream  shown  in  Fig.  69,  DE  represents  the  indi- 
cated work  and  AB  the  theoretical  work.  Evidently  the  Cylin- 
der Efficiency  is 


For  example,  if,  in  the  case  of  the  steam  engine  previously 
cited,  the  work  per  pound  of  steam  shown  by  the  actual  indicator 
diagram  is  AE',  and  if  AEi  is  the  work  with  the  Clausius  cycle, 

AE' 
then  the  lEf  =  —  -^-  ,  and  DE  in  Fig.  69  represents  AE'. 


(f)  Mechanical  Efficiency.  The  ratio  of  work  delivered  by 
the  engine  to  work  received  by  the  piston  (equal  to  the  ratio  of 
delivered  power  to  indicated  power)  is  called  the  Mechanical 
Efficiency,  MEf.  Thus 

MEf  =  d.h.p.  -5-  i.h.p  ......     (216) 

This  fraction  gives  the  proportion  of  the  power  received  by  the 
piston  which  actually  becomes  available  as  mechanical  power  for 
the  consumer.  The  loss  is  a  mechanical  one  due  to  friction  of  the 
mechanism. 

*  In  the  case  of  steam  engines  the  A.S.M.E.  Power  Test  Code  (1915)  calls  this 
the  "  Rankine  Cycle  Ratio  referred  to  the  i.h.p."  and  assumes  that  the  cycle  fol- 
lowed is  the  Clausius,  or  Rankine  Complete  Expansion  Cycle.  Many  authors  term 
this  th  :  "  Efficiency  Ratio,"  which  is  recommended  by  the  British  Inst.  C.  E.,  Vol. 
CXXXIV,  p.  796. 


100  HEAT-POWER  ENGINEERING 

In  Fig.  69,  JK  represents  the  energy  delivered  by  the  engine, 
and  DE,  or  JL,  shows  the  indicated  work  done  on  the  piston; 

TK 

hence  the  mechanical  efficiency  is  -==•  • 

J  LI 

(g)  Thermal  Efficiency  on  the  I.h.p.  The  ratio  of  indicated 
work  done  (GH  in  Fig.  69)  to  heat  supplied  in  the  working  sub- 
stance (XZ  or  GI)  is  useful  in  showing  the  combined  efficiency 
of  the  cycle  and  the  cylinder  with  appurtenances.  It  will  be 
called  the  Thermal  Efficiency  on  the  i.h.p.,  abbreviated  TIEf, 
and  is 

_   Indicated  work  in  B.t.u.  .       . 

Heat  supplied  to  cylinder  ' 

Obviously,  this  efficiency  equals  the  product  of  the  Cycle  Effi- 
ciency by  the  Indicated  Efficiency,  that  is, 

TIEf  =  CEfXlEf  ......     (218) 


The  TIEf  is  shown  in  Fig.  69  by  J:he  ratio 

Lrl 

(h)  Thermal  Efficiency  on  the  Brake  or  Delivered  Power. 
The  ratio  of  delivered  work  (PQ  in  Fig.  69)  to  the  heat  supplied 
the  engine  will  be  called  the  Thermal  Efficiency  on  the  Brake  or 
Delivered  Power,  TDEf.  Thus 

mr^r      Work  delivered  in  B.t.u. 
Heat  supplied  cylinder 

Also,  it  is  evident  that 

TDEf  =  TIEf  X  MEf.       .    '.  f-v"  .     (220) 

pQ 

The  TDEf  is  shown  in  Fig.  69  by  the  ratio  -=^> 

r  K. 

(i)  The  Overall  Efficiency  of  the  Engine.  The  true  efficiency 
of  the  engine  as  a  whole,  compared  with  the  ideal  or  thermody- 
namic  engine  with  the  same  cycle,  will  be  called  the  Overall 
Efficiency,  OEf.  This  takes  account  of  both  the  cylinder  and  the 
mechanical  losses.*  Hence 

OEf  =  IEfXMEf.    .    ,.     .  '..,     ^  (221) 

The  OEf  in  Fig.  69  is  the  ratio  MN/AB  or  MN/MO. 

A  study  of  Fig.  69  shows  that  all  of  these  efficiencies  follow 
one  another  in  logical  order,  and  that  each  has  a  definite  bearing 
upon  the  analysis  of  the  performance  of  real  engines. 

*  Tn  the  case  of  steam  engines  the  A.S.M.E.  Power  Test  Code  (1915)  calls  this 
the  "  Rankine  Cycle  Ratio  referred  to  the  br.  h.p." 


POWER,  EFFICIENCY,  AND  PERFORMANCE  191 

106.  Engine  Performance,  (a)  The  relative  performance  of 
two  heat  engines  can  be  determined  by  comparison  of  the  amounts 
of  heat  used  to  produce  a  given  amount  of  work.  The  unit  of 
work  usually  adopted  for  comparison  is  either  the  indicated 
horse-power  hour  or  the  delivered  horse-power  hour.  Thus  the 
Rate  of  Heat  Consumption  may  be  defined  as  B.t.u.  required  per 

horse-power  hour,  that  is,  .-7- '-     r—  or  the  _,     '  '  .'    ,  as  the  case 

i.h.p.-hr.  d.h.p.-hr. 

may  be. 

(b)  If  the  amount  of  working  substance  used  per  hour  is 
weighed  and  if  the  h.p.  is  determined,  then  the  weight  of  mate- 
rial per  h.p.-hr.  can  be  computed.  Evidently,  if  Wt,  or  Wd,  is 
the  weight  of  working  substance  per  h.p.-hr.,  and  if  A<2  is  the 
heat  per  pound  of  material,  then 

B't>U'  iXAQ, (222) 


i.h.p.-hr. 
B.t.u. 


(223) 


d.h.p.-hr. 

Since  the  equivalent  of  one  h.p.-hr.  is  2545  B.t.u.,  and  since  the 
Thermal  Efficiency  is  the  ratio  of  the  work  actually  done  to  the 
heat  supplied,  it  is  evident  that 

B.t.u. 2545 ,       x 

h.p.-hr.       TIEf,  or  TDEf,  as  the  case  may  be 

If  several  engines  use  working  substances  of  the  same  kind 
with  the  same  heat  content  per  pound,  the  relative  performances 
can  be  found  by  comparing  the  Rates  of  Consumption  of  Work- 
ing Substance  (i.e.,  pounds  per  i.h.p.-hr.  or  per  d.h.p.-hr.).  These 
values  are  known  as  Engine  Economies. 

Further,  if  unit  weights  of  these  working  substances  receive 
their  store  of  heat  from  equal  weights  of  fuel,  the  Rates  of  Fuel 
Consumption  (pounds  per  i.h.p.-hr.  or  d.h.p.-hr.)  may  be  used  for 
comparison. 

(c)  Graphical  representations  of  engine  performances  are  often 
very  useful.  They  may  be  based  upon  the  scheme  shown  in 
Fig.  70,  which  applies  to  an  impossible  machine  supposed  to  con- 
vert into  mechanical  energy  all  of  the  heat  supplied  it ;  —  thus 
it  is* the  case  with  efficiency  of  100  per  cent. 

Since  2545  B.t.u.  are  equivalent  to  one  h.p.-hr.,  and  since  in 
this  case  the  efficiency  is  the  same  at  all  rates  of  power  develop- 


IQ2 


HEAT-POWER  ENGINEERING 


ment,  that  is,  at  all  "  loads,"  the  curve  showing  the  Rate  of  Heat 
Consumption,  or  R-curve,  is  a  horizontal  line  with  ordinate  2545 

B.t.u.,  as  shown  in  the  figure. 
The  scale  for  this  line  is  at  the 
right. 

The  Total  Heat  Consumption 
per  hour  at  any  load  is  the  pro- 
duct of  the  horse  power  and  the 
corresponding  rate.  Thus  the 
curve  showing  the  Total  Con- 
sumption, or  the  TC-curve,  re- 
sults from  plotting  the  products 
of  corresponding  abscissas  and 
ordinates  of  the  R-curve.  Since 


750,000 

Jj 

^/           | 

•00,000 

Dd 

/ 

1 

iOCO 

^/ 

0 

r 

*/ 

« 

/          Rat 

2545 

y 

^               R 

"-^ 

/id 

Sdx 

0 

/ 

lorse  Power 

o 

100                  200               300 

Fig.  70. 


the  latter  is  a  horizontal  line  in  this  case,  the  corresponding 
TC-curve  must  be  a  straight  line  passing  through  the  origin  and 
with  slope  corresponding  to  the  rate.  The  scale  for  this  curve  is 
given  at  the  left  of  the  figure. 

(d)  When  the  B.t.u.  per  pound  of  working  substance  remains 
constant,  it  is  sometimes  convenient  to  construct  curves  similar 
to  those  in  Fig.  70  but  for  the  consumption  of  the  working  sub- 
stance instead  of  B.t.u.     Thus  the  R-curve  would  represent  the 
Rate  of  Consumption  of  Working  Substance  (as  pounds  of  steam 
per  h.p.-hr.,  or  cubic  feet  of  gas  per  d.h.p.-hr.,  etc.),  and  the 
TC-curve  would  represent  the  total  consumption  of  working  sub- 
stance (as  total  weight  of  steam  or  cubic  feet  of  gas  per  hour). 

Sometimes  similar  curves  are  drawn  to  represent  the  rate  and 
total  consumption  of  fuel  used  (as  pounds  of  coal  per  h.p.-hr., 
and  total  weight  per  hour). 

(e)  According  to  assumption  the  efficiency  of  this  impossible 
device  is  constant,  and  if  the  efficiency  line  were  drawn  it  would 
be  horizontal  at  a  height  corresponding  to  100  per  cent.     Even 
in  the  best  theoretical  cycles,  that  is,  the  Carnot,  and  the  other 
reversible  ones,  the  work  performed  is  very  much  less  than  the 
mechanical  equivalent  of  the  heat  supplied,  and  the  efficiency  is 
always  much  less  than  unity. 

(f)  In  the  real  engine  the  efficiency,   and   hence  the  rate, 
instead  of  being  constant,  varies  characteristically  with  the  toad ; 
thus,  instead  of  being  straight,  as  in  Fig.  70,  the  lines  representing 
the  efficiency  and  rate  may  be  curved,  as  is  shown  for  one  real 


POWER,   EFFICIENCY,  AND  PERFORMANCE 


100  H    200 

Horse  Power 
Fig.  71. 


engine  in  Fig.  71.  Further,  the  TC-curve  will  not  pass  through 
the  origin  of  coordinates,  but  will  have  a  positive  intercept  on 
the  Y-axis,  as  shown  in  Fig.  71.  This  is  because  there  is  a  heat 
loss  when  the  external  load  equals 
zero;  for,  even  when  an  engine  is 
running  without  delivering  power, 
there  is  heat  lost  in  radiation  and 
conduction  and  in  overcoming  fric- 
tion, and  if  the  engine  is  motionless 
at  the  operating  temperature,  there 
is  still  the  loss  due  to  radiation  and 
conduction. 

(g)  The  ordinate  scales  in  Fig. 
71,  as  in  the  case  of  Fig.  70,  may 
be  made  to  read  in  thermal  units, 
pounds  of  working  substance  or  pounds  of  fuel. 

The  ratios  of  the  number  2545  to  the  different  ordinates  of 
the  heat-rate  curve  evidently  give  values  of  the  Thermal  Effi- 
ciencies at  different  loads,  as  shown  by  the  curve  Ef  in  Fig.  71. 
This  curve  will  give  either  the  TIEf  or  the  TDEf,  according  to 
the  basis  used  in  determining  the  R-curve.  Also,  the  Thermal 
Efficiencies  are  given  by  the  ratios  of  ordinates  in  Fig.  70  to 
the  corresponding  ones  in  Fig.  71. 

Similar  comparisons  between  the  curves  for  any  theoretical 
cycle  with  those  for  the  Carnot  cycle  will  give  the  Relative 
Efficiencies  for  the  former. 

(h)  In  Fig.  71  a  dotted  line  is  drawn  from  the  origin  tangent 
to  the  TC-curve.  The  point  of  tangency,  Z,  determines  the 
abscissa,  or  horse-power  output,  at  which  the  efficiency  is  maxi- 
mum and  the  rate  minimum.  Evidently,  the  best  economy  is 
obtained  when  the  engine  develops  this  power,  and,  other  things 
being  equal,  an  engine  should  be  of  such  size  as  to  operate  most 
of  the  time  at  or  near  this  load.  If  the  engine  normally  fur- 
nishes more  or  less  than  this  power,  it  is  either  too  large  or  too 
small  from  the  standpoint  of  economy  only.  It  will  appear  later, 
however,  that  many  other  considerations  enter  into  the  choice 
of  size  of  engine  best  suited  for  a  given  set  of  conditions. 


CHAPTER   XIV. 

THE  THEORETICAL  STEAM  ENGINE. 

107.  General,     (a)    In  the  actual  steam  engine  only  a  por- 
tion of  the  heat  supplied  in  generating  the  steam  is  converted 
into  useful  work.     This  portion  at  maximum  is  only  about  25 
per  cent  and  ordinarily  is  from  5  to  12  per  cent.     All  the  rest 
of  the  heat,  from  75  to  95  per  cent,  is  lost,  and  represents  a  pro- 
portionate waste  of  fuel  and  of  money  spent  for  it.     It  is  very 
important  for  one  who  is  to  be  connected  with  steam  engineering 
to  understand  why  this  great  loss  occurs  and  how  it  can  be 
minimized. 

(b)  The  greater  part  of  the  heat  loss  would  occur  even  in 
the  theoretically  perfect  engine,  —  because  of  imperfections 
inherent  in  the  ideal  cycle;  and  the  exact  extent  of  the  loss  in 
this  case  can  be  readily  computed.  The  further  losses  that 
occur  in  the  actual  engine  are  due  to  physical  imperfections; 
and  their  amounts  can  be  determined  experimentally,  while 
their  causes  and  proportionate  distribution  can  be  studied  by 
comparing  the  actual  cycle  with  the  ideal.  Many  of  the  losses 
can  be  determined  by  comparing  the  actual  cycle  with  the  ideal 
ones,  —  the  Carnot,  Clausius,  and  Rankine. 

1 08.  The  Carnot  Cycle  and  the  Steam  Engine,     (a)   As  the 
Carnot  cycle  (Section  91)  gives  the  greatest  possible  efficiency, 
it  would  seem  to  be  the  most  desirable  cycle  to  use  in  any  type 
of  engine. 

Heretofore,  in  discussing  this  cycle,  it  was  assumed  that  all 
operations  were  performed  within  a  single  nonconducting  cyl- 
inder, to  the  end  of  which  could  be  Attached  the  hot  body,  or 
the  cold  body,  or  the  nonconducting  head,  as  required  during 
the  cycle.  While  such  an  arrangement  is  conceivable,  it  cannot 
be  realized  materially,  and  to  obtain  an  apparatus  of  practical 
value  it  is  necessary  that  some  parts  of  the  cycle  shall  be  per- 

•M 


THE   THEORETICAL  STEAM  ENGINE  195 

formed  outside  of  the  cylinder.  In  this  latter  case,  however, 
the  result  will  be  the  same,  provided  the  cycle  is  carried  through 
in  the  same  manner  as  before.  Thus  the  cycle  may  be  per- 
formed in  the  following  apparatus: 

(b)  Let  the  cylinder,  the  cylinder  end,  and  the  piston  be  per- 
fectly nonconducting,  and  let  the  cylinder  end  be  permanently 
attached.     Then,  instead  of  a  hot  body,  let  there  be  a  pipe  with 
a  valve  ("  Steam  Valve  ")  connecting  the  cylinder  to  a  boiler 
which  will  supply  steam  (heat)  at  the  constant  temperature  7\, 
corresponding  to  pressure  pi]  and  in  place  of  the  cold  body  let 
there  be  another  pipe  with  a  valve  ("  Exhaust  Valve  ")  con- 
necting the  cylinder  to  the  condenser,  in  which  the  temperature 
is  maintained  constantly  at   TZ  ,  corresponding  to  the  exhaust 
pressure  p%.     Such  an  arrangement,  with  the  addition  of  a  feed 
pump  to  return  the  condensate  from  the  condenser  to  the  boiler, 
completes  the  apparatus,  which  contains  the  simple  elements  of 
a  steam  power  plant. 

(c)  In  performing  the  Carnot  cycle,  note  that  (see  Section  53)  : 

(1)  All  heat  from  the  external  source  must  be  received  at  the 
constant  temperature  7\  of  the  source. 

(2)  All  heat  discharged  to  the  cold  body  must  be  rejected  at 
the  constant  temperature  T%  of  the  cold  body.     Hence: 

(3)  Before  heat  is  received  at  the  upper  temperature  TI,  the 
working  substance  must  be  brought  to  that  temperature  with- 
out receiving  heat  energy  from  the  outside ;  so 

it  must  be  done  by  adiabatic  compression  from 
T2  to  TI,  and 

(4)  Before  heat  is  rejected,  the  temperature 
must  be  lowered  from  T\  to  Tz  without  losing 
heat  as  such  to  the  outside;  so  this  must  be 
accomplished  by  adiabatic  expansion. 

Referring  to  Fig.  72  (a)  for  the  PV-diagram 
and  to  Fig.  72  (b)  for  the  T0-diagram  (the 
two  figures  being  lettered  alike),  the  cycle 
would  be  performed  in  the  following  manner: 

(d)  Isothermal   Expansion    (line  ab).     Since   in   the   Carnot 
cycle  the  working  substance  must  receive  all  its  heat  from  the 
outside  source  at  the  upper  temperature  7\f  the  cycle  must  begin 
with  water  (say  one  pound)  which  has  already  been  raised  to 
this  temperature.     In  the  first  operation,  —  starting  with  the 


I96  HEAT-POWER  ENGINEERING 

steam  valve  open,  the  exhaust  valve  closed,  and  piston  against: 
the  cylinder  head,  —  the  boiler  will  supply  the  latent  heat  (at 
a  constant  temperature)  to  form  the  vapor,  which  will  then 
occupy  the  volume  Vb,  the  piston  meanwhile  moving  out  until 
it  has  swept  through  a  volume  equal  to  this.  This  first  part  of 
the  cycle  constitutes  the  period  of  admission.  The  steam  valve 
is  then  closed,  and  the  steam  supply  is  "  cut  off  "  at  point  b. 

(e)  Adiabatic  Expansion  (be  in  the  figures).     The  steam  is 
then  allowed  to  expand  adiabatically  from  b.  to  c,  within  the 
cylinder,  doing  external  work  by  moving  the  piston  against  a 
resistance  until  the  temperature  T2  of  the  condenser  is  reached. 
The  pressure  is  then  fa,  the  volume  is  Vc,  and  the  piston  is  at 
the  end  of  its  stroke.     This  completes  the  second  part  of  the 
cycle.     The  exhaust  valve   is  then   opened   to  "  release  "  the 
steam  from  the  cylinder,  allowing  it  to  flow  to  the  condenser. 

(f)  Isothermal    Compression    (cd).     On    the    return    stroke 
the  piston  drives  the  steam  out  of  the  cylinder  into  the  con- 
denser, where,  by  the  abstraction  of  heat,  it  is  liquefied.     During 
this  operation  the  temperature  remains  constant  at  T% ,  so  the 
heat  is  rejected  to  the  cold  body  isothermally  at  the  lowest 
temperature,  as  in  the  Carnot  cycle.     This  completes  the  third 
part  of  the  cycle  and  constitutes  the  period  of  "  exhaust." 

So  far  the  Carnot  cycle  has  been  followed  without'  variation. 

(g)  Adiabatic    Compression    (da).     To    complete   the   cycle, 
adiabatic  compression  should  begin  at  the  point  d,  so  selected 
that  when  the  piston  reaches  the  end  of  the  stroke,  all  of  the  work- 
ing substance  will  be  returned  to  the  initial  condition.    But  since 
a  part  of  the  steam  has  been  reduced  to  water  in  the  condenser 
and  is  no  longer  in  the  cylinder,  it  appears  that  the  cycle  can- 
not be  completed  by  any  process  entirely  within  the  cylinder 
itself. 

It  is  possible,  however,  in  theory  at  least,  to  complete  the 
Carnot  cycle  by  using  a  combined  vapor-and-water  pump, 
which,  when  the  point  d  is  reached,  will  receive  all  the  water  of 
condensation  from  the  condenser  and  the  vapor  remaining  in 
the  cylinder  at  the  point  d,  and  by  compression  complete  the 
condensation  of  the  vapor,  and  bring  the  whole  charge  back 
to  the  initial  condition  by  a  process  that  is  strictly  adiabatic. 
But  while  this  is  conceivable  it  would  be  very  difficult  to  carry 
out  without  introducing  practical  evils  which  would  more  than 


THE  THEORETICAL  STEAM  ENGINE  197 

counterbalance  the  thermodynamic  advantage.  In  practice 
this  last  operation  would  be  omitted,  and,  instead,  the  steam 
would  either  be  expelled  from  the  cylinder  and  condensecj  in 
a  "  condenser  "  or  else  exhausted  into  the  atmosphere.  The 
water  of  condensation,  or  an  equivalent  amount  of  "  make-up 
water,"  is  then  pumped  to  the  boiler,  where  the  heat  is  added 
to  bring  the  temperature  gradually  back  to  the  initial  value, 
which  is  not  in  accordance  with  the  requirements  of  the  Carnot 
cycle. 

(h)  It  is  true  that  in  the  actual  steam  engine  compression 
is  employed,  but  this  must  not  be  confused  with  the  adiabatic 
compression  of  the  Carnot  cycle.  But  little  of  the  steam  is 
involved  in  this  operation,  and  it  is  used  principally  for  the 
purpose  of  "  cushioning  "  the  reciprocating  parts  in  order  to 
make  the  engine  operate  quietly.  It  has  little  effect  on  the 
thermodynamic  operation  of  the  engine. 

(i)  Although  the  Carnot  cycle  is  not  ordinarily  followed  by 
the  steam  engine,  it  is  often  very  useful  to  determine  the  efficiency 
and  the  work  that  would  be  done  with  this  cycle,  within  the 
temperature  range  of  the  steam  engine,  in  order  to  find  the 
maximum  output  that  could  be  theoretically  attained  by  any 
engine,  using  any  kind  of  working  substance  with  the  same 
temperature  limits. 

Previous  discussion  of  this  cycle  (Section  92)  showed  that  for 
saturated  steam  the  Carnot  Cycle  Efficiency,  Efc,  is  given  by 
Eq.  (170),  that  the  heat  available,  A<2i,  can  be  computed  by 
Eqs.  (172)  to  (174),  and  that  the  work  done  is  AE  =  Aft  X  Efe 
from  Eq.  (171). 

Since  superheat  is  supplied  in  practice  with  gradually  in- 
creasing temperature,  the  Carnot  cycle  is  not  a  satisfactory 
standard  for  comparison  for  engines  using  superheated  steam, 
and  hence  this  case  will  not  be  considered. 

(j)  As  one  h.p.-hr.  is  equivalent  to  the  expenditure  of  2545 
B.t.u.,  and  as  each  pound  of  steam  makes  available  AE  B.t.u. 
for  doing  external  work,  the  Rate  (W)  of  Steam  Consumption 
per  h.p.-hr.,  with  the  Carnot  cycle,  is  evidently 


W  =  .......     (225a) 


2545 


Aft  X  Efc' 


(225b) 


HEAT-POWER  ENGINEERING 


200          300          400 
Initial  Temperature  °~F, 


(k)  In  practice  some  steam  engines  "  exhaust  "  to  the  atmos- 
phere, with  the  temperature  of  heat  rejection  theoretically 
equal  to  212°  F.,  corresponding  to  an  absolute  pressure  of  14.7 
pounds  per  square  inch;  while  other  engines  exhaust  to  a  con- 
denser maintaining  a  vacuum  of  about  26 "  of  mercury,  the 

absolute  pressure  being  a 
little  less  than  2  pounds  per 
square  inch  and  temperature 
about  125°  F.  The  steam 
turbine,  which  is  one  form  of 
steam  engine,  is  often  oper- 
ated with  a  vacuum  of  about 
28"  of  mercury  or  a  little  less 
than  one  pound  "  back  pres- 
sure," the  temperature  being 
about  1 00°  F. 

(1)  Fig.  73  shows  curves 
of  efficiency,  B.t.u.  of  work 
per  pound  of  steam,  and 
water  rate,  for  the  ideal  en- 
gine operating  on  the  Carnot 
cycle  with  steam  initially  dry 
saturated  and  with  the  three 
exhaust  pressures  mentioned 
above.  A  scale  for  satu- 
ration temperatures  corre- 
sponding to  the  different 
initial  pressures  is  also 
given. 

(m)  These  curves  show 
clearly  that  better  results 
are  obtained  by  increasing 
the  initial  temperature  (or 
pressure)  and  by  lowering 
the  temperature  (or  pressure) 

of  exhaust.  A  given  temperature  difference  low  on  the  tempera- 
ture scale  gives  better  efficiency  than  the  same  temperature 
difference  at  a  higher  range,  as  the  denominator  T\  in  Eq.  (170) 
is  lower.  It  is  therefore  theoretically  advantageous  to  have  T% 
as  low  as  possible  in  any  case. 


B.T.U.  per  Lb.  of  Steam 

0  i  i  i  1 

m%% 

1  §   i    i      i         i 

-t2  =  l<* 

o 

Vac.  28 

' 

S, 

^ 

~t^ 

Vac.   26 

/ 
x 

s^ 

-i?* 

Wo 

"kDo 

le 

/ 

)            100          200          300          100          500          60 
Initial  Pressure  (Abs.)  Dry  Saturated  Steam 

100          200          300          400          500 
InitialJ>res8ure(Ab8.)  Dry  Saturated  Steam 


Fig.  73- 


THE  THEORETICAL  STEAM  ENGINE 


199 


109-   Tne  Regenerative   Steam-Engine   Cycle,     (a)   The  T<£- 

diagram,    Fig.   74,    shows   that  if  bci  is  drawn  parallel  to  the 

water  line  adi,  the  area  abc\d\  will  equal  the  area  abed  of  the 

Carnot    cycle.      Thus,     if 

steam   is    carried    through 

the  cycle  abc\d\,  and  if  heat 

is  received  only  along  the 

line  ab,  as   in   the  Carnot 

cycle,  the  two  cycles  must 

have  equal  efficiencies. 

(b)  The     cycle     abcidi, 
called     the     Regenerative 

Cycle,  can  be  obtained  un-  Fi 

der  ideal  conditions  in  the 

following  manner :  While  the  steam  is  expanding  an  infinitesimal 
amount  from  b,  with  drop  in  temperature  from  7\  to  (Ti  —  AT), 
let  a  sufficient  quantity  of  the  steam,  or  heat  from  the  steam,  be 
abstracted  from  the  cylinder  to  cause  the  expansion  to  be  along 
bbi ;  and  let  this  heat  be  used  to  raise  the  feed  water  from  ( TI  —  A  T) 
to  TI,  changing  the  water  from  condition  a\  to  a.  The  heat  ab- 
stracted from  the  cylinder  during  this  process  is  shown  by  the 
area  below  bib]  and  that  given  to  the  water,  by  the  equal  area 
below  a\a.  Similarly,  while  steam  expands  through  another 
increment,  bi  to  b2,  let  sufficient  heat  be  abstracted  from  the- 
cylinder  to  raise  the  water  from  condition  0%  to  a\.  Continue 
this  process  for  each  increment  of  expansion  until  the  final 
temperature  T%  is  reached.  In  this  way  the  expansion  bci  is 
made  parallel  to  adi.  Obviously,  in  each  instance  when  heat 
is  supplied  to  or  abstracted  from  the  working  substance,  the 
transfer  is  at  a  constant  temperature  (considering  the  A  T  as 
insignificantly  small).  Thus  the  surrender  of  heat  by  the 
steam  and  the  reception  of  heat  by  the  water  correspond  to 
the  regenerative  action  in  the  Joule  and  the  Stirling  gas  cycles. 
After  the  water  has  thus  been  brought  to  condition  a,  the  boiler 
can  supply  the  latent  heat  for  vaporization  at  the  constant 
temperature  7\;  and  when  expansion  has  reached  the  point  c\t 
the  heat  is  rejected  at  constant  temperature  T2. 

(c)  As  the  reception  of  heat  from  the  hot  body  and  rejection 
of  heat  to  the  cold  body  are  thus  all  isothermal  and  reversible 
processes,  and  as  the  temperature  changes  are  equivalent  to 


200  HEAT-POWER  ENGINEERING 

adiabatic  ones,  this  cycle  is  the  equivalent  of  the  Carnot  cycle, 
and  the  equations  of  Section  92  and  curves  given  in  Section  108 
for  the  latter  can  also  be  used  for  this  Regenerative  cycle. 

(d)  This  Regenerative  cycle  has  been  used  but  little  in 
practice.  It  is  approximated  in  some  engines  built  by  Nord- 
berg,*  in  which  the  steam  is  expanded  in  steps,  by  passing  it 
successively  through  several  cylinders.  The  theoretical  expan- 
sion in  the  first  cylinder  corresponds  to  W  in  Fig.  74,  but  with 
a  finite  instead  of  an  infinitesimal  temperature  drop;  that  in 
the  second  cylinder  to  bib"  \  and  similarly  for  the  expansions  in 
each  of  the  other  cylinders.  Heat  represented  by  the  area 
below  bib'  is  abstracted  from  the  steam  from  the  first  cylinder, 
(or  from  its  steam  jacket)  and  is  used  to  raise  the  water  from 
state  a"  to  a! \  heat  corresponding  to  the  area  below  b2b",  with- 
drawn from  the  second  cylinder,  raises  the  condition  of  the 
water  from  a'"  to  a"  \  and  similarly  from  each  of  the  other 
cylinders,  heat  is  transferred  to  the  water.  Thus  heat  is  ab- 
stracted by  steps  from  the  expanding  steam  and  is  used  for 
progressively  heating  the  feed  water  in  small  increments,  each 
with  but  small  rise  in  temperature.  If  these  increments  could 
be  made  infinitesimal,  the  heat  additions  would  be  isothermal 
and  the  Regenerative  cycle  would  result.  Nordberg  used  four 
steps  only,  but  the  remarkable  results  obtained  with  these 
engines  when  the  heaters  were  in  use,  as  compared  with  their 
performance  without  the  heaters,  seem  to  indicate  that  there 
may  be  considerable  advantage  to  be  gained  by  using  the  regen- 
erative principle  even  with  but  few  steps.  One  Nordberg 
engine  attained  73.7  per  cent  of  the  efficiency  of  the  Carnot 
cycle  for  the  same  temperature  limits. 

no.  The  Clausius  Cycle,  (a)  The  theoretical  cycle,  approxi- 
mated by  the  ordinary  steam  engine,  as  was  shown  on  pp.  195- 
197,  is  as  follows:  The  working  substance,  starting  as  water  at 
the  boiling  point,  receives  heat  isothermally  during  the  process 
of  vaporization;  it  then  expands  adiabatically  from  the  higher  to 
the  lower  temperature;  it  is  next  condensed  isothermally;  and 
finally,  after  being  returned  to  the  boiler,  is  brought  back  to 
the  initial  state,  not  by  adiabatic  compression,  but  by  the  ap- 
plication of  heat.  This  cycle  will  be  recognized  as  the  Clausius 
cycle  (Sections  93  and  94),  and  not  only  is  it  the  theoretical 
*  Transactions  A.  S.  M.  E.,  1900,  p.  181,  and  1907,  p.  705. 


THE   THEORETICAL  STEAM  ENGINE 


201 


cycle  of  the  steam  engine,  but  also  that  of  the  steam  turbine, 
as  will  be  seen  later;  it  therefore  is  of  value  not  only  in  com- 
paring the  performances  of  steam  engines  with  each  other,  but 
also  in  comparing  engines  with  turbines. 

(b)  The  Clausius  cycle,  with  the  lower  temperature  taken  as  that 
of  the  exhaust  steam,  was  adopted  in  1898  by  the  British  Institution 
of  Civil    Engineers*   as  the 

standard  of  comparison  for 
steam  engines  and  turbines, 
but  is  called  by  them  the 
"  Rankine  cycle, "t  it  having  |  20 
been  published  simultane- 
ously but  independently  by 
both  Clausius  and  Rankine. 
The  use  of  this  temperature 
was  subsequently  adopted 
by  the  American  Society  of 
Mechanical  Engineers  in 
their  "  Power  Test  Code  " 
of  1915.  The  temperature 
of  the  steam  is  measured  in 
the  exhaust  pipe  near  the 
engine,  or  turbine,  as  the 
case  may  be. 

(c)  The  work  in  B.t.u.  per 
pound  of  steam  (AE)  can  be    £ 
computed   for  this  cycle  by 
using  JEqs.  (188)  and  (191), 
or  it  can  be  found  directly 
and  more  conveniently  from 
the  Mollier  chart,  Plate  II, 
in  the  Appendix.     (For  ac- 
curate results  a  larger  chart 
should  be  used  than  is  there 
given.) 

The  efficiency  of  the  Clau- 
sius cycle  can  be  computed  from  Eq.  (192)  or  (193). 

*  Proceedings,  1898. 

t  Note  that  the  name  "  Rankine  cycle  "  is  used  in  this  book  to  designate  a 
different  cycle,  i.e.,  the  Clausius  with  incomplete  expansion. 


50  100  150  200  250 

Initial  Pressure  Lbs.  Sq.  In.  Abs. 


50  100  150  200  250 

Initial  Pressure  Lbs.  Sq.  In.   Abs. 


300 


Fig.  75-  —  Clausius  Cycle. 
Steam. 


Dry  Saturated 


202 


HEAT-POWER  ENGINEERING 


(d)  Fig.  75  gives  curves  for  the  efficiencies,  water  rates,  and 
work  in  B.t.u.  for  the  three  cases  that  were  considered  with  the 
Carnot  cycle,  Section  108  (1),  namely,  with  atmospheric  exhaust 
pressures  and  with  vacuums  of  26"  and  28"  Hg. 

(e)  A  comparison  of  these  curves  with  those  for  the  Carnot 
cycle  (Fig.  73)  shows  lower  efficiency  in  this  case,  as  would  be 
expected.     The  work  per  pound  of  steam  is  larger,  however, 
which  at  first  seems  wrong,  but  which  is  explained  by  the  fact 
that  the  heat  supplied  per  pound  from  the  source  is  much  larger 
in  the  Clausius  cycle  than  in  the  Carnot,  being  (xr  +  q)i  —  q2 
for  the  former  as  against  x\r\  for  the  latter,  when  dry  saturated 
steam  is  used.     Thus  with   the  Clausius   cycle  less   weight  of 
steam  is  used  per  h.p.-hr.,  but  each  pound  receives  more  heat  and 
this  is  used  less  efficiently  than  with  the  Carnot  cycle. 

(f)  Comparing  the  Clausius  cycle  efficiencies  when  the  steam 
is  superheated  with  those  when  it  is  dry  saturated  (other  condi- 
tions of  operation  remaining  the  same)  shows  that  with  superheat 
the  efficiencies  are  so  little  higher  that  superheating  would  seem 
hardly  worth  while,  when  the  additional  expense  of  equipment 
and  maintenance  of  superheating  apparatus  are  considered.     It 
will  be  seen  later,  however,  that  superheating  may  give  beneficial 
results  which  are  not  in  any  way  connected  with  the  theoretical 
cycle,  hence  it  is  frequently  used  in  steam-engine  practice. 


in.  The  Rankine  Cycle,  (a)  In  the  reciprocating  steam 
engine,  instead  of  expanding  to  the  point 
di,  Fig.  76,  it  is  the  general  practice  to  dis- 


(°0 


Fig 


continue  at  some  point  d,  and  release  the 
steam  at  constant  volume,  along  the  line 
de,  as  is  done  in  what  has  been  previously 
called  the  Rankine  cycle  (Sections  95  and 
96).  The  "  toe  "  of  the  diagram  is  thus 
cut  off  and  the  work  represented  by  the 
area  dd\e  is  lost.  The  reason  for  sacrific- 
ing this  work  is  twofold:  (i)  By  reduc- 
ing the  maximum  volume  involved,  that 
is,  from  Vd\  to  'Ve,  the  size  of  the  cylinder 
is  proportionately  decreased,  and  this  re- 
sults in  material  reduction  of  the  size 


and  cost  of  the  engine.     (2)  There  is  a  loss  in  power  and  effi- 


THE   THEORETICAL  STEAM   ENGINE 


203 


ciency  if  expansion  is  carried  beyond  the  pressure  that  is  just 
sufficient  to  overcome  the  frictional  resistance  of  the  engine;  for 
in  Fig.  76  (a),  if  expansion  were  completed,  the  additional  work 
done  by  the  steam  is  shown  by  the  area  edd\\  whereas,  if  de  repre- 
sents a  pressure  equal  to  the  mean  frictional  resistance  of  the 
engine,  the  additional  work  in  friction,  with  the  greater  piston 
movement  df,  would  be  given  by  the  area  edifd,  which  is  greater 
than  the  useful  area  eddi,  by  the  area  dfdi.  The  latter  area 
represents  the  net  loss  accompanying  an  increase  in  expansion 
from  d  to  d\. 

(b)  In  the  steam  turbine,  which  has  very  little  mechanical 
friction,  the  expansion  is  continued  down  to  the  exhaust  pressure, 
as  in  the  Clausius  cycle.  That  the  reciprocating  steam  engine 
does  not  do  the  same  is  a  fault  chargeable  against  it  and  one  that 
cannot  be  entirely  remedied.  Hence,  as  a  standard  of  compari- 
son for  both  the  steam  engine  and  the  turbine,  the  Clausius 
cycle  is  preferable  to  the  Rankine,  and  for  that  reason  the  latter 
cycle  will  not  be  further  considered  here. 

112.  Clearance  and  Compression,  (a)  In  the  theoretical 
cycles  previously  discussed  it  was  considered  that  no  steam  space 
existed  between  the  cylinder  head  and  the  piston  at  the  begin- 
ning of  the  stroke,  and  hence  that  the  initial  volume  of  steam  in 
the  cylinder  was  zero.  In  practice,  however, 
the  piston  must  not  touch  the  cylinder  head, 
and  the  shortest  distance  between  them  is 
called  the  "  mechanical  clearance,"  with  values  ^  (a) 

from  |  inch  to  f  inch  or  more.  The  cubical 
contents  of  this  space,  including  the  passages 
to  the  valves  and  all  other  spaces  that  must 
be  filled  with  steam  before  the  commencement 
of  the  stroke,  is  termed  the  "  clearance  vol- 
ume." It  equals  the  initial  volume  on  the 
PV-diagram,  as  shown  by  cl  in  Fig.  77.  The 
percentage  of  "  clearance  volume  "  as  com- 
pared with  the  piston  displacement,  or  volume 
displaced  by  the  piston  per  stroke,  is  from  2  Fig.  77. 

to  15  per  cent  in  practice.* 

*  The  term  "  clearance  "  is  used  rather  loosely  as  applying  either  to  the  linear 
or  volumetric  quantity,  but  the  kind  of  clearance  meant  is  usually  apparent  from 
the  context. 


-TV 


(6) 


204  HEAT-POWER  ENGINEERING 

(b)  The  clearance  theoretically  influences  the  amount  of  steam 
heat  consumed  per  unit  output  of  work.     If  the  engine  operates 
with  a  theoretical  PV-diagram  of  rectangular  form,  Fig.  77  (a), 
the  clearance  space  must  be  filled  with  steam  each  cycle,  before 
the  piston  starts,  and  as  nearly  all  of  this  steam  is  exhausted 
with  that  which  performs  the  work,  it  theoretically  represents 
a  direct  waste,  the  percentage  of  waste  being  equal  to  the  per- 
centage of  clearance  volume. 

(c)  If  the  cycle  is  that  shown  in  Fig.  77  (&),  a  still  greater  pro- 
portion of  the  steam  heat  is  wasted  because  of  the  clearance 
space;  for  in  this  case  the  clearance  volume  is  greater  in  pro- 
portion to  the  total  volume  of  steam  admitted  than  in  the  pre- 
ceding instance. 

(d)  If  the  cycle  followed  is  that  shown  in  Fig.  77  (c),  in  which 
there  is  adiabatic  compression  along  ab,  there  is  theoretically  no 
loss  due  to  the  clearance;  for  at  each  stroke  the  weight  of  steam 
entrapped  at  a  and  compressed  along  ab  can  be  considered,  dur- 
ing expansion,  as  following  back  along  ba,  just  as  if  this  amount 
of  steam  were  separated  from  the  rest  by  a  flexible  diaphragm 
and  were  compressed  and  expanded  adiabatically  without  being 
exhausted  from  the  cylinder. 

(e)  If  the  compression  is  not  carried 
to  the  initial  pressure,  but  is  along  some 
line  ka  in  Fig.  78,  the  case  is  intermediate 
between  (c)  and  (d).  If,  in  addition,  the 
expansion  is  incomplete,  terminating  at 


Fj      g  some  point  d  in  Fig.  78,  the  clearance  loss 

is  theoretically  a  minimum  when  com- 
pression is  carried  to  a  point  somewhat  below  b* 

(f)  In  the  actual  case  there  are  certain  influences  to  be  dis- 
cussed later,  which  modify  the  theoretical  effect  of  compression. 
Whether  or  not  compression  in  the  actual  engine  improves 
the  steam  consumption  is  still  a  matter  of  discussion.  The 
influence  is  so  small  that  the  effect  is  difficult  to  determine 
experimentally. 

113.  Cushion  Steam  and  Cylinder  Feed,  (a)  It  is  sometimes 
convenient  to  consider  the  weight  of  working  substance  present 
in  an  engine  cylinder  as  composed  of  two  parts,  namely,  that 

*  See  Heck's  "  Steam  Engine,"  Vol.  I,  p.  97. 


THE  THEORETICAL  STEAM  ENGINE 


205 


entrapped  during  compression  and  that  fed  from  the  boiler  during 
each  cycle. 

(b)  The  steam  entrapped  during  compression  is  called  the 
"  cushion  steam."  It  is  difficult  to  determine  its  quality  through- 
out compression,  but  it  is  customary  to  assume  it  dry  when  com- 
pression begins.  Since  almost  immediately  after  release  the 
steam  pressure  drops  to  the  back  pressure, 
there  is  but  little  steam  in  the  cylinder 
soon  after  the  beginning  of  the  back  stroke. 
That  part  subsequently  trapped  in  the 
clearance  and  compressed  is  subject  to  the 
higher  temperature  of  the  cylinder  walls 


throughout  nearly  the  whole  of  the  return  Fl&-  79- 

stroke,  hence  must  be  practically  dry  when  compression  begins. 
With  this  assumption,  the  weight  of  the  cushion  steam  at  k, 
Fig-  79»  can  be  computed  from 

u>k  =  Vk  +  Vk,     .....     .     (226) 

in  which  Vk  can  be  scaled  from  diagram  and  V&  is  the  specific 

volume,  as  given  in  the  Steam  Tables,  for  the  pressure  p%  existing. 

If  the  same  weight  of  steam  is  raised  to  the  initial  pressure  pi 

and  is  maintained  dry  and  saturated,  it  will  occupy  the  volume 

Vb'  =  wk  X  Vlf     ......     (227) 

where  Vi  is  the  specific  volume  at  the  initial  pressure  pi.  The 
volume  Vb  is  shown  by  the  abscissa  at  the  point  b'  in  Fig.  79, 
in  which  b'k  is  the  saturation  curve  for  a  weight  of  steam  equal 

tO  Wk. 

Evidently  when  the  valve  opens  to  admit  steam  to  the  cylinder 
this  weight  Wk  is  already  present,  and  it  occupies  the  volume  TV 
as  soon  as  its  pressure  is  raised  to  that  of  the  entering  steam. 

(c)  The  steam  that  is  supplied  to  the  cylinder  from  the  boiler 
at  every  cycle  is  called  the  "  cylinder  feed  "  (wf).  The  cylinder 
feed  may  be  determined  by  finding  the  weight  of  steam  delivered 
to  the  engine  in  a  given  time  and  dividing  this  by  the  correspond- 
ing number  of  cycles. 

If  the  boiler,  without  loss,  furnishes  to  the  engine  all  the  steam 
it  generates,  the  weight  of  steam  supplied  is  equal  to  the  weight 
of  water  fed  to  the  boiler  in  the  given  time.  If  a  surface  con- 
denser is  used,  Wf  can  be  determined  from  the  weight  of  the 


206  HEAT-POWER  ENGINEERING 

steam  condensed  in  the  given  time,  provided  there  is  no  leakage 
in  the  condenser. 

In  Fig.  79  the  volume  of  the  cylinder  feed  is  shown  by  the 
distance  b'c.  It  would  be  represented  by  be  only  in  case  the 
compression  terminated  at  point  b. 

(d)  The  total  weight  (w)  of  steam  in  the  cylinder  during 
expansion  is  evidently  made  up  of  the  cylinder  feed  (wf)  and  the 
cushion  steam  (wk) ;  thus  w  =  w/  +  Wk.  Its  theoretical  volume 
at  the  time  of  cut-off,  if  it  is  dry  and  saturated,  is  Vc  =  w  X  Vc, 
where  Vc  is  the  specific  volume  of  the  steam  at  the  cut-off  pressure. 

114.  Saturation  and  Quality  Curves,  (a)  If  the  weight  of 
steam  (w)  present  in  the  cylinder  is  considered  to  be  dry  and 
saturated,  it  occupies  at  any  time  a  volume  Vs  =  wV,  where  V 
is  the  specific  volume  for  the  pressure  under  consideration.  By 
plotting  on  the  PV-diagram  the  values  of  V8  for  different  pres- 
sures, a  Saturation  Curve  is  obtained.  Such  a  curve  is  shown  by 
cs  in  Fig.  80,  and  is  of  value  in  determining  the  quality  of  steam 
it  different  points  during  expansion  (Section  70).  For  example,  in 
Fig.  80,  in  which  the  expansion  line  cd  is  adiabatic,  the  quality 

AC 
of  steam  at  any  point  C  is  x  =  -j-~ ,  and  the  "wetness  factor"  is 

CS 


(b)  If  qualities  are  determined  for  several  points  along  the 
expansion  line  and  are  plotted  as  ordinates  on  the  corresponding 
volumes,  as  in  the  upper  part  of  Fig.  80, 
a  Curve  of  Qualities  is  obtained,  which 
shows  how  x  varies  during  the  expansion. 
The  quality  curve  in  this  case  shows  the 
condensation  that  takes  place  in  order  to 
make  heat  available  for  doing  external 
work  during  the  adiabatic  expansion.  In 
the  figure  the  steam  is  assumed  to  be  dry 
and  saturated  at  c,  hence  the  saturation 
_V_  curve  must  pass  through  that  point. 
Quality  curves  for  any  other  kind  of  ex- 
pansion line  can  be  found  in  the  same 

AC' 
way;  thus,  if  c'y  is  the  line,  the  quality  at  C'  is  -7-~r,  if  the  weight 

^T.O 

of  material  present  is  the  same  as  before. 


THE   THEORETICAL  STEAM  ENGINE. 


207 


S  ' 


(c)  Should  the  expansion  line  cross  the  saturation  curve,  as 
in  Fig.  81,  the  quality  ratio  would  be  greater  than  100  per  cent, 
which  would  indicate  that  the  steam  becomes  superheated  during 
expansion.     If  the  weight  (w)  of  steam  is 

known,  the  specific  volume  of  the  super- 

y 
heated  material  follows  from  V  =  — ,   in 

w 

which  V  is  the  volume  scaled  on  the  dia- 
gram.    Then  the  absolute  temperature  of  v 
the  steam  may  be  computed  by  solving 

Tumlirz's  Eq.  (134).  Thus  T  =  p  (V  +  0.256)  -T-  0.5962,  in  which 
p  is  the  absolute  pressure  in  pounds  per  square  inch.  By  sub- 
tracting from  T  the  absolute  temperature  of  saturation  at  the 
pressure  p  the  degrees  of  superheat  D  can  be  found. 

(d)  On  page  156  it  was  shown  that  under  certain  conditions 
the  adiabatic  expansion  of  wet  steam  can  be  represented  quite 
accurately  by  PVn  —  const.,  where  n  has  different  values  which 
depend  on  the  quality  x  at  the  beginning  of  expansion.     The  re- 
lation between  n  and  x  was  given  in  Eq.  (156),  thus  the  initial 
quality  can  be  determined  if  n  is  known.     The  value  of  n  in 
any  case  can  be  found  in  several  ways,  but  probably  the  most 
convenient  method  is  to  replot  the  expansion  curve  using  loga- 
rithmic coordinates,  in  which  case  n  is  the  slope  of  the  expansion 
line  (page  55).     With  the  quality  and  volume  known  at  the  be- 
ginning of  expansion,  the  corresponding  weight  of  steam  in  the 
cylinder  and  the  water  rate  can  be  determined  readily. 


CHAPTER  XV. 
ACTION  OF  STEAM  IN  REAL  ENGINES. 

115.  Cylinder  and  Thermal  Efficiencies  of  the  Steam  Engine. 
(General.)  (a)  The  actual  behavior  of  the  steam  in  a  cylinder  is 
quite  different  from  the  theoretical,  because  of  modifications  of  the 
ideal  cycle,  heat  interchanges  between  the  steam  and  the  cylinder 
walls,  and  leakage  of  valves,  piston,  etc.  The  greater  the  per- 
fection attained  in  the  design,  construction,  and  operation  of  the 
engine,  cylinder,  piston,  valves,  etc.,  the  closer  will  the  actual 
behavior  approach  the  ideal.  The  measure  of  this  perfection  is 
given  by'the  indicated  or  cylinder  efficiency  (/£/),  Section  105  (e), 
which  can  be  computed  by  Eq.  (215),  or  by  the  following: 

j-pf  _  Actual  B.t.u.  of  indicated  work  per  Ib .  of  steam  _  Hi     . 

Theoretical  B.t.u  of  work  with  Clausius  cycle     AE 
_  B.t.u.  equivalent  of  1  i.h.p.-hr.  _     2545  .       , 

Heat  available  per  i.h.p.-hr.     "  W^AE 
Theoretical  Ibs.  of  steam  per  h.p.-hr.       W 

=  -L £ £ =  _ — 

Actual  Ibs.  of  steam  per  i.h.p.-hr.         Wi 
In  which 

AE  =  B.t.u.  work  with  Clausius  cycle  per  Ib.  of  steam. 

Hi  =  Actual  B.t.u.  indicated  work  per  Ib.  of  steam  = 

W  =  Pounds  of  steam  theoretically  needed  per  i.h.p.-hr.  with 

Clausius  cycle  =  2545  ~=~  AE. 

Wi  =  Pounds  of  steam  actually  used  per  i.h.p.-hr.  as  found 
by  weighing  the  water  used. 

(b)  The  cylinder  efficiencies  of  steam  engines  and  turbines 
range  from  46  per  cent  to  80  per  cent,  and  in  one  exceptional  case 
88.2  per  cent  was  attained.  The  reasons  for  the  differences 
occurring  between  the  real  cycle  and  the  Clausius,  and  for  the 
losses  which  they  represent,  and  the  methods  of  reducing  these 
losses,  will  be  discussed  in  the  succeeding  sections. 

208 


ACTION  OF  STEAM  IN  REAL  ENGINES.  209 

If  the  same  Clausius  cycle  is  followed  by  two  reciprocating 
steam  engines,  or  by  a  reciprocating  engine  and  a  steam  turbine, 
the  ratio  of  the  consumptions  of  steam,  or  heat,  per  i.h.p.-hr.  of 
the  two  engines  is  equal  to  the  inverse  ratio  of  the  cylinder 
efficiencies.  If  the  theoretical  cycles  are  not  the  same,  such  a 
comparison  should  not  be  made.  & 

(c)  It  is  at  times  necessary  to  predict  the  performance  of  a 
new  engine,  or  turbine,  when  operating  under  certain  definite 
conditions.     In  such  cases  the  B.t.u.  of  work,  AE,  done  by  the 
Clausius  cycle,  per  pound  of  steam,  can  be  obtained  from  Eqs. 
(188)  and  (191),  or  from  the  Mollier  or  Ellenwood  diagrams  in 
the  Appendix;  then  if  the  proper  value  of  the  Cylinder  Efficiency 
(lEf)  can  be  found,  from  data  relating  to  similar  engines  oper- 
ating under  like  conditions,  the  probable  number  of  heat  units 
that  will  be  converted  into  work  per  pound  of  steam  is,  from 
Eq.  (228a), 

H>=AEX  lEf,      .—...,     (229) 

and,   from   Eq.    (228b),   the   probable  steam  consumption  per 
i.h.p.-hr.  is  ^ 

w. ?545 , 

Wt  ~  (AJE  X  IE})  ' 

(d)  The  Thermal  Efficiency  on  the  i.h.p.  (TIEf),  Section  105 
(g),  is  the  ratio  of  the  indicated  work  to  the  heat  supplied  for 
doing  this  work ;  it  is  therefore  a  measure  of  combined  efficiency 
of  the  cycle  and  of  the  cylinder  with  its  appurtenances. 

The  engine  cannot  use  heat  that  is  of  temperature  lower  than 
that  of  the  exhaust  steam  T2,  and,  theoretically  at  least,  the  heat 
remaining  in  the  condensate  can  be  returned  to  the  boiler  with 
the  feed  water;  hence  the  heat  of  the  liquid  below  this  lower 
temperature  is  not  chargeable  against  the  engine. 

Therefore, 

Trj7f  _   B.t.u.  indicated  work  per  Ib.  of  steam  (2^1  a) 

*  ==  Heat  supplied  above  T2  per  Ib.  of  steam 


(Aft  - 


2545  .     .     (231  c) 

i  (A<2i  -  22) 


2io  HEAT-POWER  ENGINEERING  , 

Where  Hi  =  B.t.u.  of  actual  indicated  work  per  pound  of  steam 
=  2545  +  Wi  =  AE  X  lEf  .     .     .....     (232) 

A&  =  (xr  +  q  +  Cp£>)i  ..........     (233) 

q2  =  heat  of  liquid  above  32  degrees  when  at  the  tem- 

perature TZ    of  the  exhaust  steam. 

Wi  =  Pounds  of  steam  actually  used  per  i.h.p.-hr.   as 
found  by  weighing  the  water  used. 

The  value  of  TIEf  varies  with  the  kind  of  engine  and  condi- 
tions of  operation,  and  ranges  in  practice  from  5  per  cent  to  25.05 
per  cent,  this  latter  value  being  the  maximum  yet  recorded. 

In  the  case  of  a  new  engine,  the  probable  performance  may  be 
computed,  if  the  value  of  TIEf  for  similar  engines  and  conditions 
are  known,  by  using  the  following  equations,  derived  from  Eq. 

(216):  w.  =  2545  .5.  {(AQi  _  qz)  x  Tim    t    §    (234) 

Hi  =  (Aft  -  &)  X  TIEf.       .....     (235) 

(ej  The  Mechanical  Efficiency  (MEf)  of  the  steam  engine 
mechanism  varies  from  85  to  97  per  cent. 

(f)  The  measure  of  the  combination  of  the  efficiencies  of  the 
cycle,  cylinder,  and  engine  mechanism  is  the  Thermal  Effi- 
ciency on  the  d.h.p.  (TDEf),  Section  105  (h).  The  TDEf  can 
be  computed  from  Eqs.  (219)  and  (220).  Since  it  is  the  ratio  of 
the  B.t.u.  of  work  delivered,  to  the  heat  supplied  in  doing  that 

W0rk' 

(236) 


in  which  Wd  is  the  weight  of  working  substance  supplied  to  the 
engine  per  d.h.p.-hr.,  and  AQi  is  the  heat  per  pound  as  given  by 
Eq.  (233),  and  ft  is  the  heat  of  the  liquid  at  exhaust  tempera- 
ture T2. 

The  TDEf  is  from  85  to  97  per  cent  of  the  TIEf,  the  ratio 
being  equal  to  the  mechanical  efficiency. 

The  probable  performance  of  an  engine  on  the  basis  of  de- 
livered power  may  be  estimated  by  using  the  following  equations, 

Wd  =  2545  -s-  5(A<2i  -ft)  X  TDEf  I  =  Wi  4-  MEf     (237) 
H*=  TDEf  (&&-&),  ..........     (238) 

where  Hd  is  the  B.t.u.  of  work  delivered  per  pound  of  steam. 


ACTION  OF  STEAM  IN  REAL  ENGINES  211 

(g)  The  measure  of  the  performance  of  the  engine  as  a  whole 
as  compared  with  the  ideal  engine  following  the  Clausius  cycle 
is  given  by  the  Overall  Efficiency  (OEf).  This  is  the  combined 
efficiency  of  cylinder  and  mechanism,  hence  OEf  =  IEf  X  MEf 
as  in  Eq.  (221).  Since  it  is  the  ratio  of  work  actually  delivered 
to  that  which  would  be  delivered  by  the  ideal  engine, 


in  which  W*  is  the  weight  of  steam  actually  used  per  d.h.p.-hr., 
and  AE  is  work  theoretically  obtainable  per  pound  of  steam  fol- 
lowing the  Clausius  cycle.  AE  can  be  computed  by  using  Eqs. 
(188)  to  (191). 

The  overall  efficiency  of  steam  engines  is  from  35  to  78  per 
cent. 

The  probable  performance  of  the  steam  engine,  based  on  the 
delivered  output,  can  be  estimated  from 

Wd  =  2545  +  (AE  X  OEf)  .....     (240) 
and 

Hd=AEx  OEf  .........     (241) 

1  1  6.   Actual  Behavior  of  Steam  in  an  Engine  Cylinder,     (a) 

The  materials  with  which  the  steam  comes  in  contact  in  the 
engines  previously  considered  have  been  assumed  to  be  perfect 
nonconductors  of  heat;  but  materials  actually  used  are  good 
heat  conductors,  and  this  modifies  the  behavior  of  steam  in  real 
engines. 

(b)  The  steam  on  its  way  from  boiler  to  engine  gives  up  to 
the  pipe  a  part  of  its  heat,  which  is  lost  by  conduction,  radiation, 
and    convection.     Because   of   this,    the   steam   arrives   at   the 
engine  with  quality  or   superheat   reduced.     There   is  another 
loss  due  to  the  drop  in  pressure  necessary  to  cause  the  steam 
to  flow  from  the  boiler  to  the  engine  against  resistances  due  to 
friction  of  the  pipe  and  inertia  of  the  steam  itself.* 

(c)  At  the  engine  the  steam  on  its  way  to  the  cylinder  passes 
through  a  "  Throttle  Valve."     If  this  valve  is  only  partly  open, 
the  steam  is  "  Throttled  "  or  "  Wire-drawn,"  with  an  accom- 
panying drop  in  pressure.     These  changes  take  place  with  such 

*This  kind  of  loss  will  be  considered  later  in  the  chapter  on  flow  of  steam 
through  pipes. 


212  HEAT-POWER  ENGINEERING 

t 

great  rapidity  and  within  such  small  space  that  little  heat  loss 
to  the  outside  can  occur,  but  as  there  is  an  increase  in  the  veloc- 
ity of  the  steam  there  is  a  small  amount  of  heat  expended  in  im- 
parting kinetic  energy.  This,  however,  returns  as  heat  when 
the  velocity  is  reduced  in  the  engine.  The  heat  lost  while  the 
pressure  is  decreased  is  so  small  as  to  be  negligible,  hence  the 
process  may  be  considered  one  in  which  the  total  associated  heat 
remains  constant.  The  throttling  increases  the  quality  (or 
superheat),  the  value  of  which  can  readily  be  found  by  follow- 
ing along  the  proper  constant-heat  line  either  on  the  Mollier 
diagram  or  on  the  T0-diagram,  from  the  point  for  the  initial 
condition  to  that  for  the  lower  pressure  (or  temperature). 

A  further  wire-drawing  takes  place,  with  a  similar  effect  on 
the  condition  of  the  steam,  while  the  steam  passes  the  more  or 
less  restricted  opening  of  the  admission  valve  on  its  way  to  the 
cylinder. 

(d)  When  the  steam  enters  the  clearance  space  in  the  cylinder, 
it  comes  in  contact  with  surfaces  that  were  cooled  during  the 
period  of  exhaust  of  the  preceding  cycle.  In  the  resulting  inter- 
change of  heat,  the  temperature 
of  the  clearance  walls  is  raised, 
and  ordinarily  from  10  to  40 
per  cent  of  the  steam  is  con- 
densed. The  corresponding  de- 
crease in  the  quality  of  the 
steam  is  shown  by  the  inclina- 
tion of  the  quality  curve  Xibi  in 
Fig.  82. 

As  the  piston  recedes  during 
admission  (be),  an  increasing 
amount  of  the  cylinder  wall  is 

rig.   52.  it. 

exposed  to  the  entering  steam 

and  further  condensation  takes  place  (as  shown  by  the  slope  of  bid) 
until,  at  the  point  of  cut-off,  from  20  to  50  per  cent  of  the  steam 
has  usually  been  condensed.  Next  to  the  heat  loss  inherent  in 
the  theoretical  cycle,  this  Initial  Condensation,  as  it  is  called, 
causes  the  largest  loss  that  ordinarily  occurs  in  the  steam  engine 
and  is  therefore  the  one  most  desirable  to  minimize. 

(e)^  During  admission  the  pressure  is  decreased  by  the  wire- 
drawing of  the  steam  while  passing  the  admission  valve  and 


ACTION  OF  STEAM  IN  REAL  ENGINES  213 

while  flowing  through  the  passages  to  the  cylinder.  This 
causes  small  loss  of  heat  but  decreases  availability.  It  improves 
the  quality  or  superheat  of  the  entering  steam  somewhat  and 
may  reduce  the  initial  condensation  a  very  slight  amount. 
The  decrease  of  pressure  by  wire-drawing  and  the  effect  of  con- 
densation during  admission  are  shown  by  the  downward  slope 
of  the  admission  line,  be. 

(f)  After  cut-off  (c),  the  condensation  continues,  until  expan- 
sion has  reached  a  point  (/)  where  the  temperature  of  the  steam 
equals   the   mean   temperature   of   the  exposed   cylinder  walls. 
The  accompanying  change  in  quality  is  shown  by  the  curve 
CI/L     With    further    expansion    the    average    quality   of   steam 
increases;  steam  is  still  condensed  on  the  surfaces  newly  un- 
covered by  the  continued  motion  of  the  piston,  but  the  heat 
thus  absorbed  by  the  cooler  portion  of  the  cylinder  wall  is  less 
than  that  given  up,  to  evaporate  moisture,  by  the  rest  of  the 
wall  which  is  at  relatively  higher  temperature.     The  increase' 
in  quality  is  shown  by  t\r\.     Of  course,  the  condensation  during 
expansion  is  not  all  due  to  the  influence  of  the  cylinder  walls, 
for  heat  must  be  used  in  performing  the  external  work,  as  was 
shown  in  Section  114  (b). 

The  quality  curve  c\t\r\,  for  the  period  of  expansion,  is  readily 
obtainable  after  the  saturation  curve  has  been  drawn  for  the 
total  weight  of  mixture  in  the  cylinder;  but  that  part  of  the 
quality  curve  which  relates  to  admission  (xibid)  is  indeter- 
minate and  is  therefore  shown  dotted  in  the  figure. 

(g)  Theoretically,    expansion    should    be    continued    to    the 
point  d  on  the  back  pressure  line;  therefore,  in  the  actual  case 
there  is  a  loss  due  to  incomplete  expansion,*  measured  by  the 
area  rde. 

During  release  (re)  the  steam  is  dried  to  some  extent  by  the 
heat  that  is  given  up  by  the  cylinder  wall  to  the  steam,  which 
is  now  at  a  low  temperature,  and  also  by  the  heat  released  from 
the  steam  itself  while  decreasing  in  pressure. 

(h)  During  exhaust  (ek)  the  confining  walls  are  cooled  by 
the  outflowing  steam,  and  by  the  evaporation  of  the  film  of 
moisture  on  the  walls.  The  greater  the  amount  of  moisture, 
within  limits,  the  cooler  will  the  walls  become  and  the  greater 
will  be  the  amount  of  steam  condensed  during  admission  in  the 

*See  Section  in. 


214  HEAT-POWER  ENGINEERING  f 

next  stroke.  The  exhaust  pressure,  or  back  pressure,  is  some- 
what higher  than  the  theoretical  because  of  the  resistance  to 
steam  flow  offered  by  the  valve  opening  and  passages,  by  the 
inertia  of  the  steam  itself,  and  because  of  the  evaporation  of 
moisture. 

(i)  During  compression  the  quality  of  the  steam  is  indeter- 
minate. It  is  usually  assumed,  however,  that  the  steam  is  dry 
at  the  beginning  of  compression,  and  this  is  accurate  enough  for 
most  practical  purposes  because  of  the  small  weight  of  steam 
involved.  During  the  first  part  of  compression  the  steam  will 
probably  be  slightly  superheated  owing  to  the  reception  of  heat 
from  the  hotter  walls  of  the  cylinder.  If  the  compression  is 
high,  the  temperature  from  compression  may  rise 
above  that  of  the  cylinder  walls,  in  which  case 
condensation  will  follow.  Further  compression 
of  the  now  saturated  steam  will  be  at  constant 


pressure,  and  on  the  PV-diagram  the  line  be- 
comes horizontal,  thus  forming  the  "  hook  "  as  in  Fig.  83.* 

(j)  The  cycle  is  further  influenced  by  the  leakage  of  steam 
past  the  valves  and  around  the  piston,  which  would  modify  the 
actual  diagram. 

(k)  The  loss  of  heat  from  the  cylinder  walls  by  radiation, 
conduction,  and  convection  lowers  the  mean  temperature  of  the 
walls  and  adds  slightly  to  the  condensation. 

117.  Diagrammatic  Representation  of  the  Heat  Interchange 
in  the  Cylinder,  (a)  In  the  PV-diagram,  Fig.  84  (a),  the  point 


w 

Fig.  84. 

C  represents  the  total  charge  of  steam  and  water  in  the  cylinder, 
considered  raised  to  the  initial  pressure  and  in  a  dry  saturated 
condition.  CC'  is  an  adiabatic  expansion  line  drawn  through 

*A  somewhat  similar  hook  occurs  when  there  is  leakage  past  the  piston  or 
valve. 


ACTION  OF  STEAM  IN   REAL  ENGINES 


215 


this  point,  and  fCC'g  is  the  Clausius  diagram  which  this  charge 
should  theoretically  give.  The  actual  diagram  (omitting  com- 
pression and  clearance)  is  fbcreg.  If  through  c  the  adiabatic 
dCz  is  drawn,  then  fc&g  is  the  Clausius  diagram  for  the  vapor 
actually  present  at  cut-off.  Thus  the  loss  of  area  from  initial 
condensation  is  seen  to  be  c\CC'c^  and  that  due  to  wire  drawing 
is  bcci.  That  the  expansion  line  from  c  to  /  has  greater  slope 
than  CC2  shows  that  the  condensation  takes  place  more  rapidly 
than  it  would  with  adiabatic  expansion.  At  t  the  temperature 
of  the  steam  is  the  same  as  that  of  the  cylinder  walls,  and  from 
/  to  r  reevaporation  takes  place,  as  shown  by  the  expansion  line 
being  more  nearly  horizontal  than  the  adiabatic. 

The  loss  due  to  early  release  is  shown  by  the  area  rde,  in  which 
rd  is  an  adiabatic  line. 

(b)  The  diagram  for  the  compression  of  the  cushion  steam 
is  shown  separately  in  Fig.  84  (b)  by  gkaai ;  and  above  it  is  the 
area  didbf  for  admission  at  constant  volume.      By  subtracting 
Fig.  84  (b)  from  Fig.  84  (a)  the  net  diagram  is  obtained,  as  in 
Fig.  84  (c). 

(c)  The  use  of  a  T<£-Diagram  to  represent  the  heat  inter- 
changes occurring  in  the  cylinder  is  more  or  less  conventional 
and  is  only  partly  correct  from  the  theoretical  standpoint.     In 


Fig.  85. 

Fig.  85,  which  is  lettered  to  correspond  with  Fig.  84,  JCC'g  is 
the  Clausius  diagram  for  the  total  weight  of  charge  used  per 
cycle;  fbcreg  conventionally  represents  the  actual  diagram,  neg- 
lecting clearance  and  compression;  and  fciCzg  is  the  Clausius 
cycle  for  the  vapor  actually  present  at  the  time  of  cut-off. 
The  loss  of  heat  to  the  cylinder  wall  due  to  initial  condensation 
is  given  by  area  below  c\C  down  to  the  <£-axis;  but  as  that 
part  below  c2C'  could  not  be  utilized,  the  net  loss  of  area  from 
this  cause  is  dCC'c2.  The  wire-drawing  loss  is  represented 


2i6  HEAT-POWER  ENGINEERING 

approximately*  by  the  area  bcci.  That  heat  is  lost  to  the 
cylinder  wall  after  cut-off  is  shown  by  the  sloping  of  the  expan- 
sion line  ct  to  the  left  of  the  adiabatic  cc^,  which  indicates  that 
the  quality  decreases  more  rapidly  than  it  would  with  adiabatic 
expansion.  At  t  condensation  ceases;  and  from  /  to  r  reevapo- 
ration  takes  place,  accompanied  by  an  increase  in  the  quality. 
The  loss  due  to  early  release  is  represented  approximately  by  the 
area  erd. 

(d)  The  T$-diagram  for  compression  of  the  small  weight  of 
cushion  steam  is  shown  in  Fig.  85  (b)  by  the  negative  area  kaa^g 
drawn  to  the  same  scale  as  before,  except  that  the  width  has 
been  reduced  in  proportion  to  the  weight  of  working  substance 
involved.     Here  it  is  assumed  that  the  steam  is  dry  at  the  be- 
ginning of  compression,  in  which  case  the  saturation  curve  S 
would  pass  through  the  point  k.     The  heat  lost  to  the  cylinder 
walls  during  compression  is  shown  by  the  area  under  ka,  and 
the  qualities  during  compression  can  be  readily  determined  in 
the  usual  manner  on  such  diagrams. 

In  Fig.  85  (c)  the  intercepts  between  a'g  and  ak  are  the  same 
as  those  between  the  similar  lines  in  Fig.  85  (b) ;  ab  is  the  line  for 
the  constant  volume  during  admission  (corresponding  to  ab  in 
Fig.  84) ,  and  fbcreg  is  the  same  as  in  Fig.  85  (a) .  The  area  abcrek 
evidently  approximately  represents  the  work  done  during  the 
actual  cycle. 

(e)  Obviously,  cr  is  the  only  part  of  the  diagram  that  shows 
the  true  behavior  of  all  the  steam  used  per  cycle;  for,  during  the 
other  parts  of  the  cycle,  only  a  part  of  the  steam  is  within  the 
cylinder.     As  the  T<£-diagram  is  ordinarily  used  in  connection 
with  the  actual  steam  engine,  it  is  assumed  that  if  x  parts  of  dry 
steam  are  present,  the  associated  heat  is  the  same  as  that  of 
all  the  steam  when  at  quality  x,  and  the  state  point  is  located 
on  the  diagram  accordingly.     This  is  fallacious,  since  x  (r  +  <z) 
is  not  the  equivalent  of    (xr-\-q).     Thus,    the   T0-diagram   is 
correct  only  for  the  expansion  process  (the  weight  of  material 
being  constant);  it  is  erroneous  to  use  it  quantitatively  for  the 
other  processes,  but  it  shows  in  a  general  way  what  interchanges 
occur  in  these  other  cases.     As  the  T<£-diagram  is  ordinarily 
interpreted,  it  would  be  said  that  while  tracing  the  line  from 
b  to  c  the  quality  would  be  increasing,  but  in  this  case  it  is  the 

*  The  reason  this  is  approximate  will  appear  later. 


ACTION  OF  STEAM  IN  REAL  ENGINES  217 

volume  of  the  vapor  that  is  increasing  in  the  cylinder,  while  at 
the  same  time  its  quality  is  usually  decreasing.  Again,  while 
ek  is  being  drawn,  the  volume  of  the  steam  in  the  cylinder  is 
decreasing,  and  the  quality  is  increasing. 

(f)  In  the  foregoing  discussion  the  upper  and  lower  temper- 
atures were  taken  as  those  occurring  in  the  cylinder  itself.  If 
isothermals  corresponding  to  the  boiler  and  condenser  temper- 
atures are  drawn  on  the  diagram,  the  added  areas  would  show 
the  losses  between  the  boiler  and  cylinder  and  between  the 
cylinder  and  condenser. 

118.  Derivation  of  a  T0-Diagram  from  a  PV-Diagram.  (a) 
First  Method.  On  the  PV-diagram  draw  the  saturation  curve 
for  the  total  weight  of  mixture  (w)  involved;  take  numerous 
points  around  the  diagram;  and  for  each  get  the  temperature 
(jT),  and  the  ratio  (X)  of  the  actual  volume  to  that  of  dry 
saturated  steam  as  given  by  the  saturation  line.  Note  that 
during  expansion  X  will  be  the  quality, 
while  during  other  parts  of  the  cycle  it  is 
simply  a  ratio  of  volumes. 

Prepare  a  T</>-chart  as  in  Fig.  86,  by 
drawing  the  water  and  saturation  curves. 
This  may  be  done  conveniently  by  using 
absolute  temperatures  and  entropies  of 
water  and  vapor  given  in  the  Steam  fig.  86. 

Tables,  the  entropies  being  multiplied  by  w 

before  plotting.  For  each  value  of  T  draw  the  isothermal  line  TC. 
Then  the  distance  AC  is  the  entropy  of  vaporization.  Locate 

the  point  B  on  A  C  in  such  position  as  to  make  -^  equal  to  the 

value  of  X  obtained  from  PV-diagram.  The  locus  of  points  B 
thus  found  will  be  the  desired  diagram. 

(b)  The  foregoing  applies  only  to  saturated    steam.     If  X 
should  be  greater  than  100  per  cent,  the  temperature  (T8)  of 
the  superheated  steam  must  first  be  found,  and  this  may  be 
done  by  using  Tumlirz's  formula  in  the  manner  explained  in 
Section  114  (c) ;  then  the  corresponding  point  Ba  (Fig.  86)  must 
be  located  in  the  region  of  superheat  on  the  pressure  line  P  at 
the  temperature  elevation   Ts. 

(c)  If  a  T0-chart  for  one  pound  instead  of  for  (w)  pounds 
is  constructed  like  Plate  I  in  the  Appendix,  it  may  be  used  for 


218 


HEAT-POWER  ENGINEERING 


the  derivation  of  a  T0-diagram  by  plotting  corresponding 
values  of  T  and  X  directly;  and  it  can  be  used  regardless  of 
the  weight  of  steam  involved,  thus  avoiding  the  construction 
of  a  new  chart  for  each  case.  It  must  be  remembered,  however, 
that  the  areas  on  such  diagrams  represent  the  heat  for  only  one 
pound  of  steam. 

(d)  Second  Method  (Graphical).  In  this  method  it  is  first 
necessary  to  prepare  a  Boulvin  Chart*  such  as  is  shown  in 
Fig.  87,  in  which  there  are  four  quadrants  with  related  co- 


Fig.  87. 

ordinates.  The  first  quadrant  (I)  is  for  temperature-entropy 
(T<£)  relationships;  the  second  (II)  for  temperature-pressure 
(TP);  the  third  (III)  for  pressure-volume  (PV);  and  the  fourth 
(IV)  for  entropy- volume  (0V). 

(e)  In  the  PV-quadrant  let  the  saturation  curve  ssf ,  for  the 
weight  of  steam  w,  be  drawn  with  any  convenient  scales  for  the 
pressures  and  volumes.  Then,  in  the  PT-quadrant,  plot  a 
curve  showing .  the  pressure-temperature  relation  for  saturated 
steam,  using  the  same  pressure  scale  as  before  and  any  suitable 
one  for  absolute  temperatures.  Next,  in  the  T0-quadrant, 
using  the  same  temperature  scale  and  any  convenient  one  for 
entropy,  construct  the  curves  for  water  and  for  saturated  steam. 
Then  for  any  pressure  p,  the  chart  shows  that  the  volume  of 
the  saturated  steam  is  ps\  that  the  temperature  is  pz  =  ot\ 

*  "  Entropy  Diagram,"  by  J.  Boulvin,  published  by  Spon  and  Chamberlain. 


ACTION  OF  STEAM  IN  REAL  ENGINES  219 

that  the  entropy  of  the  water  is  tf\  and  that  the  entropy  of 
vaporization  is  fS. 

(f)  While  steam  is  being  generated,  the  entropy  of  vaporization 
increases  uniformly  with  the  volume  of  vapor  formed.     For  the 
particular  pressure,  p,  under  consideration,  this  relation  may  be 
shown  in  the  remaining  fourth  quadrant  (IV)  by  the  straight 
</>V-curve  fiSi.     This  curve  is  obtained  by  projecting  downward 
from  the  points  /  and  5  on  the  T<£-diagram  and  by  making  gfi  = 
the  volume  occupied  by  the  water  =  w  X  0.017,*  and  hSi  =  ps  = 
(the  volume  of  w  pounds  of  dry  saturated  vapor).     To  complete 
the  chart,  similar  <£V  lines  must  be  drawn  for  each  of  the  other 
pressures  used. 

(g)  On  this  chart  the  actual  PV-diagram  can  now  be  drawn  in 
the  PV-quadrant  (III)  and  from  it  the  corresponding  T<£-diagram 
can  be  obtained  by  simple  projection.     For  example,  starting 
with  the  points  u  and  U  (at  the  pressure  p)  on  the  PV-diagram, 
project  horizontally  to  the  <£V-curve,  fiSi,  for  that  pressure,  and 
thence  upward  to  intersect  the  corresponding  isothermal  line  at 
HI  and  Ui.     The  points  thus  found  are  on  the  T$-diagram  desired 
and  other  points  can  be  located  in  a  similar  manner.     By  passing 
curves  through  the  points,  the  complete  diagram  is  obtained. 

(h)  With  superheated  steam,  this  construction  does  not  apply, 
and  in  this  case  the  procedure  would  be  that  outlined  in  (b)  of 
this  section, 

(i)  If  a  Chart  for  One  Pound  of  Steam  is  constructed,  it  may  be 
used  for  any  case  regardless  of  the  weight  (w)  of  steam  involved. 

Then,  however,  the  volumes  to  be  used  on  the  chart  are  f  —  Jth 

of  the  actual  volumes  occupied  by  the  steam  in  the  cylinder;  and 
the  areas  represent  the  work,  or  heat,  for  only  one  pound  of  steam. 

119.  Hirn's  Analysis,  (a)  If  certain  data,  which  can  readily 
be  obtained  during  an  engine  test  and  from  the  indicator  dia- 
gram, are  available,  the  numerical  values  of  the  heat  interchanges 
between  the  cylinder  walls  and  the  steam  can  be  calculated  by 
a  method  originated  by  Him  (in  1876)  and  formulated  later  by 
Dwelshauvers-Dery. 

With  such  information  before  him,  the  engineer  can  analyze 
the  distribution  and  extent  of  the  losses  in  each  case,  and,  by 
comparing  these  results  with  those  obtained  with  the  best  engines, 
*  This  is  too  small  to  be  scalable,  but  is  shown  exaggerated  in  Fig.  87. 


220  HEAT-POWER  ENGINEERING 

he  can  determine  wherein  improvements  can  be  made  in  the 
engine  he  is  considering. 

(b)  With  the  weight  of  steam  per  cycle,  and  the  pressure  and 
quality  of  steam  known  at  any  two  points  (i  and  2)  in  the  cycle, 
the  associated  heat  (Hi  and  H2)  present  in  the  steam  at  those 
points  can  be  computed.     Then  (Hi  —  Hz),  if  positive,  is  the 
heat  surrendered  by  the  steam  between  the  two  points;  and  if 
negative,  it  is  the  heat  the  steam  receives.     The  B.t.u.  work  (A) 
actually  done  between  points  I  and  2  of  the  cycle  is  shown  on  the 
indicator  diagram  by  the  area  below  the  cycle  line  between  those 
points  and  extending  to  the  line  of  absolute  zero  pressure.     Of 
course,  if  all  the  heat  that  is  available  is  converted  into  work, 
A  will  equal  (Hi  —  H^).     In  the  actual  case,  however,  there  is 
some  heat  interchange  between  the  cylinder  walls  and  the  steam. 
Thus,  if  A  is  less  than  (Hi  —  H2),  the  steam  has  lost  heat  to  the 
cylinder  walls  equal  to  the  difference;  and  if  A  is  greater,  heat 
has  been  surrendered  by  the  walls  to  the  steam  and  has  been 
converted  into  work. 

(c)  The  data  needed  for  Hirn's  analysis  are: 

(1)  The  weight   (w/)  of  "  cylinder  feed  "  per  cycle  and  its 
quality  (x/)  as  it  enters  the  cylinder,  as  determined  by  test  of 
engine.     This  gives  means  of  computing  the  heat  H/  supplied 
by  the  entering  steam. 

(2)  The  weight  of  "  cushion  steam  "  (wk)  per  cycle  and  its 
quality  (%k)  at  the  beginning  of  compression. 

(3)  An    average    indicator    card,    with     PV-axes,    saturation 
curve,  and  quality  curve,  as  in  Fig.  88  (a)  and  (b). 

(4)  The  B.t.u.  equivalent  of  work  per  cycle  as  determined  from 
the  areas  Aaj  Ac,  Ar,  Ae,  and  Ak  on  the  diagram,  Fig.  88  (c)  and  (d). 

(5)  The  heat  (K^  in  the  water  of  condensation,  and  the  heat 
(Kz)  carried  away  by  the  condensing  water,  supposing  a  surface 
condenser  is  used. 

The  leakage  must  be  practically  zero  and  is  considered  such  in 
this  analysis.  Account  must  also  be  taken  of  the  fact  that 
during  the  reception  of  steam  at  constant  pressure,  the  A  Pu 
quantity  is  abstracted;  thus  throughout  expansion  and  com- 
pression the  heat  in  the  stearnjs  (xp  +  q)  instead  of  (xr  +  q)_  for 
saturated  steam,  and  is  (X  +  CPD  —  APtis)*  instead  of  X  +  CPD, 

"Here  us  =  (V8  —  0.017)  =  the  increase  in  volume  accompanying  the  forma- 
tion of  superheated  steam  from  one  pound  of  water,  i.e.,  it  is  the  increase  of  volume 
during  vaporization  and  during  superheating. 


ACTION  OF  STEAM  IN  REAL  ENGINES 


221 


for  superheated  steam.  This  also  is  true  of  the  steam  contained 
in  the  cylinder  at  each  point  in  the  cycle,  because  at  some  time 
before  the  point  is  reached  the  piston  has  moved  out  against 
resistance  to  make  available  the  necessary  volume  and  the  APu 
quantity  has  thus  been  utilized. 

(d)  During  the  first  part  of  the  cycle,  heat  (Hf)  is  supplied 
by  the  entering  steam  (cylinder  feed)  and  this  is  added  to  the 
heat  (Ha)  in  the  cushion  steam  at  the  end  of  compression. 

The  heat  associated  with  ("  in  ")  the  entering  "  cylinder  feed  " 
is,  in  the  case  of  saturated  steam,  , 

Bt-wtbr  +  gfiWVffitQ    (242) 
and  for  superheated  steam  is 

Hf  =  w,(\+CpD)f  ......     (243) 


At  k  (Fig.  88)  the  steam  is  assumed  to  have  100  per  cent  quality, 
as  explained  in  Section  113  (b);  hence  the  weight  of  the  cushion 

steam  is  Wk  =  */  ,  where  Vk  is  the  absolute  volume  at  k  and  V*  is 
V& 

the  specific  volume  for  the  pressure  at  that  point. 


V 

Fig.  88. 

The  weight  of  that  part  of  the  cylinder  content  that  is  in  the 
form  of  vapor  at  a  is  similarly  wa  =  y2 .     Hence  the  quality  at  a 

is  Xa  =  —  and  the  heat  in  the  steam  at  this  point  is 

Wk 

Ha    =  Wk  (XP  +  q)a.      --  •*<"   •        •        (244) 

Then  at  the  end  of  admission  (point  c)  the  heat  in  the  steam  is 

Hc  =  (wk  +  wf)  (#p,+  q)e,     _•_  •     -     •     (245) 
in  which  xc  is  found  from  the  quality  curve~(Fig.  88  (&)). 


222  HEAT-POWER  ENGINEERING 

The  work  in  B.t.u.  per  cycle  actually  done  on  the  piston  during 
admission  is  Aa,  as  determined  from  diagram  Fig.  88  (c);  and 
the  heat  given  up  by  the  steam  is  (H/  4-  Ha)  —  Hc',  hence  the 
heat  interchange  during  admission  is 

La   =    (Ha  +   Hf)    -He-Aa.         .        .        (246) 

A  positive  result  indicates  that  heat  is  lost  to  the  cylinder  and 
a  negative  one  shows  that  the  steam  has  received  heat  from  the 
cylinder.  The  same  will  be  true  for  the  other  equations  for  heat 
interchange  that  follow. 

The  proportion  of  heat  that  is  interchanged  is  La  -f-  (Ha  +  Hf 
—  He),  and  this  is  a  close  measure  of  the  proportion  of  steam 
that  is  condensed,  that  is,  it  is  a  measure  of  the  "  initial  conden- 
sation." 

(e)  At  the  beginning  of  expansion  the  heat  in  steam  (at  c)  is 
Hc  from  Eq.  (245). 

The  heat  in  steam  at  r  is 

Hr  =  (wk  +  wf)  (xp  +  q)r,     ...     .     (247) 

in  which  xr  is  obtained  from  the  quality  curve  in  Fig.  88  (b). 

The  work  in  B.t.u.  actually  done  during  expansion  is  deter- 
mined from  area  Ac  on  the  diagram. 

Then  the  net  heat  transfer  from  steam  to  cylinder  wall  during 
expansion  is 

Lc  =  (He-  Hr)  -Ac.       .     .     t;   .     (248) 

A  negative  result  indicates  that  the  steam  receives  heat  from  the 
cylinder  wall. 

Note  that  the  loss  between  cut-off  and  any  other  point  on  the 
expansion  line  can  be  computed  in  a  similar  manner;  thus  it  is 
possible  to  determine  the  interchanges  between  cut-off  and  all 
points  throughout  expansion. 

(f)  If  the  exhaust  steam  is  condensed  in  a  surface  condenser, 
the  condensate  (of  temperature  /«)  per  cycle  will  contain  heat 
above  32  degrees, 

KI  =  Wf  (te  —  32°),  or  more  accurately  =  wfqe\  .     (249) 

and  the  condensing  water  (of  weight  wx  per  cycle,  with  initial 
temperature  /0  and  discharge  temperature  td)  will  take  away 
heat, 

%2  =  ivx  (td  —  /0),  or  more  accurately,  =  wx  (qd  —  qQ).     (250) 


ACTION  OF  STEAM  IN   REAL  ENGINES  223 

Between  r  and  k,  the  steam  for  a  while  does  work,  as  shown 
by  A  r  on  the  indicator  diagram;  afterwards  work  is  done  upon 
it,  as  shown  by  Ae.  At  r  the  heat  in  the  steam  is  Hr  (from 
Eq.  (247)),  and  at  k  there  is  left  in  the  steam  Hk  =  Wk  (p  +  <z)*, 
since  Xk  is  taken  as  unity. 

Hence  the  heat  interchange  during  exhaust  is 

Le  =  (Hr  -  Hk)  -  (K,  +  K2)  -  (Ar  -  Ae),    ~.     (251) 

in  which  positive  and  negative  results  have  the  same  meanings 
as  explained  in  connection  with  Eq.  (246). 

(g)  If  the  steam  is  exhausted  to  the  atmosphere,  the  heat 
discharged  is  indeterminate.  An  approximation  can  be  made  if 
the  mean  quality  of  the  exhaust  steam  is  known,  but  it  cannot 
be  computed  accurately  because  the  weight,  pressure,  and 
quality  of  steam  are  variable  throughout  the  exhaust  period. 

(h)    During  compression  the  change  of  associated  heat  is 

(Hk   ~    Ha), 

inwhich  Hk=wk(P+q)k  ......  .    .     (252) 


Ha=Wk(xp+q)a      .      .:.;;•       .        •        (253) 

The  work  actually  done  upon  the  steam  per  cycle  is  shown 
by  Ak.  Hence  the  heat  interchange  during  compression  is 

Lk  =  Hk  -  Ha  +  At,      .     .'  '.     .     .     (254) 

in  which  the  sign  of  Lk  has  the  same  meaning  as  before. 

(i)  Ideally,  the  heat  given  to  the  cylinder  walls  should  equal 
that  given  up  by  them  to  the  steam.  Actually,  in  the  case  of  an 
ordinary  engine,  the  heat  given  up  is  less  than  that  received, 
and  this  is  because  of  conduction  and  radiation.  Evidently, 
the  conduction  and  radiation  loss  in  B.t.u.  per  cycle  is 

R=La  +  Lc  +  Lr  +Lk.      .     .     .         (255) 

(j)  If  the  steam  is  initially  superheated,  the  analysis  would 
be  carried  through  in  a  manner  similar  to  that  just  given.  If 
the  engine  is  steam-  jacketed  (Section  129),  or  is  a  compound 
engine  with  reheating  receivers  (Section  130),  account  must  be 
taken  of  the  heat  furnished  by  the  jacket  steam. 

120.  Experimental  Determination  of  the  Actual  Performance 
of  Steam  Engines,  (a)  The  indicated  horse  power  of  an  engine 
can  be  determined  from  the  indicator  diagram,  if  the  diameter 


224  HEAT-POWER  ENGINEERING 

of  cylinder,  length  of  stroke,  and  r.p.m.  of  the  engine  are  known. 
The  delivered  horse  power  can  be  measured  by  a  Prony  brake 
or  other  form  of  dynamometer  and  in  other  ways  which  need 
not  be  considered  here.  The  mechanical  efficiency  of  the 
engine  and  power  lost  in  engine  friction  can  then  be  calculated. 
The  total  amount  of  steam  used  per  hour  may  be  determined 
by  weighing  the  water  pumped  to  the  boiler  which  supplies  the 
engine,  making  proper  allowance  for  loss  or  withdrawal  of 
working  substance  between  the  pump  and  the  engine;  or  it 
may  be  found  by  weighing  the  condensate,  if  a  surface  conden- 
ser is  used,  and  making  correction  for  leakage.  The  weight  of 
steam  used  per  h.p.-hr.,  or  Water  Rate,  can  then  be  obtained 
as  in  Section  106. 

(b)  If  these  measurements  are  made  for  a  range  of  loads  on 
the  engine,  the  resulting  data  can  be  used  in  plotting  curves  of 
Total  Consumption  of  Steam  (TC)  and  of  Rate  of  Consumption 
(R),  as  in  Fig.  71.     These  curves  show  the  performance  of  the 
engine  under  all  conditions  of  loading,  and  determine  the  power 
output  at  which   the  engine  operates  most  economically.     The 
curve  of  total  consumption  is  usually  nearly  straight.     If  the 
abscissas   are  d. h.p.-hr.,  the  Y-intercept  shows  the  steam  used 
in  overcoming  the  friction  of  the  engine  alone. 

(c)  If  two  engines  receive  steam  of  the  same  pressure  and 
quality,  their  relative  performance  is  shown  by  comparing  their 
Water  Rates.     In  other  cases  the  only  true  measure  of  econ- 
omy is  on  the  basis  of  heat  used  per  unit  of  power,  and  in  order 
to  determine  the  heat  in  the  steam  as  it  enters  the  engine  the 
quality,  or  superheat,  must  be  known. 

The  quality  of  the  steam  can  be  determined  by  using  instru- 
ments which  will  be  described  in  the  next  section. 

121.  Steam  Calorimeters.*  (a)  The  apparatus  used  to  de- 
termine the  quality  of  steam  is  called  a  "  steam  calorimeter." 
There  are  several  kinds  of  calorimeters,  which  will  be  considered 
very  briefly. 

The  Barrel  Calorimeter. 

(b)  If  into  a  barrel  containing  water,  of  known  weight  (W) 
and  temperature  (/i),  a  sample  of  the  steam' is  piped,  and  con- 

*  For  more  detailed  discussion  see  Carpenter  and  Diederichs'  "  Experimental 
Engineering,"  published  by  John  Wiley  &  Sons. 


ACTION  OF  STEAM  IN  REAL  ENGINES 


22$ 


densed,  and  if  the  increase  (w)  in  weight  of  water  and  the  result- 
ing temperature  (k)  are  measured  simultaneously,  there  are  suf- 
ficient data  for  determining  the  quality  of  the  sample  of  steam, 
provided  the  steam  pressure  is  known. 
The  heat  given  up  by  the  steam  is 


and  that  received  by  water  is 
Aft  = 

assuming  Cp  of  the  liquid  as  unity. 
which  the  quality  is  found  to  be 


Evidently  Aft  =  Aft,  from 


_ 

00   ~~~ 


wr 


(256) 


Correction  should  also  be  made  for  conduction 
and  radiation  losses  in  accurate  work. 

The  Separating  Calorimeter. 

(c)    In  using  the  Separating  Calorimeter  (Fig. 
89) ,  a  sample  of  steam  is  first  led  to  the  sepa- 
rating chamber  C,  where  the  moisture  is  thrown 
out  and  collected  (the  amount  w  being  shown 
by  the  gauge  glass  G),  then   the  resulting  dry         To Wa'ter  Cmv 
steam  passes  into  the  jacket  /  and  out  through 
the  orifice  0  to  a  can  of  water  in  which  it  is  condensed  and  its 
weight  W  determined.     Using  simultaneous  values  of  w  and  W, 
the  quality  evidently  is 

W 

(257) 


x  = 


w  +  W 


The  Throttling  Calorimeter. 

(d)  In  this  case  a  sample  of  wet  steam  is  passed  through  the 
device  shown  in  Fig.  90,  and  is  superheated  by  being  throttled 
through  the  valve  V  while  expanding  into  the  cup  C,  where  the 
pressure  is  low. 

This  pressure  is  usually  nearly  atmospheric  when  high-pressure 
steam  is  being  sampled.  If  the  sample  of  steam  is  at  pressure 
near  or  below  that  of  the  atmosphere,  the  cup  may  be  connected 
with  a  condenser  to  obtain  a  sufficiently  low  pressure  therein. 

The  temperature  te  of  the  superheated  steam  in  this  cup  C  is 


226 


HEAT-POWER  ENGINEERING, 


measured  by  the  thermometer  T;  and  the  degrees  of  superheat  D 
are  found  by  subtracting  from  ta  the  saturation  temperature  4 
corresponding  to  the  cup  pressure  shown  by  the  manometer. 
The  expansion  through  the  valve  causes  the  jet  of  steam  to 
acquire  a  high  velocity  at  that  point,  hence  some  of  the  associated 
heat  is  converted  into  kinetic  energy.  In  the  cup,  the  velocity 
of  steam  is  reduced  and  this  kinetic  energy  is  reconverted  into 
associated  heat.  If  the  velocity  in  the  cup,  where  the  tempera- 
ture t,  is  measured,  is  the  same  as  that  in  the  main  steam  pipe 
(which  is  usually  approximately  true),  and  if  there  are  no  radia- 


Height  of 


tion  or  conduction  losses  (and  these  are  usually  almost  negligible), 
the  associated  heat  is  the  same  before  and  after  the  steam  passes 
the  expansion  valve. 

Before  throttling,  the  amount  of  heat  per  pound  is 

Aft  =  xiri  +gi; 
afterward,  it  is 

Aft  =  X2  +CP  (D)  =  X2  +  0.48*  (/.  -  /2). 
Then  since 

Aft  =  Aft, 
the  quality  is  found  to  be 


*  For  cup  pressures  other  than  atmospheric  substitute  the  proper  value  of 
for  0.48. 


ACTION  OF  STEAM  IN  REAL  ENGINES  227 

The  Electric  Calorimeter. 

(e)  In  using  this  calorimeter  the  sample  of  wet  steam  is  dried 
by  letting  it  flow  over  coils  of  wire  which  are  heated  by  an  elec- 
tric current,  the  energy  input  being  measured  by  a  wattmeter. 
The  watts  are  gradually  increased  until  a  value  E  is  reached  at 
which  the  thermometer  in  the  calorimeter  outlet  starts  to  rise, 
which  is  supposed  to  show  that  all  moisture  has  been  dried  by 
the  heat  from  the  coils,  by  expending  an  amount  of  heat  corre- 
sponding to  E.     If  the  quantity  of  mixture  (w)  flowing  through 
the  calorimeter  in  a  given  time  is  weighed,  or  otherwise  deter- 
mined, the  heat  (h)  added  to  dry  one  pound  of  the  steam  can  be 
computed  from  the  electrical  input.     Then 

r  —  h  , 

^  =    -7- (259) 

The  Degrees  of  Superheat. 

(f)  This  is  determined  by  subtracting  the  saturation  tempera- 
ture, for  the  existing  pressure  (as  shown  by  a  pressure  gauge), 
from  the  actual  temperature  of  the  steam,  as  shown  by  a  ther- 
mometer placed  in  the  steam. 

122.  Weight  of  Steam  Accounted  for  by  the  Indicator 
Diagram,  (a)  Not  only  is  it  possible  to  draw  a  theoretical  PV- 
diagram  for  a  given  weight  of  steam  per  cycle,  as  has  already 
been  done,  but  obviously,  if  a  diagram  is  given  and  the  scale  of 
volumes  is  known,  it  is  possible  to  determine  the  theoretical 
weight  of  steam  that  the  given  cycle  would  use.  This  not  only 
applies  to  theoretical  diagrams,  but  also  to  actual  ones.  The 
theoretical  weight  of  dry  steam  per  actual  cycle  can  be  found  in 
exactly  the  same  way  as  for  the  theoretical  cycle.  The  ratio  of 
what  is  called  the  "  Steam  Accounted  for  by  the  Diagram," 
"  Indicated  Steam  Consumption,"  or  "  Diagram  Steam,"  to  the 
steam  actually  used  by  the  engines  is  useful  in  showing  the  per- 
fection of  performance  within  an  engine  cylinder.  This  ratio  can 
be  easily  obtained,  and  the  difference  between  the  weight  of  dry 
steam  actually  used  and  the  theoretical  is  the  amount  liquefied 
by  cylinder  condensation. 

In  the  actual  case  it  is  convenient  to  consider  the  working  sub- 
stance within  the  cylinder  as  a  mixture  of  dry  steam  and  water. 
The  indicator  diagram  shows  the  behavior  of  the  vapor  only. 


22g  HEAT-POWER  ENGINEERING 

(b)   Suppose  the  clearance  line  and  zero-pressure  line,  that  is, 
the  PV-axes,  have  been  drawn  on  an  actual  diagram,  Fig.  91. 

Then  let  Vz  be  the  volume  as  scaled 
to  some  point  z  on  the  expansion 
line,  between  cut-off  and  release* 
and  let  Vz  be  the  specific  volume  at 
the  corresponding  pressure.  Then 
the  total  indicated  weight  of  dry 
vapor  in  the  cylinder  at  that  time  is 

Fig.  91.  w,  =y£.    .     •       (260) 

Similarly,  at  any  point  k  on  the  compression  line  the  weight  of 
dry  "  cushion  "  steam  is 

wk=~^,    .......     (261) 

in  which  Vk  is  the  actual  volume  as  scaled  to  point  k  and  V*  is 
the  specific  volume  for  that  pressure. 

Subtracting  the  cushion  steam  from  the  total  in  the  cylinder 
gives  the  indicated  cylinder  feed  (w/)  per  cycle;  thus 

»/  =  (w.  -  «fc)  =     -     .  .    .   ;   .    (262) 


As  the  quality  changes  during  expansion  and  compression,  the 
value  of  w/  will  depend  on  the  locations  of  points  z  and  k.  It 
is  customary  to  take  z  either  near  the  beginning  or  near  the  end 
of  expansion,  and  k  is  usually  assumed  near  the  beginning  of 
compression. 

(c)    Now  let  yc  =  clearance  volume  -5-  piston  displacement  per 

stroke  =  -j  in  Fig.  91, 

yz  —  fraction  of  stroke  completed   corresponding 
to  any  point  on  the  diagram 

a  =  area  of  piston  in  square  inches. 
pm  =  m.e.p. 
L  =  stroke  in  feet. 
n  =  number  of  cycles  per  minute. 

Then  the  piston  displacement  in  cubic  feet  per  stroke  is(  -  ) 

\I44/ 


ACTION  OF  STEAM  IN  REAL  ENGINES  229 

and  the  volume  of  vapor  when  any  fraction  yz  of  the  stroke  is 
completed  is 


Substituting  this  and  a  similar  value  for  the  volume  Vk  in 
Eq.  (262)  gives  for  the  number  of  pounds  of  Indicated  Cylinder 
Feed,  per  cycle, 

,  _  aL  ty.  +  yc      yk  +  ye\  (       , 

-^-       -~ 


Multiplying  this  by  (60  X  n)  cycles  per  hour  and  dividing  by 

r—  —  ),  gives  the  number  of  pounds  of  steam  per  i.h.p.-hr., 
33>ooo/ 

or  "  Diagram  Water  Rate,"  as 

W,  -  I3>75°  (y*  +  y°  -  yk  +  y*\ 

pm    (    V,  V,     /' 

If  points  z  and  k  are  taken  at  the  same  pressure  level,  p,  then 
V2  =  V,  =  Vp  and 

tty*  +  yJ  -(?*  +  *)!  =  '3v5v  (y.-y*)-  (265) 

W  p  pm  A    Vp 

If  the  pressure  is  taken  as  that  at  the  end  of  compression, 
then  yk  =  o  and 

*  ......    (266) 


(d)  If  W  =  xi  X  cylinder  feed,  represents  the  dry  steam 
actually  supplied  per  i.h.p.-hr.  and  W*  is  the  indicated  water 
rate  corresponding  to  the  point  2  located  at  the  cut-off,  the 
"  Cylinder  Condensation,"  or  weight  of  steam  condensed  by 
the  cylinder  walls  and  that  lost  by  leakage,  is  approximately 
(W  —  Wd)  per  i.h.p.-hr.;  and  the  proportion  of  the  whole  that  is 
condensed,  or  "  Condensation  Fraction,"  is 

CF  =  (W  -  Wd)  -5-  W.       ...    ,     (267) 

If  the  Condensation  Fraction,  or  "  Per  cent  Cylinder  Con- 
densation," is  known  for  a  certain  type  of  engine  under  certain 
operating  conditions,  then,  in  considering  a  prospective  engine 
of  this  class,  the  probable  water  rate  under  the  same  conditions 
can  be  estimated  by  dividing  the  theoretical  diagram  water  rate, 
found  from  the  probable  diagram,  by  (1  —  CF). 


CHAPTER  XVI. 

METHODS  OF  DECREASING   CYLINDER   CONDENSATION. 

123.  Condensation  and  Leakage,     (a)    It  has  already  been 
shown  that  the  cylinder  condensation  causes  the  largest  loss  in 
the  steam  engine,  with  the  exception  of  that  inherent  in  the 
theoretical    cycle.     Condensation    is    evidently    dependent    on, 
but  not  necessarily  proportional  to,  (i)  the  ratio  between  the 
condensing  surface  (5),  to  which  the  steam  is  exposed,  and  the 
volume  of  steam  used  per  cycle;   (2)  the  temperature  differ- 
ence (T)  between  the  entering  steam  and  the  surfaces;  and  (3) 
the  time  (t)  of  exposure,  which  is  inversely  proportional  to  the 

number  (n)  of  cycles  (i.e.,  to  -j.  For  computing  the  probable 
steam  consumption  many  formulas  have  been  proposed  in- 
volving functions  of  S,  T,  /,  or  -,  and  numerical  coefficients 

determined  from  experimental  data.  Such  formulas  are  suffi- 
ciently accurate  for  ordinary  purposes,  when  there  is  no  leakage 
past  piston  and  valves.* 

(b)  Unfortunately,  while  it  is  possible  to  determine  experi- 
mentally whether  or  not  leakage  does  occur,  the  amount  of 
leakage  per  cycle  cannot  be  closely  evaluated ;  thus  it  is  impossible 
to  separate  the  loss  due  to  leakage  from  that  due  to  condensa- 
tion. Hence  cylinder  condensation  and  leakage  must  be  con- 
sidered together. 

Formulas  for  cylinder  condensation  should  be  derived  from 
a  study  of  data  from  engines  that  are  known  to  have  little  or  no 
leakage.  Unfortunately,  most  of  the  data  available  are  from 
engines  which  were  not  tested  for  tightness  of  valves  and  pistons 
and  hence  are  unsuitable  for  the  purpose. 

124.  Size    and    Proportions   of   [Cylinder,     (a)  The    size    of 
cylinder  has  an  important  influence  on  the  cylinder  condensa- 
tion.    It  can   be  shown  by   computation  that  Jarge  cylinders 

*  For  formulas  and  data  see  Heck's  "Steam  Engine,"  and  Thurston's  "Manual 
of  the  Steam  Engine." 

230 


METHODS  OF  DECREASING  CYLINDER  CONDENSATION     231 

have  a  smaller  ratio  of  surface  to  volume  inclosed  than  have 
small  cylinders  of  the  same  proportions.  It  is  therefore  to  be 
expected  that  large  engines  will  have  less  cylinder  condensation 
and  consequently  will  give  better  economy  than  small  ones; 
and  that  is  actually  the  case.  Very  small  engines  may  use 
twice  as  much  as,  or  even  more,  steam  per  i.h.p.-hr.  than  very 
large  ones  of  the  same  proportions  and  same  conditions  of 
operation. 

(b)  The  amount  of  surface  in  the  clearance  space  (including 
that  of  the  steam  passages  between  valves  and  cylinder)  has 
a  predominating  influence  on  the  amount  of  cylinder  condensa- 
tion that  takes  place;  for,  just  after  admission,  the  piston  is 
moving  so  slowly  that  the  time  of  exposure  of  the  steam  to  these 
surfaces  is  comparatively  long,  hence  the  amount  of  condensation 
that  occurs  is  large.     Probably  the  greater  part  of  the  cylinder 
condensation    occurs    in    the    clearance    space.     The    cylinder 
passages  and  clearance  space  should  therefore  be  designed  to 
present  the  minimum  amount  of  surface  consistent  with  the 
other  considerations  involved. 

(c)  The    cylinder    condensation    is    also    dependent    on   the 
length  of  stroke  of  the  engine.     If  long  and  short  cylinders  are 
of  the  same  diameter  and  have  their  passages  and  clearance  space 
identically  the  same,  and  cut-off  steam  at  the  same  per  cent  of 
stroke,   obviously  the  ratio  of  clearance  surface  to  the  total 
surface  exposed  per  stroke  of  the  engine  is  smaller  in  the  long- 
stroke  engine  than  in  the  one  with  shorter  stroke.     Neglecting 
the  time  element,   the   long-stroke  engine  should    give  better 
economy  than  the  short-stroke  one;  and  in  general  that  is  the 
case,  though  this  is  in  part  due  to  the  fact  that  the  long-stroke 
engines  are  usually  also  larger,  have  cylinders  that  are  better 
designed,  and  have  better  valve  gear  than  those  with  shorter 
stroke. 

The  time  element  may  have  an  important  influence,  however; 
for  example,  due  to  the  fact  that  most  of  the  condensation 
occurs  in  the  clearance  space  and  because  of  the  shorter  time  of 
exposure,  some  of  the  short-stroke  "  high-speed  "  Corliss  engines 
give  as  good  or  even  better  economy  than  the  long-stroke  low- 
speed  Corliss  engines. 

(d)  In  many  engines  the  exhaust  steam  flows  over  the  outer 
surface  of  the  cylinder  wall,  on  its  way  to  the  exhaust  pipe. 


232 


HEAT-POWER  ENGINEERING, 


100 


CyL  Conde 
/ 

^"'1 

/ 

Mixture 

DryS 

inCy 
team 

*f  (a) 

10     20 


30     40     60     60     70 
$  Cutoff 


(6) 


Because  of  the  high  velocity  of  flow,  this  steam  carries  away 
heat  more  rapidly  than  would  stagnant  air  in  contact  with  the 
same  surface.  This  lowers  the  mean  temperature  of  the  cylinder 
walls  and  increases  the  cylinder  condensation.  In  the  better 
designed  engines  the  exhaust  steam  is  not  brought  in  contact 
with  the  cylinder  walls  after  it  leaves  the  exhaust  valve. 

125.  Influence   of   Point   of   Cut-off,     (a)   As   most   of   the 
cylinder  condensation  occurs  in  the  clearance  space,  the  later 

the  cut-off  (or  the  greater  the  vol- 
ume of  steam  admitted  per  cycle), 
the  less  will  be  the  percentage  of 
steam  condensed,  although  the 
amount  may  be  greater,  (i)  The 
percentage  of  steam  not  condensed 
is  shown  in  Fig.  92  (a),*  by  the  or- 
dinates,  the  abscissas  being  percent- 
age of  stroke  at  cut-off.  (2)  The 
work  theoretically  done  per  pound 
of  steam  decreases  as  the  cut-off  is 
advanced  in  the  stroke  (because  of 
the  reduction  of  expansion),  hence 
the  theoretical  steam  consumption 
per  unit  of  work  is  greater  the  later 
the  cut-off  occurs,  as  shown  by  the 
brdinates  of  the  curve  in  Fig.  92  (b). 
(3)  Evidently,  dividing  the  theo- 
retical water  rate  per  h.p.-hr.,  Fig. 
92  (6),  by  the  percentage  of  steam 
not  condensed,  Fig.  92  (a),  will  give  the  true  consumption  at  the 
various  cut-offs.  The  values  of  the  actual  "water  rate,"  ob- 
tained in  this  way,  are  shown  by  the  lower  curve  in  Fig.  92  (c). 
Similar  "  water-rate "  curves  can  be  drawn  by  using  data 
obtained  by  direct  engine  test,  in  which  the  water  per  i. h.p.-hr. 
is  measured  with  engine  operating  under  different  loads  (i.e., 
different  cut-offs).  Usually  the  water  rates  are  plotted  with 
respect  to  power  output  instead  of  cut-offs. 

(b)    Inspection  of  the  water-rate  curve  makes  it  evident  that, 

*This  is  for  large  four-valve  engines  having  little  leakage.      $ee  "Engine 
Tests,"  by  G.  H.  Barrus. 


10  20 


1 

£ 
•3  + 


30  .40   50  60 
$  Cutoff 


10   20   30  40   50 
#  Cutoff 


Fig.  92. 


METHODS  OF  DECREASING  CYLINDER  CONDENSATION     233 

to  give  the  best  economy,  the  engine  should  be  operated  with  cut-off 
corresponding  to  the  lowest  point  on  this  curve. 

The  most  economical  cut-off  for  noncondensing  simple  slide- 
valve  engines  is  about  \  stroke,  and  for  simple  Corliss  engines 
it  is  between  |  and  i  stroke.  In  practice  these  are  the  cut-offs 
which  predominate. 

(c)  Usually  the  "  water-rate  curve  "  is  more  nearly liorizontal 
to  the  right  of  the  lowest  point  than  it  is  to  the  left  (as  in  Fig.  92), 
hence  it  is  better  to  "  overload  "  an  engine  than  to  "  underload  "  it. 

126.  Compounding  of  Cylinders,  (a)  By  using  earlier  cut-off 
the  amount  of  steam  used  per  h.p.-hr.  is  reduced  theoretically 
because  of  the  greater  expansion  of  the  steam.  But  it  was  seen 
in  the  case  of  the  simple  engine  that  cylinder  condensation 
becomes  excessive  with  very  early  cut-offs  because  of  the  greater 
temperature  range  and  thus  defeats  the  advantage  which  should 
be  gained  theoretically.  Therefore,  to  economically  use  larger 
expansions  than  are  possible  with  the  ordinary  simple  engine, 
the  cylinder  condensation  must  be  reduced  in  some  way.  It 
was  shown  in  Section  123  that  cylinder  condensation  can  be 
reduced  by  decreasing  the  surface  (especially  that  of  the  clear- 
ance space)  to  which  the  high  temperature  steam  is  exposed  and 
by  reducing  the  temperature  range  in  the  cylinder.  Both  of 
these  methods  can  be  combined  in  the  following  manner. 

(b)  Suppose  a  small  amount  of  steam  is  admitted  to  a  small 
cylinder  (say  with  J  the  piston  area  of  the  simple  engine)  and 
that  it  is  expanded  only  enough  to 
bring  the  temperature  TR  (Fig.  93) 
of  the  exhaust  steam  part  way  to 
that  of  the  simple-engine  exhaust 
(say  TR  is  halfway  between  T\  and 
T2  on  the  temperature  scale).  Let 
the  indicator  diagram  labelled  H.P. 
in  Fig.  93  represent  this  cycle.  Then, 
owing  to  the  smaller  cylinder  surface 


(especially  that    in   the   clearance),  Fig.  93. 

there  is  very  much  less  initial  and 

cylinder  condensation  in  this  case  than  if  the  same  weight  of 

steam  had  been  expanded  the  same  amount  in  the  cylinder  of 

the  large  simple  engine. 


234 


HEAT-POWER  ENGINEERING 


Now  let  the  steam  exhausted  from  the  small  cylinder  enter  one 
of  the  same  size  as  that  of  the  simple  engine,  and  let  it  be  further 
expanded  in  this  cylinder  until  the  back  pressure  of  the  simple 
engine  is  reached.  The  indicated  diagram  for  this  case  is  shown 
by  L.P.  in  Fig.  93.  During  this  expansion-the  temperature  range 
(  TR  to  jy  is  low,  hence  cylinder  condensation  is  also  small  here. 

(c)  It  is  evident  that  an  engine  operating  in  this  manner  will 
use  much   less  steam  per   h.p.-hr.  than  will  a  simple  engine; 
roughly,  it  uses  only  about  §  to  J  as  much.     The  best  economy 
with  the  simple  engine  is  obtained  when  the  steam  is  expanded 
in  the  cylinder  to  four  or  five  times  its  initial  volume.     In  an 
arrangement  such  as  has  just  been  described,   the  expansion 
giving  the  best  results  is  from  7  to  1 6  or  more,  depending  upon 
the  conditions  of  operation. 

(d)  When  an  engine  with  two  cylinders  is  arranged  to  operate 
in  the  manner  just  discussed,  it  is  called  a  "  Compound  Engine  " 
or   "  2X   Engine."     The  small   cylinder   is  named   the    "  high- 
pressure  (H.P.)  cylinder  "  and  the  large  one  is  the  "  low-pressure 
(L.P.)  cylinder." 

Other  engines  are  arranged  to  expand  the  steam  in  three  steps, 
or  stages,  using  in  succession  three  cylinders  that  progress  in 
size.  These  are  called  Triple -Expansion  Engines  ("  3X  "),  and 
the  cylinders  are  termed  respectively  the  "  high- pressure/' 
"  intermediate-pressure  (/.P.),"  and  the  "  low-pressure."  Triple- 
expansion  engines  use  considerably  less  steam  per  i. h.p.-hr. 
than  do  the  compound  engines. 

In  the  Quadruple-Expansion  Engine  ("4X"),  four  cylinders 
are  used  in  succession.  They  are  termed  the  H.P.  cylinder,  the 
11  first  intermediate  (I. PL),  the  second  intermediate  (I.P2.),  and  the 
L.P.  cylinder.  Quintuple  engines  have  been  made,  but  their 
number  is  very  small. 

Strictly  speaking,  the  term  "  Compound  Engine  "  includes  all 
multiple -expansion  steam  engines,  but  it  has  become  customary 
to  apply  it  only  to  those  with  two  cylinders. 

Multiple-expansion  engines  will  be  discussed  more  in  detail  in 
a  later  chapter. 

A  comparison  of  the  performance  of  simple,  compound,  and 
triple  engines  operating  under  the  same  conditions  is  shown  *  in 

*  See  report  of  test,  Carpenter,  Trans.  A.  S.  M.  E.,  Vol.  XVI.  Also  Thurston. 
A.  S.  M.  E.,  XVIII. 


METHODS  OF   DECREASING   CYLINDER  CONDENSATION     235 

Fig.  94.  The  triple-expansion  Corliss  engine  in  the  laboratories 
of  Sibley  College  was  tested  with  high-pressure  cylinder  operat- 
ing alone  as  a  simple  engine,  then  with  the  high  and  intermediate 
cylinders  acting  as  a  compound  engine,  and  finally  with  all  three 
cylinders  as  a  triple-expansion  engine.  The  results  are  shown  in 


uO 
30 

10 
0 

I 

"SIBLEY" 
CORLISS  ENGINE 
9"l6|'24"x  36" 
INITIAL  PRES.  135  LBS.  ABS. 
VACUUM  1O.8  LBS.  ABS. 
WITHOUT  JACKETS. 

i 

/ 

^r 

'^ 

,u 

•*>? 

Compc 

undJJ 

hi-^"*^r 

viple  __ 



"    13 

\ 





5           10          15          20           25          30           35          4C 
Ratio  of  Expansion 

Fig.  94. 

this  figure.  Larger  engines  and  those  with  jacketing,  super- 
heating, etc.,  would  give  better  results,  but  this  figure  shows  the 
relative  value  of  using  the  different  expansions. 

(e)  Hirn's  Analysis  can  be  applied  to  the  multiple-expansion 
engine,  each  cylinder  being  considered  independently.  The  data 
needed  for  such  an  analysis  (in  addition  to  those  required  in  the 
case  of  a  simple  engine)  include  the  quality  and  pressure  of  the 
steam  entering  and  leaving  each  cylinder,  the  weight  of  con- 
densate  "trapped  off"  from  each  receiver  and  the  weight  and 
condition  of  the  steam  condensed  in  the  reheating  coils  of  the 
receiver,  if  such  are  used.  It  is  then  possible  to  compute  the  heat 
in  the  steam  entering  and  leaving  each  cylinder  and  each  receiver. 
Thus  besides  being  able  to  analyze  the  heat  interchanges  and 
losses  of  each  cylinder  considered  separately,  the  same  thing 
can  also  be  done  for  each  receiver,  and  for  the  engine  as  a  whole. 

127.  Gain  Due  to  Condensing  the  Exhaust  Steam.  If  an 
engine  when  operating  "  noncondensing  "  (i.e.,  exhausting  to  the 


236  HEAT-POWER  ENGINEERING . 

atmosphere)  gives  the  indicator  diagram  shown  by  the  full  lines 
in  Fig.  95,  with  mean  effective  pressure  equal  to  pm,  then,  if  the 
back  pressure  line  is  lowered  (as  shown  dotted)  an  amount  equal 
to  pk  pounds,  the  area  of  the  indicator  dia- 
gram will  be  increased  as  shown,  the  mean 
effective    pressure   will    be    raised   to   pmk  = 
(pm  +  pk) ,  and  the  ratio  of  the  power  of  the 
engine  to  its  value  when  operating  non-con- 
densing  wjn   be    (pm  +  pk)  -f-  pm.      Theoreti- 
cally, however,  there   will  be   no   change  in 


Fig.  95.  the  amount  of  steam  required  nor  in  the 

quantity  of  heat  it  brings  to  the  engine. 

By  condensing  the  exhaust  steam  in  a  "  condenser  "  (which, 
being  supplied  constantly  with  cold  water,  acts  as  a  "  cold 
body  "  in  maintaining  a  low  temperature),  the  pressure  of  the 
exhaust  steam  can  be  reduced,  —  and  its  value  will  be  that 
corresponding  to  the  condenser  temperature.  The  reduction 
in  pressure  below  atmospheric  may  be  from  10  to  14  pounds,  or 
even  more. 

Evidently,  in  developing  the  same  power,  a  "  condensing 
engine  "  would  be  much  smaller  than  one  operating  noncondens- 
ing,  other  things  being  equal.  However,  owing  to  the  additional 
cost,  operating  expense,  increased  cylinder  condensation,  and 
attention  involved  with  a  condensing  outfit,  it  is  seldom  used 
with  simple  engines.  Multiple-expansion  engines,  however,  are 
more  commonly  operated  condensing  than  not. 

128.  Effect  of  Superheated  Steam,  (a)  The  cooling  of  the 
cylinder  walls  during  exhaust  is  largely  due  to  their  surrender  of 
the  heat  used  in  evaporating  the  moisture  on  their  surfaces.  As 
the  latent  heat  of  vaporization  corresponding  to  the  exhaust  pres- 
sure is  very  large,  roughly  1000  B.t.u.  per  pound,  the  evaporation 
of  a  small  amount  of  water  results  in  a  very  considerable  reduc- 
tion of  the  mean  temperature  of  the  cylinder  walls  and  conse- 
quently in  an  increase  in  the  cylinder  condensation  when  the 
steam  is  admitted. 

When  superheated  steam  is  used  there  is  less  moisture  in  the 
exhaust  steam,  and  partly  because  of  this,  partly  because  of  the 
slow  rate  of  heat  transfer  between  superheated  steam  and  metal, 
and  partly  because  the  incoming  superheated  steam  can  give 


METHODS  OF  DECREASING  CYLINDER   CONDENSATION     237 

up  heat  without  condensing,  the  cylinder  condensation  is  reduced, 
and  the  economy  of  the  engine  is  improved.  Thus  by  sacri- 
ficing superheat  to  heat  the  cylinder  walls,  less  heat  is  required 
at  the  boiler  for  evaporating  the  water  and  for  superheating 
the  steam  used.  It  is  even  possible  to  superheat  sufficiently 
high  to  prevent  all  initial  condensation.  In  general,  however, 
it  seems  probable  that  superheat  should  not  be  so  high  that  the 
exhaust  steam  is  superheated;  although  there  is  some  doubt  as 
to  this,  for  one  engine  test  showed  better  results  with  exhaust 
slightly  superheated  than  when  just  dry.* 

In  experiments  by  Ripper f  on  a  small  steam  engine,  it  was 
found  that  7J°  F.  of  superheat  would  prevent  one  per  cent  of 
cylinder  condensation.  The  specific  heat  of  superheated  steam 
under  the  test  conditions  is  about  0.53,  hence  the  B.t.u.  used 
in  preventing  one  per  cent  of  condensation  was  (yj  X  0.53)  =  4.0 
per  pound  of  steam.  For  larger  engines  and  other  conditions 
from  15°  to  25°  F.  and  from  8  B.t.u.  to  12  B.t.u.  per  pound  are 
used  per  percent  of  saving  of  condensation.  J 

(b)  The  saving  effected  by  superheating  can  best  be  shown 
by  an  example: 

Let  the  pressure  of  steam  used  by  an  engine  be  135  pounds 
absolute,  for  which  the  latent  heat  is  870  B.t.u.  Then,  if  it  is 
assumed  that  8  B.t.u.  superheat  will  effect  a  reduction  of  one 
per  cent  in  the  cylinder  condensation,  it  will  save  (870  X  o.oi) 
=  8.7  B.t.u.  that  would  otherwise  be  wasted  by  cylinder  con- 
densation; thus  the  saving  is  1.09  times  the  expenditure. 

If  the  cylinder  condensation  is  30  per  cent,  it  could  be  entirely 
eliminated  if  (8  X  30)  =  240  B.t.u.  superheat  were  added  per 
pound  of  steam.  Using  0.52  as  the  specific  heat  of  superheat, 
the  temperature  increase  would  be  240  -r-  0.52  =  461°  F.  to 
effect  this  result.  (Note  that  this  is  a  much  higher  degree  of 
superheat  than  is  commonly  employed.) 

Assume  that  the  boiler  furnishes  1000  B.t.u.  of  heat  for  each 
pound  of  steam  generated  and  that  30  pounds  of  steam  (or 
30,000  B.t.u.)  are-  furnished  per  i.h.p.-hr.  Then,  since  the 
assumed  condensation  is  30  per  cent,  the  diagram  water  rate  is 

*  Carpenter,  Trans.  A.  S.  M.  E.,  Vol.  XXVIII. 

f  Superheated  Steam  Engine  Trials,  Proc.  Inst.  C.  E.  (London),  Vol.  CXXVIII. 
{For  data  and  references  see  Kent's  "  Pocket  Book  "  and  Gebhardt's  "  Steam 
Power  Plant  Engineering,"  both  published  by  Wiley  &  Sons. 


238  HEAT-POWER  ENGINEERING 

(30  X  0.70)  =  21  pounds  of  steam  per  i.h.p.-hr.  If  the  steam 
is  sufficiently  superheated  to  eliminate  all  cylinder  condensation, 
it  will  furnish  (1000  +  240)  B.t.u.  per  pound;  or  21  X  1240 
=  26,040  B.t.u.  will  be  furnished  per  i.h.p.-hr.  Then  the 

.    /30,ooo\ 
economy  of  the  engine  is  improved  in  the  ratio  (    ^         I  =  1.15, 

while  the  water  rates  are  in  the  ratio  (ff)  =  1.43.  Thus  it  is 
seen  that  the  reduction  of  water  rate  is  not  an  accurate  measure  of 
the  saving  effected  in  the  heat  used.  This  example  is  intended 
only  to  show  in  a  very  general  way  the  effect  of  superheat. 
The  numerical  quantities  for  other  cases  may  be  very  different 
from  those  used  here. 

(c)  The  saving  to  be  expected  by  superheating  is  dependent 
upon  the  amount  of  cylinder  condensation  that  would  occur  in 
the  same  engine  if  no  superheat  is  used.     Evidently  the  greater 
this  condensation,  the  larger  is  the  saving  possible.     Ordinarily 
the  steam  consumption  is  reduced  about  6  per  cent  with  50°  F. 
and  about  9  per  cent  with  100°  F.  superheat.     A  reduction  of 
15  per  cent  is  frequent  and  as  much  as  40  per  cent  has  been 
attained. 

(d)  It  is  found  that  with  high  temperatures  of  superheat 
there  is  difficulty  from  warping  of  cylinder  and  valves  and  from 
failure  of  lubricants  unless  they  are  of  the  highest  grade.     A 
total  temperature  of  500°  F.  is  about  as  high  as  can  be  used  to 
advantage  in  ordinary  steam  engines.     Cylinders  and  valves  for 
higher  temperatures  should  be  specially  designed  for  the  service. 
Above  750°  F.  there  is  difficulty  in  finding  materials  that  will 
endure  the  temperature  for  long  periods  of  time. 

129.  Use  of  Steam  Jackets,  (a)  Some  cylinders  are  so 
designed  as  to  be  surrounded  by  "  live  "  steam  (usually  at 
high  and  constant  temperature).  Such  cylinders  are  said  to 
be  "  steam- jacketed."  Their  walls  are  maintained  at  higher 
mean  temperature  and  have  less  temperature  fluctuation  than 
in  the  ordinary  cylinder,  consequently  there  is  less  cylinder 
condensation.  The  heat  received  by  the  cylinder  wall  from 
the  "  jacket  steam  "  is  the  latent  heat  freed  by  the  condensa- 
tion of  a  portion  of  this  steam.  If  the  jacket  steam  is  at  the 
same  temperature  as  the  steam  entering  the  cylinder,  the  mean 
temperature  of  the  walls  will  be  but  little  below  that  of  the 
entering  steam,  hence  the  condensation  will  be  small. 


METHODS  OF  DECREASING  CYLINDER   CONDENSATION     239 

At  first  it  may  appear  that  the  weight  of  cylinder  condensa- 
tion thus  avoided  cannot  be  more  than  the  steam  simultaneously 
condensed  in  the  jacket,  in  cases  where  the  condition  of  the 
steam  entering  both  the  cylinder  and  the  jacket  is  the  same. 
Because  of  this,  and  because  the  jacket  has  radiating  surface 
which  is  larger,  and  which  is  maintained  at  a  higher  mean 
temperature,  than  in  the  case  of  the  ordinary  cylinder,  it  would 
seem  that  no  advantage  is  possible  from  the  use  of  a  steam 
jacket. 

(b)  That  the  steam  jacket  is  beneficial  is  largely  due  to  the 
fact  that,  with  its  use,  the  amount  of  moisture  evaporated  from 
the  inner  walls  of  the  cylinder  during  exhaust  is  greatly  reduced, 
thus  less  heat  is  abstracted  from  these  walls  by  the  exhaust 
steam  and  less  steam  is  used  in  the  cylinder.     It  has  been  seen 
that  one  pound  of  moisture  evaporated  from  the  cylinder  walls 
carries  away  roughly  1000  B.t.u.  from  which  there  is  no  return. 
In  the  case  of  the  jacket,  however,  the  condensate  formed  in 
the  jacket  can  be  returned  directly  to  the  boiler,  and,  as  it  is  at 
boiler  pressure  and  temperature,  it  will  carry  back  from  250  to 
300  B.t.u.   per  pound.     Thus  the  net  result  with  the  steam 
jacket  may  be  a  gain  in  economy. 

In  considering  the  performance  of  a  jacketed  engine  the  heat 
supplied  to  the  jacket  steam  must  be  considered  and  the  water 
rate  must  be  modified  accordingly.  If  the  weight  of  steam 
condensed  in  the  jacket  per  h.p.-hr;  is  W3;  the  heat  used  per 
h.p.-hr.  by  the  jacket  is  PF,r/;  and  if  (AQi  —  qz)  is  the  heat 
added  per  pound  of  steam  supplied  to  the*cylinder,  then  the 
true  water  rate,  supposing  the  jacket  condensate  is  returned 
to  the  boiler  without  loss  of  heat,  is 

- (268) 

in  which  Wc  is  the  weight  of  steam  delivered  to  the  cylinder 
per  h.p.-hr. 

(c)  As  most  of  the  cylinder  condensation  occurs  in  the  clear- 
ance space,  this  is  the  most  important  part  of  the  cylinder  to 
jacket.     It  is  usually  only  on  large  engines,  however,  that  the 
cylinder  heads  are  jacketed,  in  addition  to  the  cylindrical  walls. 
It  would  be  desirable  to  jacket  the  piston,  that  is,  fill  it  with 
steam,  but  practical  difficulties  prevent  this.     As  there  is  prob- 


240  HEAT-POWER  ENGINEERING 

ably  no  advantage  from  having  the  exhaust  steam  superheated, 
the  temperature  of  the  jacket  steam  should  usually  not  be  much 
higher  than  that  of  the  steam  entering  the  cylinder.  This  applies 
especially  in  the  case  of  the  low-pressure  cylinders  in  multiple- 
expansion  engines. 

(d)  Steam  jackets  are  not  always  sources  of  heat  economy. 
There  may  be  a  net  loss  (i)  if  they  are  used  with  superheated 
steam,  (2)  if  the  cylinder  condensation  is  so  small  that  the  jacket- 
ing results  in  superheating  the  exhaust  steam,  and  (3)  if  their 
condensate  is  not  returned  to  the  boiler  with  little  loss  of  heat. 
They  apparently  give  smaller  returns  on  large  engines  than  on 
small  ones. 

The  gain  in  economy  is  from  30  per  cent  down  to  a  negative 
quantity.  Many  engineers  are  skeptical  as  to  their  advantage, 
as  the  data  from  various  engine  tests  are  somewhat  contradictory, 
and  as  somewhat  greater  expense  is  involved  in  supplying  the 
jacket  equipment. 

130.  Reheating  Receivers,    (a)  In  multiple-expansion  engines, 
it  is  sometimes  the  practice  to  place  coils  of  pipe,  containing 
11  live  "   steam,  in  the    "  receivers  "    through  which   the  steam 
passes  on  its  way  from  one  cylinder  to  the  next.     As  the  steam 
in  the  coils  is  at  relatively  high  temperature,  it  superheats  (or 
reheats)  the  receiver  steam,   provided  the  moisture  has  been 
properly  separated  from  this  latter. 

The  presence  of  moisture  in  the  working  substance  defeats 
the  purpose  of  the  reheating  receiver.  This  moisture  should  be 
removed  before  the  steam  reaches  the  reheating  coils,  for  it  can 
be  evaporated  to  better  advantage  in  the  boiler. 

(b)  The  action  of  the  reheating  coils  is  similar  to  that  of  the 
steam  jacket;  and  the  heat  surrendered  by  the  condensation  of 
steam  in  the  coils  of  pipe  is  to  be  charged  against  the  engine. 

131.  Other   Methods   of   Reducing   Cylinder   Condensation. 
(a)    Cylinders  are  always  "  lagged  "  with  some  nonconducting 
material  such  as  asbestos,  mineral  wool,  magnesia,  etc.,  to  reduce 
the  radiation.     Some  small  compound  "  Lokomobile  "*  engines, 
which  have  phenomenal  economy,  are  so  arranged  that  the  cylin- 
ders are  surrounded  by  the  furnace  gases  as  they  pass  to  the  stack. 

*Herr  E.  Josse  in  Zeitschrift  des  Vereins  deutscher  Ingenieure,  Sept.  12,  1908. 
Also  see  report  of  test  of  a  Wolf  engine,  (London)  Engineering,  Oct.  8,  1909. 


METHODS  OF  DECREASING  CYLINDER   CONDENSATION     241 

(b)  It  is  of  course  evident  that  the  higher  the  rotative  speed, 
(or  the  greater  the  frequency  of  cycles),   the  less  will  be  the 
cylinder  condensation,  because  the  entering  steam  is  exposed  a 
shorter  time  to  the  cylinder  walls.     For  example  the  high-speed 
Corliss   engines  use  less  steam  than  the  low-speed    engines   of 
that  type,  under  the  same  conditions.     There  are  practical  con- 
siderations, however,  which  place  limits  on  the  speeds  of  rotation 
that  can  be  used. 

(c)  It  has  been  seen  that  theoretically  the  larger  the  temperature 
range  in  the  cylinder,  the  greater  is  the  cycle  efficiency.     In  the 
actual  engine  these  greater  temperature  ranges  may  be  obtained 
by  using  higher  pressures,  and  it  has  been  shown  by  experi- 
ments*  that,   within  limits,   there  is  an  increase  in  economy 
accompanying  their  use,  even  though  the  cylinder  condensation 
is  also  increased  somewhat. 

The  gauge  pressures  (Ibs.  sq.  in.)  usual  in  practice  are  about 
as  follows: 

USUAL  GAUGE  PRESSURES.    TABLE  IV. 

Simple  engines     .      . 80  to  125 

Compound  high-speed  engines  .      .      . .    .  100  to  170 

Compound  low-speed  engines   .      .      .      .  125  to  200 

Triple-  and  quadruple-expansion  engines  .  125  to  225 

(d)  It  has  already  been  shown  that  the  heat  economy  of  the 
steam  engine  can  be  improved  by  approximating  the  Regenera- 
tive cycle  (Section  109).     It  can  also  be  bettered  by  selecting  the 
proper  compression  and  the  best  pressure  drop  at  release,  and 
by  reduction  of  wire-drawing  through  the  throttle  valve,  the 
admission  and  exhaust  valves,  and  the  cylinder  passages.     In 
some  cases,  however,  the  throttling  of  the  steam  has  been  bene- 
ficial, probably  because  the  steam  at  the  reduced  pressure  is 
superheated  a  little  by  the  process. 

(e)  By  the  use  of  a  Binary  Engine  it  is  possible  to  use  some 
of  the  heat  in  the  exhaust  steam  to  vaporize  a  second  and  more 
volatile  fluid  (such  as  sulphur  dioxide)  and  to  use  the  resulting 
vapor  in  another  cylinder  from  which  it  is  exhausted  to  a  con- 
denser.    In  this  way  a  considerable  increase  in  power  can  be 

*Gebhardt's   "Steam  Power  Plant  Engineering,"  p.  286,  published  by  John 
Wiley  &  Sons. 


242 


HEAT-POWER  ENGINEERING-' 


obtained  with  the  same  amount  of  heat  furnished,  but  at  extra 
expense  for  equipment,  attention,  etc.* 

(f)  If  the  arrangement  of  engine  is  such  that  as  the  piston 
moves  it  uncovers  new  portions  of  the  cylinder  wall  which  are 
at  temperatures  equal  to  that  which  the  steam  has  reached  by 
its  expansion,  the  condensation  will  be  less  than  in  the  usual  case, 
in  which  the  steam  is  brought  in  contact  with  walls  the  whole 
of  which  have  been  exposed,  during  a  considerable  period  of 
time,  to  the  temperature  of  the  exhaust  steam.  Fig.  96  shows 


Fig.  96.  —  Unidirectional-Flow  Engine. 

a  diagram  of  the  "Unaflow,"  Straight-Flow  or  Unidirectional- 
Flow  engine  which  was  recently  introduced  and  which  operates 
on  the  principle  just  mentioned.  Steam  is  admitted  by  the 
Inlet  Valve  at  the  end  and  is  discharged  at  the  middle  of  the 
cylinder,  when  the  piston  uncovers  the  Exhaust  Ports.  As  the 
piston  moves  from  the  beginning  of  its  stroke  the  newly  exposed 
portions  of  the  cylinder  wall  tend  to  assume  the  temperature 
of  the  steam  with  which  it  is  brought  into  contact;  thus  there 
is  a  gradation  of  wall  temperature  from  the  inlet  valve  to  the 
exhaust  ports.  During  compression,  which  comprises  practi- 
cally the  whole  of  the  return  stroke,  the  temperature  of  the 
steam  is  raised  as  the  process  progresses,  and  as  the  volume 
becomes  less  the  steam  is  in  contact  with  decreasing  surface 
with  increasing  mean  temperature. 

As  the  expansion  proceeds,  the  steam  in  contact  with  the 
steam- jacketed  cylinder  head  becomes  superheated  and  that  in 

*  See  Peabody's  "  Thermodynamics/'  p.  280,  published  by  John  Wiley  &  Sons 


METHODS  OF  DECREASING  CYLINDER   CONDENSATION     243 

contact  with  the  piston  face  is  the  coldest  and  contains  the  most 
moisture.  When  release  occurs  the  wettest  steam  is  exhausted 
and  there  is  little  chance  for  reevaporation  of  moisture  on  the 
cylinder  walls.  Exhaust  closure  entraps  the  hottest  vapor, 
which,  when  compressed,  attains  very  high  temperature  and 
improves  the  quality  of,  or  superheats,  the  entering  steam. 

Engines  operating  in  this  manner  have  given  remarkably 
good  economies,  even  equalling  those  obtained  with  multiple- 
expansion  engines.  As  great  a  ratio  of  expansion  is  used  in  the 
single-cylinder  as  is  employed  in  the  multiple-expansion  engine. 

(g)  When  the  heat  in  all  the  steam  exhausted  by  the  engine 
can  be  used  in  drying  kilns,  in  heating  systems  for  houses  and 
factories  in  winter,  or  for  other  purposes,  the  engine  economy 
is  not  important,  for  the  heat  not  utilized  by  the  engine  is  not 
wasted.  Radiation,  conduction,  and  mechanical  friction  a,re 
always  losses,  except  in  cold  weather,  when  they  may  furnish 
the  proper  amount  of  heat  to  maintain  the  right  temperature  in 
the  engine  room;  therefore  at  such  times  they  are  not  wastes. 


CHAPTER  XVII. 

STEAM  ENGINES. 

132.  Steam-Engine  Parts,  (a)  Fig.  97  shows  diagrammatically 
one  of  the  simplest  forms  of  double-acting  steam  engine.  The 
various  parts  of  the  engine  are  generally  grouped  as  follows: 

(1)  Stationary  parts,  —  which  include  the  cylinder,  cylinder 
heads  (bonnets),  steam-chest  cover,  stuffing  boxes,  engine  frame, 
outer  bearing, -and  subbase,  if  used. 

(2)  Rotating  parts,  —  consisting  of  the  shaft,  crank  (disk),  fly- 
wheel, and  eccentric. 

(3)  Reciprocating  parts,  —  the  piston,  piston  rod,  crosshead, 
and  connecting  rod. 

(4)  Valve  gear,  —  valve,  valve  stem  (rod),  valve-rod  guide  (or 
rocker  arm),  eccentric  rod,  eccentric  strap,  and  eccentric  sheave 
(or  "eccentric"). 

(b)  The  steadiness  of  the  rotative  speed  of  the  engine  during 
the  revolution,  that  is,  during  the  completion  of  one  cycle  on 
each  side  of  the  piston,  is  controlled  by  the  flywheel.     Flywheels 
will  be  considered  in  a  later  chapter.     The  number  of  revolutions, 
or  number  of  cycles,  per  minute  —  which  is  usually  called  the 
engine    "speed"    —is   controlled  by  the    self-acting   governor, 
which  in  Fig.  9^  is  of  the  "  throttling,"  fly-ball  type. 

The  starting  and  stopping  of  the  engine  is  controlled  by  the 
hand-operated  throttle  valve  which,  in  special  cases,  may  also 
be  used  to  regulate  the  operation  of  the  engine. 

(c)  Engines  usually  have  the  following  fittings:  drain  cocks 
for  cylinder  and  steam  chest;  cocks  for  attaching  indicators; 
lubricating  devices  for  bearings,  guides,  and  cylinders;  and  shields 
to  collect  oil  thrown  by  the  crank,  the  connecting  rod,  and  the 
eccentric. 

(d)  Engines  are  mounted  on  masonry  or  concrete  foundations 
sufficiently  massive  to  prevent  noticeable  vibration  being  induced 
in  the  surroundings.     They  are  fastened  to  the  foundation  by 
"  anchor,"  or  "  foundation,"  bolts. 

244 


STEAM  ENGINES 


245 


Fig.  97. 

133.  Classification  and  Types  of  Steam  Engines,  (a)  Owing 
to  the  great  variety  of  designs  and  to  the  diversity  of  uses  to 
which  steam  engines  are  put,  it  is  impossible  to  give  any  one 
classification  that  would  be  satisfactory  in  all  cases.  The  usual 
commercial  types  of  stationary  engines  are  often  classified  in 
three  groups,  —  "high-speed,"  " medium-speed,"  and  "low-speed" 
engines.  By  "  speed  "  is  meant  the  rotative  speed,  when  used 
in  this  connection. 

(b)  High-Speed  Engines  are  those  which  have  high  rotative 
speeds  accompanied  by  strokes  which  are  very  short  when  com- 
pared to  the  diameter  of  the  cylinder,  the  piston  speed  being 
generally  in  the  neighborhood  of  600  feet  per  minute.*  The 

*  The  "  piston  speed  "  is  the  number  of  feet  the  piston  travels  per  minute. 
Thus,  if  L  is  the  stroke  in  feet  and  n  is  the  r.p.m.,  the  piston  speed  is  V  =  2  Lnt 
since  the  piston  makes  two  strokes  per  r.p.m. 


246 


HEAT-POWER  ENGINEERING 


stroke  is  usually  about  equal  to  the  diameter  of  the  cylinder. 
These  engines  almost  always  have  a  single  "  balanced  "  valve 
and  a  shaft  governor.  They  are  often  called  "  short-stroke 
engines,"  and  are  designed  to  occupy  the  smallest  space,  have 
the  least  weight,  and  "direct  connect"  to  the  smallest  dynamo, 
for  a  given  power,  of  any  of  the  stationary  commercial  types. 
This  class  includes  only  engines  of  comparatively  small  power, 
the  cylinders  usually  not  being  made  larger  than  20  inches  in 
diameter.  Fig.  98  shows  a  center-crank  engine  of  this  type. 


Fig.  98.  —  Center-Crank  Engine  with  Inertia  Type  of  Governor.     (The  engine 
is  mounted  on  a  cast-iron  subbase.) 


(c)  Low-Speed  Engines  have  long  strokes  (from  2  to  4  times 
the  diameter  of  the  cylinder)  and  usually  operate  at  less  than  120 
r.p.m.,  the  speed  being  limited  by  the  valve  gear,  the  action  of 
which  becomes  unreliable  at  higher  speeds.     This  class  includes 
engines  having  the  "  Corliss  "  and  other  types  of  "  trip  cut-off 
gear."     The  governor  is  usually  of  the   "  fly-ball  "   type.     An 
engine  of  this  kind  is  illustrated  in  Fig.  99. 

(d)  Medium-Speed  Engines  have  rotative  speeds  and  strokes 
intermediate  between  the  foregoing.     Positively  driven  multiple 
valves  are  generally  used.     The  cut-off  is  positive  and  is  often 
effected  by  a  separate  valve.     The  governor  is  nearly  always  of 
the  "  shaft  type."     The  piston  speed  is  around  600  feet  per 
minute,  being  higher  on  the  larger  engines.     The  engine  shown 
in  Fig.  100  is  of  this  type. 


STEAM  ENGINES 


247 


Fig.  99.  —  Low-Speed  Engine  with  Corliss  Valve  Gear.     Direct  connected  to  an 

electric  generator. 


Fig.  100.  —  Medium-Speed  Engine  —  Shaft  Governor  —  Positive  Cut-off. 

The  medium-  and  low-speed  engines  are  usually  of  larger 
power  than  the  high-speed. 

There  is  no  sharp  dividing  line  between  these  different  types 
of  engines,  and  it  is  sometimes  difficult  to  decide  in  which  class 
an  engine  belongs. 

(e)  Vertical  Engines  (Fig.  101)  occupy  less  floor  space,  have 
smaller  foundations,  have  less  cylinder  wear,  and  have  slightly 
greater  mechanical  efficiency,  than  do  horizontal  engines,  When 


248 


HEAT-POWER  ENGINEERING. 


large,  they  are  more  difficult  to  erect,  and  caring  for  them  in- 
volves more  effort,  as  certain  parts  are  reached  only  by  ladders. 


Fig.  101.  —  Vertical  Corliss 
Engine. 


Fig.  102. — Vertical  Twin-Cylinder, 
Single-Acting  Engine. 


In  some  special  instances  engines  have  been  constructed  with 
axis  inclined  with  the  horizontal. 

(f)  Single-Acting  Engines  (Fig.  102)  give  half  as  much  power 
as  do  double-acting  engines  with  the  same  diameter  and  stroke 
of  piston,  consequently  a  larger  engine  is  required  for  a  given 
output.      They  use  pistons  of  the  bucket,  or  trunk,  type,  and 
have  no  piston  rod,  therefore  they  are  shorter  than  double-acting 
engines. 

(g)  Reciprocating  Engines  are  so  called  because  they  have 
pistons  that  reciprocate  within  the  cylinder.     They  are  the  type 

that  is  most  common,  although  engines  with 
rotary  piston  would  apparently  be  more  de- 
sirable.    Many  unsuccessful  attempts  have 
been  made  to  devise  an  engine  of  the  latter 
form.      The  difficulty  lies  in  the  production 
of  a  machine  that  is  economical  in  the  use 
Fig.  103.  — Rotary     of  steam  after  the  parts  have  become  worn. 
Engine.  Prior  to  1902  there  were  issued  over  2000 

patents  on  Rotary  Engines,  and  none  have  yet  been  able  to  com- 
pete with  the  reciprocating  engine  as  regards  steam  economy. 


STEAM  ENGINES 


249 


In  some  instances,  where  small  size  is  more  important  than  oper- 
ating cost,  they  may  be  used  to  advantage.  Fig.  103  shows  one 
of  the  simplest  engines  of  this  type. 

.  In  some  instances  Oscillating  Engines,  such  as  that  shown  in 
Fig.  104,  have  been  used.  The  connecting  rod  and  crosshead 
are  dispensed  with  and  the  shaft  is  thereby 
brought  closer  to  the  cylinder.  Steam  is 
admitted  through  one  trunnion  and  ex- 
hausted through  the  other.  This  causes  a 
side  thrust,  for  which  proper  provision  must 
be  made.  When  the  cylinder  reaches  its 
extreme  position,  its  inertia  causes  great 
pressure  to  exist  between  the  stuffing  box 
and  the  piston  rod,  and  these,  parts  must  be 
designed  to  properly  resist  this  force. 

(h)  Fig.  105  shows  two  horizontal  "  side- 
crank  engines."    Engines  of  this  type  have     Fig.  104.  — Oscillating 
the    disadvantage    of    having    a    separate  Engine. 

outer  bearing  which  must  be  aligned  with  the  main  bearing. 
They  possess  the  advantage  that  there  are  only  two  bearings  to 


Fig.  105.  —  Side-Crank  Engine —  Right  Hand  and  Left  Hand  —  Running  Over 
and  Running  Under. 

be  kept  in  alignment  even  when  the  engine  is  direct-connected 
to  an  electric  generator,  as  in  Fig.  99. 

A  horizontal   side-crank  engine  is  said  to  be  right-hand  in 
arrangement  when  an  observer,   standing  at  the  end  of  the 


250  BEAT-POWER  ENGINEERING 

cylinder  (at  5  in  Fig.  105)  and  facing  the  crank,  finds  the  valve 
gear  and  governor  parts  are  to  his  right;  otherwise  the  engine  is 
11  left-hand." 

A  horizontal  engine  is  said  to  be  running  over  if  the  crank  pin 
is  receding  from  the  cylinder  when  the  crank  is  above  the  hori- 
zontal center  line  of  the  engine;  otherwise  it  "runs  under"  (see 
Fig.  105).  If  a  double-acting  engine  "  runs  over  "  the  crosshead 
will  exert  downward  pressure  on  the  guides  during  both  strokes; 
hence  engines  are  usually  operated  in  this  manner. 

(i)  Fig.  1 06  shows  a  Center-Crank  Engine.  In  this  type  the 
crank  is  located  between  the  two  main  bearings,  BB,  and  the 

belt-  and  flywheels   are  overhung.     If 
small,  these   engines   may  be  shipped 
assembled,  ready  to  be  mounted  on  their 
foundations.     If  direct-connected  to  an 
electric  generator,  this  latter  is  substi- 
tuted for  the  belt  wheel  and  an  out- 
Fig.  106.  —  Center-Crank      board  bearing   is    added.      There   are 
Engine.  then  three  bearings  to  be  kept  in  line, 

which  is  a  disadvantage,  as  very  accurate  adjustment  of  bearings 
is  required. 

(j)  In  some  engines  the  crank  case  and  crosshead -guide 
chamber  are  inclosed  so  as  to  be  dustproof  and  prevent  the 
throwing  and  waste  of  oil  (see  Figs.  102  and  109). 

Some  inclosed  engines  are  arranged  to  be  self-oiling  as  regards 
the  crosshead,  connecting  rod,  and  main  bearing.  In  these  cases 
oil  is  maintained  at  such  a  level  in  the  bottom  of  the  crank  case 
that  the  crank  disk  dips  into  it,  and  while  rotating  throws  the 
oil  into  the  crosshead  and  into  collecting  pockets  from  which  it 
is  fed  to  the  bearings.  The  oil  then  automatically  drains  back 
to  the  crank  case  and  is  used  repeatedly  without  being  purified. 
Other  inclosed  engines  are  provided  with  forced  or  gravity 
oil-feeding  systems,  in  which  the  lubricant  is  filtered  each  time 
before  reusing. 

(k)  Compound  engines  have  their  cylinders  arranged  in  many 
different  ways. 

If  the  two  pistons  are  on  the  same  piston  rod,  as  in  Fig.  107, 
the  engine  is  called  a  Tandem  Compound.  Such  an  engine  occu- 
pies no  greater  width  than  a  simple  engine  of  the  same  power 
and  type,  but  has  greater  length.  A  vertical  engine  of  this  type 


STEAM  ENGINES 


251 


("steeple  compound")   occupies  the  same   floor  space  as  the 
equivalent  simple  engine. 

Either  the  high-  or  low-pressure  cylinder  may  be  placed  next 
to  the  frame. 


Fig.  107.  —  Tandem-Compound  Cylinders. 


Fig.  108.  —  Cross-Compound  Engine. 

If  the  cylinders  are  side  by  side,  as  in  Fig.  108,  the  engine  is 
called  a  Cross  Compound.  This  engine  occupies  greater  width 
than  the  tandem  compound,  but  its  length  is  about  the  same  as 
that  of  the  simple  engine.  As  it  has  two  frames,  and  as  other 


252  HEAT-POWER  ENGINEERING' 

parts  are  duplicated,  it  is  more  expensive  than  the  tandem;  but 
because  the  cranks  may  be  set  at  right  angles  it  is  possible  to 
obtain  greater  uniformity  of  turning  effort  than  with  simple  or 
tandem  engines,  and  therefore  a  smaller  flywheel  can  be  used. 

In  some  cases,  with  this  arrangement  of  cylinders  the  cranks 
are  placed  diametrically  opposite  (180  degrees  apart),  but  the 
turning  effort  is  then  about  as  variable  as  with  the  single-crank 
engine.  K ' 

When  the  cylinders  are  immediately  adjacent  to  each  other,  as 
in  Fig.  109,  and  have  their  piston  rods  attached  to  the  same  cross- 
head,  with  single  connecting  rod  and  crank,  the  engine  is  usually 


Fig.  109.  —  Duplex-Compound  Engine. 

called  a  Duplex  Compound.  The  engine  occupies  the  same 
amount  of  space  and  has  the  same  crank  effort  as  a  simple  engine. 

The  arrangement  of  engine  known  as  the  Angle  Compound, 
shown  in  Fig.  no,  occupies  the  same  floor  space  as  a  simple  engine, 
has  the  uniformity  of  crank  effort  obtained  with  cranks  at  90 
degrees  (for  in  this  case  connecting  rods  are  at  90  degrees  and  are 
attached  to  the  same  crank  pin),  and  is  easily  counterbalanced. 

In  triple-  and  quadruple-expansion  engines  the  cylinders  are 
arranged  in  various  ways  and,  looking  at  the  end  of  the  shaft, 
there  may  be  various  sequences  with  which  the  cranks  pass  a 
given  point.  The  arrangement  of  cylinders  and  the  sequence 
and  angle  between  cranks  have  a  predominating  influence  on 
the  counterbalancing  of  such  engines,  as  will  be  seen  later  when 
the  subject  of  counterbalancing  is  discussed. 

(1)  Engines  are  used  for  a  great  variety  of  purposes,  and  are 
often  referred  to  by  their  use;  thus  there  are  marine  engines 
(Fig.  in),  hoisting  engines,  pumping  engines,  rolling-mill 
engines,  air-compressor  engines,  steam-hammer  engines,  etc. 


STEAM  ENGINES 


253 


Electric 
Generator 


L.  P.  Cylinder 


Fig.  1 10.  —  Angle-Compound  Engine. 


Fig.  in.  —  Vertical  Triple-Expansion  Marine  Engine  —  Arrangement. 


254  HEAT-POWER  ENGINEERING,- 

Engines  are  also  classified  as  stationary,  portable,  semi- 
portable,  mobile  (marine,  locomotive,  traction,  road  roller,  and 
automobile  engines). 

The  uses  to  which  some  engines  are  put  require  that  they  be 
capable  of  being  reversed  by  hand.  This  is  true  of  marine 
engines,  some  rolling-mill  engines,  hoisting  engines,  traction 
engines,  etc.  Such  engines  are  called  "reversing  engines"  and 
have  special  valve  gears,  either  of  the  "  link  "  or  "  radial  "  types, 
which  will  be  discussed  later. 


CHAPTER  XVIII. 

STEAM-ENGINE  GOVERNORS. 

134.  Governing,  (a)  The  term  "  governing  "  is  applied  to 
the  adjusting  of  the  power  output  or  speed  of  an  engine,  or  both 
of  these,  to  fit  the  variable  demand. 

(b)  An  engine  may  be  governed  in  four  ways:    It  may  be 
(i)      hand-governed,"  as  in  the  case  of  automobile,  marine,  and 
locomotive  engines;  (2)  "mechanically  regulated"  by  a  "  gov- 
ernor "  that  acts  automatically,  as  in  the  usual  stationary  en- 
gine; (3)   "  resistance  governed,"  its  operation  being  controlled 
directly  by  the  external  resistance;  or  (4)  governed  by  any  com- 
bination of  these  methods. 

(c)  The   ordinary  stationary  engine  is  usually  mechanically 
regulated  to  maintain   approximately   constant  speed  of  rota- 
tion at  all  loads.     An  engine  operating  uniformly  will  develop 
indicated  power  just  sufficient  to  overcome  the  friction  losses  and 
meet  the  external  demand  for  power.     Should  a  decrease  in  the 
external  load  occur,  it  would  result  in  an  excess  of  indicated  power, 
causing  an  acceleration  of  the  moving  parts  of  the  engine,  which 
would  continue  until  the  mechanism  ruptured  under  the  induced 
stresses,  unless  a  governor  should  come  into  action  to  prevent. 
On  the  other  hand,  an  increase  in  load  would  stop  the  engine 
unless  the  indicated  power  were  increased  proportionately. 

Thus,  to  maintain  constant  speed,  a  "  governor  "  must  auto- 
matically adjust  the  indicated  power  to  balance  the  friction  and 
external  load  at  all  times.  Exact  uniformity  of  speed  is  impos- 
sible, as  a  change  in  speed  is  necessary  to  cause  a  governor  to  act. 
This  change,  however,  may  be  made  so  small  as  to  be  negligible 
in  most  cases. 

(d)  Resistance  governing  is  exemplified  by  an  engine  directly 
driving  a  pump  which  discharges  fluid  into  a  closed  reservoir  or 
system  of  piping.     The  pump  will  raise  the  fluid  pressure  in  the 
system  to  the  limit  of  the  engine's  capacity,  when  the  engine 
will  become  ineffective.     Should  fluid  then  be  withdrawn  from 

255 


256  HEAT-POWER  ENGINEERING,. 

the  system,  the  drop  in  pressure  will  cause  the  engine  to  start 
again  and  to  continue  running  until  the  pressure  once  more 
reaches  the  limiting  value.  To  prevent  the  engine  from  over- 
speeding  in  case  of  sudden  withdrawal  of  fluid,  or  rupture  of 
pipe,  a  "  mechanical  governor  "  or  "  safety  stop  "  is  usually  pro- 
vided, so  adjusted  as  to  automatically  come  into  operation  before 
the  safe  speed  is  exceeded.  The  limit  of  fluid  pressure  is  also 
generally  made  adjustable  by  hand. 

135.  Governing  of  Steam  Engines,  (a)  The  adjusting  of  the 
power  developed  within  the  cylinder  to  meet  the  external  de- 
mand on  the  engine  is  usually  accomplished  in  the  case  of  the 
steam  engine  either  by  throttling  the  steam  supplied  the  cylinder, 
or  by  changing  the  point  in  the  stroke  at  which  cut-off  occurs.  A 
combination  of  both  of  these  methods  is  possible  but  is  rarely 
used. 

(b)  When  the  engine  is  governed  by  throttling,  the  cut-off  is 
fixed  by  the  maximum  power  which  the  engine  is  to  develop  with 
steam  at  the  maximum  pressure.  To  obtain  less  power,  the 
steam  is  throttled,  thus  giving  lower  admission  pressure.  Fig. 
112  shows  ideal  indicator  diagrams  for  such  case. 

-Fixed  (XO. H 


Fig.  112.  —  Throttle  Governing.  Fig.  113.  —  Cut-off  Governing. 

(c)  When  governed  by  changing  the  cut-off,  the  admission 
pressure  is  constant,  and  the  amount  of  cylinder  feed  is  varied, 
as  shown  by  the  ideal  diagrams  in  Fig.  113. 

136.  Governors,  (a)  In  most  cases  the  demand  is  for  power 
at  constant  rotative  speed,  and  the  governing  device  should  there- 
fore govern  "  isochronously."  Unfortunately,  however,  govern- 
ing devices  are  driven  by  the  engine  and  operate  on  a  simple 
mechanical  principle  which  requires  a  change  in  speed  to  make 
them  act.  They  are  also  connected  to  throttling  or  cut-off 
devices,  each  of  which  must  have  a  different  position,  or  phase 
relation,  for  each  load.  l_  Hence  the  governors  must  change  posi- 


STEAM-ENGINE  GOVERNORS 


257 


tion  with  variation  of  load.  As  the  governor  adjustments  are 
brought  about  only  by  changes  in  speed,  there  is  a  definite  speed 
and  definite  governor  position  corresponding  to  each  load. 

Hence  the  "  constant-speed  "  governor  is  an  anomaly  because 
(i)  the  governor  cannot  act  until  there  is  a  change  of  speed, 
and  (2)  the  governor  cannot  maintain  the  configuration  of  valve 
gear  corresponding  to  different  loads  unless  it  runs  at  different 
speeds  for  different  loads. 

However,  with  well-designed  governors  properly  adjusted, 
the  amount  of  variation  is  small  and  isochronism  is  approached 
sufficiently  close  for  practical  purposes. 

If  nit  MZ  and  n  are  respectively  the  lowest,  highest  and  mean 
r.p.m.  of  the  engine,  then  the  degree  of  regulation  or  coefficient 


of  regulation  is  e 


which  would  of  course  be  zero  with 


isochronous  governing.* 

(b)  The  four  essentials  of  a  good  governor  are  (i)  "  closeness  " 
of  regulation,  i.e.,  small  coefficient  of  regulation,  (2)  quickness  of 
regulation,  (3)  stability  or  posi- 

tiveness,  and  (4)  power  to  move 
the  parts  controlled  and  to  re- 
sist disturbing  forces. 

(c)  Engine  governors  may  be 
divided  into  two  classes,  —  the 
"  Pendulum  "    or    "  Fly-ball  " 
Governor,    and    the    "Shaft" 
Governor. 

137.    Pendulum   Governors. 

(a)  The  simple  pendulum,  coni- 
cal, fly-ball  or  Watt  governor  is 
shown  in  Fig.  114.  Correspond- 
ing to  each  different  speed  at 
which  the  vertical  spindle  and  weights  revolve,  there  is  a  definite 
height  of  cone  (h)  at  which  the  centrifugal  force  (C)  and  weight 


Fig.  1 14.  —  Watt  Governor. 


*  It  is  common  practice  to  speak  of  the  "percentage  of  speed  variation,"  — 
thus  an  engine  speed  may  be  said  not  to  vary  in  excess  of  2\  per  cent.  Such  a 
statement  is  ambiguous,  —  by  some  it  is  used  to  refer  to  the  degree  of  regulation 
as  denned  above  and  by  others  to  refer  to  the  percentage  of  variation  above,  or 
below,  the  mean  speed  (i.e.,  to  approximately  one-half  the  degree).  Hence  the 
meaning  of  the  term  should  always  be  denned  if  used  at  all. 


258 


HEAT-POWER  ENGINEERING 


of  ball  (W)  will  give  a  resultant  (R)  which  will  be  in  line  with 
the  link  j-2,  which  is  the  condition  for  equilibrium.  For  such 
conditions  the  moments  of  C  and  of  W  about  j  must  evidently 

be  equal ;  thus, 

Wr  =  Ch .     (269) 

W       r         Wrn2 
But  C. ..-„*--.-— (270) 

in  which  co  is  the  angular  velocity  in  radians  per  second,  r  is  the 
radius  in  inches,  and  n  is  the  r.p.m.  Substituting  this  value  of 
C  in  Eq.  (269)  and  solving  gives  for  the  height  of  cone 


(27I) 


Therefore  the  height  of  cone  has  the  same  definite  value  for 
each  rotative  speed  regardless  of  the  length  of  arm,  the  method 
of  suspension,  and  the  weight  of  the  ball.  Thus  in  Fig.  115  the 


2.  Ill 


Fig.  115- 

heights  of  cones  (to  intersection  of  arms,  produced  if  necessary) 
are  all  equal  when  all  weights  revolve  at  the  same  speed. 

(b)  The   motion   necessary   to   change   the  steam   supply   is 
obtained  from  the  collar  of  the  governor.     By  referring  to  Fig. 

1 14,  it  will  be  evident  that 
for  a  given  change  of  speed 
the  collar  lift  (/)  is  twice 
the  change  in  height  of 
cone  Ah,  when  upper  and 
lower  arms  are  equal  in 
length,  that  is,  when  the 
governor  is  rhomboidal  in 
form. 

Fig.  116  gives  the 
heights  of  cone  for  speeds 
between  60  and  120  r.p.m., 

by   increments    of    10    r.p.m.       It   also    shows    the 
A/^2,  etc.),  corresponding  to 


Fig.  1 1 6. 

advancing 

different   changes  in   height 


STEAM-ENGINE  GOVERNORS 


259 


this  increment.     It  is  evident  that  a  given  amount  of  collar 

movement  may  be  obtained  with  less  variation  in  speed,  i.e., 

with  closer  "  regulation,"  when  the  r.p.m.  is  low  than  when  high  ; 

therefore,   these   governors  are 

usually  operated  at  rather  low    /t\ 

speeds.     This    results    in  their  c^J/b 

having  little   "  power  "   to  re-      T 

sist  disturbances  which  tend  to 

move  the  collar,  and  to  over- 

come resistance  offered  at  that 

point.     Such  governors  are 

therefore  ordinarily  used  only 

when  the  parts  to  be  moved  by 

the  collar  are  light  of  weight 

and  practically  frictionless. 

(c)  The  Weighted  Conical  or 
Porter  Governor  is  shown  in 
Fig.  117  and  differs  from  the 
Watt  governor  in  the  addition 
of  the  central  weight  Q  which 
rests  on  the  collar,  and  for  a 
given  speed  causes  the  weights 
to  revolve  in  a  lower  plane  (i.e., 
with  height  of  cone  greater) 


(a) 


than  in  the  simple  form.     Evi- 


Fig. 117.  —  Weighted  Governor. 


dently,  within  limits,  a  given  height  of  cone  can  be  had  at  any 
speed  by  merely  placing  the  right  amount  of  weight  at  Q. 

At  the  collar,  in  the  figure,  is  drawn  the  triangle  giving  the 

component  S  of  -  along  the  link  1-2.     The  ball  is  subjected  to 

forces  S,  C,  W,  and  a  resultant  tension  L  (in  link  3-2)  which  must 
point  toward  the  pivot  J.  These  forces  are  shown  at  (a)  in  the 
figure,  from  which  it  is  evident  that  the  vertical  component  of 

S  is  -  and  the  horizontal  component  H  is  -  tan  0  =  -  ^ ,  since 

T?  =  tan  0.  For  equilibrium  the  moments  about  3  of  the  horizon- 
tal and  vertical  forces  or  components  must  be  equal,  and  therefore 
(remembering  that  L  passes  through  j), 


26o  HEAT-POWER  ENGINEERING  , 

Substituting  the  second  value  of  C  from  Eq.  (270)  and  solving 
for  the  height  of  cone  gives* 


Comparison  of  this  equation  with  Eq.  (271)  will  show  that  it 
is  possible  for  the  loaded  governor  to  have  the  same  height  of 
cone,  and  same  degree  of  regulation  for  a  given  collar  move- 
ment, with  high  speeds,  that  can  be  obtained  with  the  simple 
conical  governor  with  low  speeds  only.  The  "  loaded  "  governor 
is  much  the  more  powerful  of  the  two  because  of  this  fact. 

(d)  Eqs.  (271)  and  (272)  show  that  to  have 
isochronous  governing  (n  =  constant)  the 
height  of  cone  (h)  must  be  constant.  Thus 
///  in  Fig.  Ii8  the  path  of  the  ball  must  be  such 
ft  ^XC^Y  tnat  t^ie  sub-normal  to  the  curve  is  constant. 
As  this  is  the  property  of  the  parabola,  the 
ball  should  be  guided  over  such  a  path  for  this 
kind  of  governing.  In  such  case,  at  the  given 
speed,  the  ball  would  be  in  equilibrium  at  any 
and  all  points  on  the  guide ;  that  is,  the  forces 
would  always  be  in  equilibrium. 

Such  an  arrangement  is,  however,  of  no  commercial  value 
because  (i)  if  a  disturbance  increased  the  speed  slightly  the 
equilibrium  would  be  destroyed,  the  centrifugal  force  would  pre- 
dominate, and  the  ball  would  seek  the  extreme  position  against 
the  outer  "stop"  b;  (2)  a  decrease  of  speed  would  cause  the 
weight  to  move  to  the  inner  stop  a;  and  (3)  there  is  no  definite 
place  for  the  ball  at  the  speed  of  isochronism  —  it  is  balanced  at 
any  position  on  the  guide;  whereas  to  be  of  practical  value  there 
must  be  a  definite  position  of  ball  corresponding  to  each  differ- 
ent load  to  which  the  engine  is  subjected.  Hence,  while  this 
governor  is  ideal  as  regards  constancy  of  speed,  it  is  unstable 
and  of  no  commercial  value.  It  serves  as  a  limit  which  actual 
governors  may  be  made  to  approach  as  closely  as  is  possible 
without  introducing  instability. 

(e)  Fig.  119  shows  an  arrangement  in  which  the  path  of  the 
ball  is  a  circular  arc  approximating  the  parabolic  path,  but  de- 

*  Note  that  this  equation  applies  only  when  the  governor  linkage  is  rhomboidal 
in  arrangement.  If  the  arrangement  is  like  that  at  (b)  in  Fig.  1 17  the  formula  must 
be  modified. 


STEAM-ENGINE  GOVERNORS 


261 


parting  therefrom  somewhat  in  order  to  have  the  difference 
between  h%  and  hi  sufficient  to  insure  stability.  Such  an  arrange- 
ment is  described  as  a  governor  with  crossed  arms. 

With  the  governor  previously  described,  which  has  the  suspen- 
sion point  located  on  the  spindle,  the  path  of  the  ball  departs 


Fig.  119. 


Fig.  1 20. 


Fig.  121. 


widely  from  the  parabola,  hence  such  governors  do  not  give  close 
regulation  except  when  the  collar  movement  is  small. 

(f)  Isochronism  can  be  approached  by  having  the  point  of 
attachment  between  links  offset  from  the  weight  arm,  as  at  a  in 
Fig.  1 20,  or  using  the  equivalent  bent  arm,  as  at  b.     The  theory 
of  this  type  of  governor  will  not  be  included  here.* 

Fig.  121  shows  another  arrangement  of  governor  with  which 
isochronism  can  be  approached.* 

(g)  Eqs.  (271)  and  (272)  apply  only  in  the  ideal  case  in  which 
there  is  no  resistance  to  be  overcome.     If  the  collar  and  pins  have 
friction,  the  speed  of  the  governor  must  change  a  considerable 
amount,  An,  before  the  centrifugal  force  is  changed  by  a  suffi- 
cient amount  to  enable  it  to  overcome  this  resistance  and  cause 
the  collar  to  start  to  move.     Thus,  if  the  change  in  speed  neces- 
sary to  overcome  the  resistance  when  the  weights  tend  to  move 
out  equals  that  when  the  tendency  is  inward,  there  can  be  a 
change  in  speed  equal  to  2  An  without  movement  of  the  collar. 
Evidently  the  degree  of  total  regulation  is  similarly  affected. 
The  greater  the  collar  friction  the  larger  the  influence,  hence  the 
collar  friction,  the  resistance  of  all  parts  moved  by  the  collar, 
and  the  friction  of  the  governor  parts  must  be  as  small  as  possi- 
ble, if  close  regulation  is  desired. 

*  See  Tolle,  "  Die  Regelung  der  Kraftmaschinen,"  Julius  Springer,  publisher, 
Berlin. 


262 


HEAT-POWER  ENGINEERING    , 


Fig.  122. 


138.  Spring-balanced  Fly-ball  Governor.     In  the  fly-ball  gov- 
ernors so  far  discussed  the  moments  of   the  centrifugal  forces 

acting  on  the  balls  were  balanced  by  the 
moments  of  the  gravity  forces.  Some  gov- 
ernors are  so  arranged  that  the  centrifugal 
forces  (or  their  moments)  are  practically 
entirely  balanced  by  one  or  more  springs, 
as  in  Fig.  122.  In  other  governors  the  cen- 
trifugal force  is  balanced  by  a  combination 
of  gravity  and  springs. 

The  degree  of  regulation  of  the  governor 
shown  in  Fig.  122  can  be  adjusted  by  means 
of  the  nuts  N,  which  can  be  used  to  change  the  initial  compression 
of  the  spring.  This  governor  operates  on  the  same  principle  as 
the  simple  centrifugal  "shaft"  governor  described  in  the  next 
section.  There  are  many  different  arrangements  of  governors  of 
this  type.  They  may  be  made  to  operate  at  high  speed  and  have 
considerable  power,  and  they  can  be  adjusted  to  give  "  close" 
regulation. 

139.  Elementary  Shaft  Governors,     (a)  The  shaft  governor 
is  so  called  because  it  is  mounted  either  in  the  flywheel  or  in 
a  governor  case  carried  by  the  main  shaft  of  the  engine. 

(b)  The  elements  of  the  simplest  form  of  this  governor  are 
shown  in  Figs.  123  to  125.     Referring  to  Eq.  (270),  it  is  seen  that 


Fig.  123. 


Fig.  124. 


if  the  speed  of  rotation  is  constant  the  centrifugal  force  C  with  a 
given  weight  varies  directly  with  the  radius  r.  Thus  in  Fig.  123, 
with  constant  speed  =  wlf  the  ordinates  (C)  of  the  line  On\  show 
the  manner  in  which  the  centrifugal  force  increases  as  the  weight 


STEAM-ENGINE  GOVERNORS  263 

W  is  moved  outward  from  the  center  of  the  shaft.  On*t  shows 
the  same  thing  for  a  higher  constant  speed  w2,  and  similar  lines 
could  be  drawn  for  each  other  speed. 

(c)  In  Fig.  124,  5  is  a  spring  with  end  at  O  when  free.     The 
ordinates  (F)  of  curve  Of  show  the  increase  of  the  spring  force 
with  the  elongation  5.     As  the  curve  is  similar  in  character  to 
those  in  Fig.  123,  it  would  be  possible  to  place  the  spring  in  the 
flywheel,  with  end  0  at  the  center  of  rotation,  and  thus , cause 
Of  to  coincide  with  one  of  the  On- 

curves.  The  centrifugal  force  would 
then  be  balanced  by  the  spring  pull 
in  all  positions  of  the  weight,  for 
that  particular  speed.  Hence  this 
arrangement  would  give  isochro- 
nism.  The  speed  at  which  this 
equilibrium  occurs  depends  of  course 
on  the  strength  of  the  spring. 

(d)  If  a  in  Fig.  125  is  the  position 
of  the  center  of  the  ball  when  against 
the  inner  stop,  then  when  the  weight 

is  in  the  "inner  position  "  the  spring  will  have  elongation  equal 
to  Oa.  The  extension  of  the  spring  with  the  weight  in  the  inner 
position  is  called  the  "  initial  elongation."  In  adjusting  the  spring 
to  give  isochronous  governing,  the  initial  elongation  5i  must  be 
equal  to  the  distance  Oa,  which  is  equal  to  r\. 

(e)  The  isochronous  shaft  governor  is  an  unstable  one;  any 
change  from  the  speed  of  isochronism  causes  the  weight  to  move 
to  one  or  the  other  extreme  position ;  and  at  the  speed  of  isochro- 
nism the  weight  is  in  equilibrium  at  any  position  in  its  path, 
that  is,  has  no  definite  position.     Therefore,  this  governor  is  of 
no  commercial  value,  but  is  the  limit  which  actual  governors  may 
be  made  to  approach  as  closely  as  is  possible  without  introducing 
instability  of  action. 

(f)  In  order  to  have  stable  governing,  there  must  be  definite 
positions  of  the  weight  W  for  each  different  load  on  the  engine. 
If  the  end  of  the  spring,  when  not  under  tension,  is  at  0',  to  the 
right  of  the  wheel  center  o  in  Fig.  126,  instead  of  at  0,  then  the 
line  o'f  will  cross  the  0w-curves;  point  I  will  correspond  to  a  speed 
equal  to  n\,  point  x'  to  nx,  and  point  2  to  w2 ;  thus,  when  the  weight 
is  at  a  the  spring  pull  will  be  balanced  by  the  centrifugal  force 


264 


HEAT-POWER  ENGINEERING 


when  the  speed  is  HI,  at  x  there  will  be  equilibrium  if  the  speed 
is  nx,  and  at  b  the  forces  are  equal  when  the  speed  is  w2. 

With  such  an  arrangement  there  is  a  definite  position  of  the 
weight  at  each  different  speed,  thus  the  arrangement  is  stable. 


Fig.  126. 

If  the  position  of  W  fixes  the  power  developed  by  the  engine, 
then  there  will  be  a  different  speed  for  each  different  power 
output. 

The  line  1-2  is  sometimes  called  the  Characteristic  Curve 
(C-curve),  as  its  position  with  respect  to  the  constant  speed 
curves,  On,  indicates  the  character  of  the  governing. 

(g)  If  a  is  to  be  the  inner  position  of  the  weight,  and  n\  the 
lowest  speed,  then  point  I  is  fixed.  The  speed  corresponding  to 
position  b  is  determined  by  the  slope  of  the  Characteristic  Curve 
1-2  relative  to  the  constant-speed  curves,  and  is  dependent  on 
the  distance  oof  or  on  the  distance  5i.  If  o'  coincides  with  0, 
the  initial  elongation  61  =  n,  and  the  governor  would  be  isochro- 
nous, as  the  C-curve  would  coincide  with  on^  The  greater  the 
distance  oo'  is,  i.e.,  the  smaller  the  initial  elongation  61  (compared 
with  ri)  the  greater  will  be  the  speed  variation  between  limits 
a  and  b,  and  the  greater  will  be  the  stability,  and  vice  versa. 

(h)  The  adjustment  of  a  governor  is  divided  into  two  parts 
as  follows: — (i)  The  initial  elongation  of  the  governor  spring, 
would  be  increased  (by  means  of  nut  at  N  in  figure)  until  the  best 
degree  of  regulation  that  is  consistent  with  stability  is  obtained. 
Note  that  the  degree  of  regulation  is  dependent  only  on  the 
amount  of  the  initial  elongation,  and  that  it  is  independent  of 
the  strength  of  spring  and  of  the  weight  of  ball. 


STEAM-ENGINE  GOVERNORS  265 

(2)  After  the  spring  has  been  adjusted  to  give  the  proper 
degree  of  regulation,  the  speed  can  be  changed  to  any  desired 
value,  within  reason,  by  changing  the  weight  W.  If  the  weight 
is  reduced  the  speed  will  increase  until  the  centrifugal  force 
balances  the  spring  pull;  if  increased,  the  effect  on  the  speed  will 
be  the  opposite. 

(i)  In  Fig.  127  the  weight  W  is  mounted  on  an  arm  pivoted 
at  J  and  with  spring  S  attached  at  I.  If  it  is  considered  that 
the  arc  ab  here  approximates  path 
ab  in  Fig.  126,  the  spring  S  would 
have  initial  elongation  61,  the  same 
as  in  that  case.  Evidently  spring 
S  can  be  replaced  by  spring  S'  if 
the  latter  is  made  l/l'  times  as 
strong  (W  remaining  the  same) 
and  if  the  initial  elongation  is 
made  equal  to  (/'//)Si. 

This  arrangement  contains  the 
elements    of   the    more    common 

forms  of  commercial   shaft   gov- 

•        i-  •  -Fig.  127. 

ernors.    It  is  adjusted  in  the  same 

manner  that  was  described  in  (h)  for  the  simple  case. 

140.  Commercial  Types  of  Shaft  Governors,  (a)  In  general, 
the  commercial  shaft  governor  has  one,  or  two,  pivoted  "  weight 
arms,"  the  centrifugal  force  acting  on  which  is  balanced  by  one 
or  more  springs  which  are  so  adjusted  that  there  is  a  differ- 
ent speed  and  a  corresponding  definite  and  distinct  position 
of  the  arm,  or  arms,  for  each  different  load  on  the  engine. 
The  "  weight  arms  "  are  connected  either  directly,  or  by 
links,  to  the  eccentric,  so  that  for  each  speed  there  is  a 
definite  and  distinct  position  of  the  eccentric,  a  corresponding 
cut-off,  and  a  definite  amount  of  power  developed.  If  the  load 
changes,  the  speed  of  the  engine  will  also  change  until  a  cut-off 
is  found  which  gives  the  right  amount  of  power  to  meet  the 
demand. 

If  the  governor  is  of  good  design  and  properly  adjusted,  the 
total  amount  of  speed  variation  is  very  small  (being  from  I  to  2\ 
per  cent  of  the  "normal  "  or  average  speed);  thus  the  speed  is 
practically  constant. 


266 


HEAT-POWER  ENGINEERING 


There  are  two  general  types  of  shaft  governors, — the  "Centrif- 
ugal" and  the  "Inertia." 

(b)  The  Sweet  governor,  which  was  one  of  the  earliest  of  the 
centrifugal  governors  and  which  is  still  widely  used,  is  shown  in 
Fig.  128.  Pivoted  to  one  of  the  arms  of  the  flywheel,  or  governor 
wheel,  is  a  "weight  arm,"  which  has  a  heavy  head  W.  When 
the  engine  is  not  running,  this  weight  arm  is  held  in  the  "inner" 
position  (that  shown  in  full  lines)  by  the  leaf  spring  5.  After 
steam  is  turned  on,  the  arm  will  remain  in  this  position  until  the 
speed  has  reached  a  certain  point  (for  example,  say  198  r.p.m.), 


Fig.  128.  — Sweet  Type  of  Centrifugal  Governor. 

when  the  centrifugal  force  C  will  just  balance  the  spring  pull. 
If  the  speed  is  raised  further,  the  increased  centrifugal  force  will 
cause  the  arm  to  move  outward  until,  at  some  speed  (say  202 
r.p.m.),  it  reaches  the  extreme  "outer"  position  (that  shown  by 
the  dotted  lines).  At  the  "  normal  "  speed  (200  r.p.m.)  the 
weight  arm  would  be  about  midway  between  these  extreme 
positions;  and  for  every  other  speed  (between  the  198  and  202 
r.p.m.)  there  are  definite  positions  of  the  arm. 

In  the  example  the  total  variation  in  speed  is  2  per  cent  of  the 
normal  r.p.m.  By  changing  the  adjustment  of  the  spring,  how- 
ever, the  amount  of  variation  can  be  altered,  but  if  it  is  made  too 


STEAM-ENGINE  GOVERNORS 


267 


small  the  friction  and  inertia  of  the  valve  gear,  and  the  other 
disturbances,  will  make  the  action  of  the  governor  uncertain,  — 
so  there  is  a  practical  limit  to  the  closeness  of  regulation. 

Again  referring  to  Fig.  128,  it  is  seen  that  the  arm  carrying  the 
eccentric  is  pivoted  at  P  to  one  of  the  arms  of  the  wheel,  and  is 
connected  by  a  link  L  to  an  extension  of  the  weight  arm..  When 
this  latter  is  in  the  inner  position,  or  is  "in,"  the  center  of  the 
eccentric  is  at  E,  the  position  for  the  latest  cut-off ;  and  when  it  is 
*  'out,"  the  eccentric  center  is  at  e,  the  position  for  zero  cut-off. 

The  manner  in  which  the  governor  operates  is  as  follows: 
When  the  engine  is  standing  still,  the  governor  holds  the  eccen- 
tric in  the  position  R  for  the  latest  cut-off.  When  steam  is 
turned  on,  the  engine  will  speed  up  until  a  certain  r.p.m.  is 
reached,  at  which  the  governor  arm  will  begin  to  move  out,  thus 
shifting  the  eccentric  towards  e  and  decreasing  the  cut-off.  This 
movement  will  continue  until  a  position  is  reached  at  which  the 
power  developed  just  equals  the  load,  and  as  long  as  this  latter 
remains  constant  the  governor  arm  will  remain  in  this  position. 
Now,  if  the  load  is  reduced,  the  engine  will  speed  up  (tending  to 
run  away) ,  and  this  causes  the  weight  arm  to  fly  out,  shifting  the 
eccentric  nearer  to  e  and  reducing 
the  power  developed  until  it  be- 
comes again  equal  to  the  demand. 
Similarly,  if  the  load  is  increased, 
the  speed  of  the  engine  will  de- 
crease, and,  as  the  weight  arm 
moves  "in,"  the  cut-off  will  be 
increased,  until  at  some  position 
of  the  arm  a  balance  is  again 
reached  between  the  power  and 
the  load. 

Fig.  129  shows  another  "centrif- 
ugal" shaft  governor;  but  in  this 
case  there  are  two  weight  arms,  symmetrically  placed,  instead 
of  one.  In  its  action,  this  governor  is  identical  with  that  which 
has  just  been  described. 

(c)  Fig.  130  shows  the  Rites  Inertia  Governor,  which  consists 
of  a  long  weight  arm  (WW),  an  eccentric  pin  E,  and  a  spring. 
The  arm  is  pivoted  at  P,  close  to  the  shaft,  and  its  end  W  is 
heavier  than  W,  so  the  center  of  gravity  is  at  G.  The  position  of 


Fig.  129.  —  Centrifugal  Governor. 


268 


HEAT-POWER  ENGINEERING 


the  parts  shown  in  full  lines  is  for  latest  cut-off,  and  is  the  one 
occupied  when  the  engine  is  not  running;  that  shown  by  the 
broken  lines  is  for  the  earliest  cut-off.  In  the  former  position, 
the  arm  is  said  to  be  "  in,"  and  in  the  latter,  "  out."  The  direc- 
tion of  rotation  is  shown  by  the  arrow.  The  governor  will  not 
operate  satisfactorily  if  the  direction  of  rotation  is  reversed  with- 
out making  changes  in  the  governor  itself. 

As  the  engine  starts  up,  the  governor  arm  remains  in  the  inner 
position  until  a  certain  speed  is  reached,  when  the  centrifugal 


fa) 


Fig.  130.  —  Inertia  Governor. 

force  C,  acting  on  the  weight  arm,  becomes  sufficiently  great  to 
balance  the  spring  pull.  Then,  with  a  further  increase  in  speed, 
the  weight  arm  will  move  out  (the  eccentric  meanwhile  moving 
toward  e)  until  a  sufficiently  early  cut-off  is  obtained. 

Now,  if  the  load  falls  off  the  engine  will  speed  up,  and  the 
increased  centrifugal  force  will  cause  the  weight  arm  to  move 
out  until  the  cut-off  is  reduced  to  the  proper  amount,  the  action 
being  just  the  same  as  in  the  case  of  the  centrifugal  governor. 
However,  in  addition  to  the  centrifugal  force  acting  on  the  arm, 
there  is  also  an  inertia  force  which  assists  the  movement. 

The  inertia  of  the  weight  arm  acts  in  this  manner:  As  the 
engine  speeds  up  the  governor  arm  tends  to  continue  to  rotate 


STEAM-ENGINE  GOVERNORS 


269 


at  its  old  speed,  because  of  its  inertia,  and  hence  lags  behind  the 
wheel,  moving  with  respect  to  the  latter  in  the  direction  shown 
by  the  arrows  /  and  /  in  the  figure.  It  is  seen  that  this  movement 
is  in  the  same  direction  as  that  caused  by  the  centrifugal  force  C. 
Again,  if  the  load  is  suddenly  increased  the  engine  will  slow  down, 
but,  because  of  its  inertia,  the  weight  arm  will  continue  at  its 
old  speed,  thus  gaining  on  the  flywheel,  and  again  assisting  the 
centrifugal  force  in  changing  the  position  of  the  eccentric  and 
weight  arm  with  respect  to  the  crank. 

It  is  seen  that  the  inertia  governor  is  primarily  a  centrifugal 
governor,  but  that,  in  addition,  the  weight  arm  is  so  pivoted, 
and  has  its  weight  so  distributed,  that  its  inertia  assists  in  mak- 
ing the  adjustment,  and  that  the  more  sudden  the  change  in  the 
load  the  greater  will  be  the  assistance  it  renders. 

In  this  form  of  governor  the  eccentric,  or  eccentric  pin,  is 
usually  mounted  directly  on  the  weight  arm.  Sometimes  the 
eccentric  is  keyed  directly  to  the  fulcrum  pin  on  the  end  opposite 
that  to  which  the  arm  is  fastened.  With  these  arrangements, 
in  order  to  have  the  inertia  of  the  weight  arm  act  in  the  right 
direction,  the  fulcrum  pin  must  be  placed  on  the  side  of  the  shaft 
opposite  to  the  crank  pin,  when  an  "external"  valve  is  used,  and 
on  the  same  side  when  the  valve  is  "  internal "  (Section  143). 

On  "center-crank"  engines  the  governor  is  frequently  placed 
in  the  outer  side  of  the 


wheel,  in  which  case,  since 
the  shaft  does  not  extend 
beyond  the  governor  wheel, 
the  arrangement  can  be 
that  shown  in  Fig.  130.  If, 
however,  the  governor  is 
placed  on  the  side  of  the 
wheel  next  to  the  engine 
frame,  both  the  governor 
arm  and  the  eccentric  must 
be  made  to  surround  the 
shaft  in  the  manner  shown 
at  a,  Fig.  130. 

Fig.  131  shows  the  Arm- 


Fig.  131.  —  Armstrong  Governor. 


strong  governor,  which  is  of  the  inertia  type.     The  weight  W  is 
mounted  on  the  end  of  the  leaf  spring  S,  and  is  subjected  to  cen- 


270  HEAT-POWER  ENGINEERING 

trifugal  force  C,  and  also  to  inertia  force  /  or  /'  when  sudden 
change  occurs. 

(d)  For  both  forms  of  shaft  governors  it  has  been  seen: 

(1)  That  there  is  a  definite  speed,  cut-off,  and  power  for  each 
position  of  the  weight  arm. 

(2)  That  when  the  arm  is  "in,"  the  speed  is  the  lowest  and 
the  cut-off  is  the  latest;  whereas,  if  the  weight  arm  is  "out,"  the 
reverse  is  the  case. 

(3)  That  an  increase  in  load  decreases  the  speed  and  causes 
the  arm  to  move  "in,"  which  gives  a  later  cut-off;  whereas,  the 
effect  of  a  decrease  in  load  is  the  reverse. 

(4)  That,  for  close  regulation,  the  friction  and  inertia  of  the 
valve-gear  parts  must  be  small,  and  especially  is  this  necessary 
when  the  inertia  form  of  governor  is  used. 

(5)  The  adjustments  of  spring  to  obtain  the  desired  degree  of 
regulation,  and  of  weight  to  obtain  the  speed  wanted,  are  made 
in  the  manner  outlined  in  Section  139  (h)  for  the  elementary 
governor. 

There  are  almost  an  unlimited  number  of  forms  of  shaft 
governors,  but  all  of  them  are  merely  modifications  of  those 
which  have  been  described. 


CHAPTER  XIX. 

THE  VALVE  GEARS  OF  STEAM  ENGINES. 

141.  Introduction.     It  is  assumed  that  the  reader  is  already 
familiar  with  the  arrangement  and  operation  of  the  simple  steam 
engine  having  the  plain  slide  valve,  and  that  he  is  able  to  use 
at  least  one  kind  of  u  valve-gear  diagram  "  for  the  analysis  or 
design  of  a  simple  "  D-valve."     The  purpose  of  this  chapter  is 
mainly  to  review  certain  definitions,  to  bring  out  certain  con- 
ceptions which  will  be  useful  in  the  later  discussions,  and  to  give 
a  brief  discussion  of  the  different  types  of  valve  gears  used  on 
steam  engines. 

142.  The  Engine.    Definitions,     (a)  The  crank  end  (C.  E.),  or 
front  end,  of  the  cylinder,  or  valve,  is  the  one  nearest  the  crank, 


MODEL  OF 
SINGLE  ACTING 

ENGINE          crank  End 


Head  End 


or  next  to  the  engine  frame.     The  opposite  end  is  the  head  end 
(H.  E.),  or  back  end. 

(b)  The  forward  (Fd.)  stroke  of  the  piston  or  valve  is  that 
towards  the  crank.     The  return  stroke  is  the  back  (Bk.)  stroke. 

271 


272 


HEAT-POWER  ENGINEERING 


(c)  Fig.  132  shows  a  model  of  a  simple  single-acting  engine 
with  piston  and  valve  driven  by  crank  and  eccentric  pins  opera- 
ting in   Scotch  yokes,  or  slotted  crossheads.      It  is  evident  that 
with  this  arrangement  the  valve  and  piston  will  have  simple 
harmonic  motions,  and  in  consequence  the  analysis  of  the  valve 
action  is  a  simple  matter. 

The  motions,  with  this  arrangement,  are  exactly  the  same  as 
would  occur  if  the  engine  had  connecting  and  eccentric  rods  oj 
infinite  length. 

(d)  Steam  engines,  of  course,  have  connecting  rods  and  eccen- 
tric rods  of  finite  length,  and  the  "  angularity  "  of  these  rods 
causes  the  motions  of  piston  and  valve  to  depart  slightly  from 
the  true  harmonic.     The  eccentric  rods  are  usually  so  long,  how- 
ever, when  compared  to  the  radius  of  the  eccentric  crank,  that 
the  departure  in  the  case  of   the  valve   is  negligible.     If  the 
analysis  of  motions  is  to  be  only  closely  approximate,  the  motion 
of  the  piston  may  also  be  taken  as  true  harmonic,  which  simplifies 
the  problem. 

(e)  The  crank  is  on  dead  center  when  the  piston  is  at  the  end 
of  the  stroke,   and   is   then   horizontal   on   horizontal   engines. 
When  the  piston  is  at  the  head  end  of  the  cylinder,  the  crank  is 
on  the  "  head-end  dead  center  ";  when  at  the  other  end,  it  is  on 
the  "  crank-end  dead  center." 

(f)  The  eccentric  (ecc.  or  E)  is  really  a  crank  with  pin  of  such 
large  diameter  as  to  surround  the  shaft.     In  the  following  dis- 
cussion the  term  "  eccentric  "  will  be  used  as  applying  to  the 
center  of  this  pin.     Like  other  cranks,  the  eccentric  has  dead- 
center  positions. 

(g)  The  throw  of  the  eccentric  is  the  "  eccentricity  "  or  length 
of  the  crank.     (There  is  a  lack  of  agreement  in  the  use  of  the 
term  "  throw,"  some  using  it  in  the  sense  given  and  others  as 
meaning  the  total  movement  of  the  valve  or  "  travel.") 

143.  The  Valve.  Definitions,  (a)  Fig.  133  shows  the  longi- 
tudinal section  of  a  simple  D-valve  suitable  for  a  single-acting 
engine  which  takes  steam  at  only  the  head  end  of  the  cylinder. 
This  valve  is  arranged  to  admit  steam  to  the  cylinder  past  the 
left  outer  edge  (when  steam  edge  s  of  the  valve  passes  to  the 
right  of  the  steam  edge  S  of  the  port),  and  to  exhaust  the  steam 
from  the  cylinder  past  the  left  inner  edge  (when  the  exhaust 


THE    VALVE  GEARS   OF  STEAM  ENGINES 


273 


STEAM 
CHEST 


Fig.  133. 


edge  u  of  the  valve  moves  to  the  left  of  the  exhaust  edge  U  of 
the  port). 

(b)  The  width  of  the  port  is  the  distance  SU  in  the  figure. 

(c)  The  valve    shown    is 
called   an   external   valve.     If 
the  valve  admitted  steam  to 
the  cylinder  past  its  inner 
edge    and    exhausted    at   the 
end,  it  would  be   an  internal 
valve,  and  would  have  to  be 
of  different  design  from  that 
shown    here.      Unless   other- 
wise stated,  the  valve  will  be 
assumed  to  be  external. 

(d)  The  terms  "  steam  chest"  "exhaust  cavity,^  and  "  valve  seat " 
should  not  need  explanation  (see  Fig.  133). 

(e)  The  valve  is  central  (or  in  mid-travel),  with  index  at  0  in 
Figs.  132  and  133,  when  the  eccentric  is  vertical,  either  up  or 
down. 

(f)  The  lap  of  the  valve  is  the  distance  between  the  valve  edge 
and  the  port  edge  with  which  it  operates,  when  the  valve  is 
central.     The  outside  lap  (or  outer  lap)  is  that  of  the  outer  edge, 
and  the  inside  lap  is  the  lap  of  the  inner  edge  of  the  valve.     The 
steam  lap  (S.  L.),  see  Fig.  133,  and  the  exhaust  lap  (Ex.  L.)  are 
respectively  those  of  the  steam  and  exhaust  edges  of  the  valve. 
The  lap  is  positive  if  the  port  is  closed  when  the  valve  is  cen- 
tral and  negative  if  open.      (Negative  lap  is  sometimes  called 
"  clearance.") 

(g)  The  valve  opening  is  variable  and  is  dependent  on  the  dis- 
placement of  the  valve;  but  the  term  is  usually  understood  as 
referring  to  the  maximum  width  of  the  opening  unless  otherwise 
stated. 

(h)  The  travel  of  the  valve  is  the  stroke  or  total  amplitude  of 
its  motion.  If  the  valve  is  direct-driven,  the  travel  is  equal  to 
the  diameter  of  the  eccentric  circle. 

(i)  The  term  "displacement,"  when  applied  to  the  valve,  will  be 
understood  to  mean  the  distance  the  center  of  that  part  has  been 
moved  from  its  central  position;  and  in  the  case  of  the  eccentric 
on  a  horizontal  engine  it  will  be  the  horizontal  distance  from  the 
center  to  the  vertical  center  line  of  the  shaft. 


274  HEAT-POWER   ENGINEERING. 

(j)  The  four  periods  of  operation  of  the  valve  are  admission 
expansion,  exhaust,  and  compression. 

(k)  The  four  principal  valve  events  are  admission  (^4),  cut-off 
(C),  release  (R),  and  compression  (K).  The  four  minor  events 
are  maximum  displacement  of  the  valve  to  the  right  (M),  same 
to  the  left  (m),  valve  central  and  moving  to  the  left  (Q),  and 
central  but  moving  to  the  right  (q). 

The  letters  given  in  the  parentheses  in  the  above  list  will  be 
used  to  indicate  the  respective  events  on  the  diagrams  which  are 
to  follow. 

(1)  Unless  it  is  specifically  stated  to  the  contrary,  it  will  always 
be  assumed  in  the  following  discussion  that  the  engine  is  horizontal, 
with  cylinder  to  the  left  of  the  crank  shaft,  that  an  "  external  valve  " 
is  used,  and  that  the  crank  rotates  in  a  clockwise  direction. 

144.  Action  of  the  D-Valve  and  Eccentric,  (a)  When  the 
valve  is  driven  by  a  Scotch  yoke,  it  is  seen,  by  referring  to  Fig. 
132,  that  (i)  the  valve  is  central  when  the  eccentric  is  on  the 
vertical  center  line  OY  through  the  center  of  the  shaft,  (2) 
the  valve  will  be  in  this  position  whether  the  eccentric  OE  is 
vertical  upward  or  downward,  and  (3)  that  at  all  times  the  dis- 
placement x  of  the  eccentric  E  equals  the  displacement  x  of  the 
valve. 

(b)  In  Fig.  133  it  is  seen  that  the  valve  must  be  displaced  to 
the  right  a  distance  equal  to  the  steam  lap  before  opening  to 
steam  occurs,  and  that  any  further  displace- 
ment represents  opening.  In  Fig.  134,  in 
which  the  radius  of  the  circle  equals  the  eccen- 
tric throw,  the  distance  from  the  eccentric 
center  (anywhere  on  this  circle)  to  the  axis 
qQ  is  the  valve  displacement.  On  this  figure 
the  "  steam-lap  line  "  AC  has  been  drawn  at 
a  distance  equal  to  the  steam  lap  to  the  right 
of  qQ.  Hence  the  steam  edge  is  open  an 
amount  equal  to  the  horizontal  distance  the  eccentric  is  to  the 
right  of  line  AC.  In  Fig.  133  it  is  seen  that  the  valve  must 
be  displaced  to  the  left  a  distance  equal  to  the  exhaust  lap 
before  exhaust  opening  occurs,  and  that  further  displacement 
in  that  direction  represents  the  amount  of  opening.  In  Fig. 
134  the  exhaust-lap  line  KR  is  at  a  distance  which  equals,  the 


THE   VALVE  GEARS  OF  STEAM  ENGINES  275 

exhaust  lap  to  the  left  of  Qq.  Hence  the  exhaust  edge  of  the 
valve  is  open  an  amount  equal  to  the  horizontal  distance  that  the 
eccentric  is  from  KR,  if  it  is  to  the  left  of  that  line.  If  the  ex- 
haust lap  is  negative,  KR  will  be  to  the  right  of  qQ. 

(c)  Starting  with  the  eccentric  center  atq  in  Fig.  134,  the  valve 
is  evidently  central  and  moving  to  the  right,  since  the-tptation  js 
clockwise.     When  the  eccentric  reaches  A,  the  valve  displace- 
ment equals  the  steam  lap,  and  admission  occurs;  when  at  B,  the 
valve  is  displaced  a  distance  BO  to  the  right  and  its  steam  edge 
is  open  an  amount  equal  to  BD;  at  M  the  valve  has  maximum 
displacement   and   maximum   steam  opening;   at   C  the  valve, 
now  moving  to  the  left,  has  displacement  equal  to  the  steam  lap, 
and  cut-off  is  occurring ;  at  Q  the  valve  is  central  and  its  edges  are 
overlapping  by  amounts  equal  to  the  respective  laps;   at  R  the 
valve  is  displaced  to  the  left  an  amount  equal  to  the  exhaust  lap, 
and  is  opening  to  release;  at  m  the  valve  displacement  is  maximum 
to  the  left,  and  maximum  exhaust  opening  is  reached ;  and  at  K 
the  displacement  is  equal  to  the  exhaust  lap,  so  that  exhaust 
closure  or  compression  is  beginning.     The  amounts  of  openings 
to  steam  and  exhaust  are  shown  by  the  lengths  of  the  horizontal 
section  lines.     Fig.  134  may  be  called  a  rectilinear  diagram  of 
valve  displacements. 

(d)  Note  that  admission  and  cut-off  are   controlled  by  the 
same  valve  edge  (steam  edge)  but  with  valve  motions  opposite. 
This  is  apparent  not  only  from  Fig.  133,  but  can  be  seen  from 
line  AC  in   Fig.    134.     Similarly,   compression  and  release  are 
controlled  by  the  same  edge  (exhaust  ^'[q 

edge).  Valve  events  controlled  by  the 
same  edge  may  be  called  conjugate 
events,  and  it  is  important  to  note 
that  changing  the  lap  affects  in  opposite  -i 
manner  the  two  conjugate  events  which 
the  edge  controls. 

(e)  Fig.  135  shows  a  polar  diagram 
of  valve  displacements,  corresponding 
to    the    different    eccentric    positions. 
This  diagram  is  not  necessary  here,  but 

it  will  be  of  use  in  connection  with  a  valve  diagram  which  will 
be  discussed  later.  Given  any  eccentric  position  OE,  the  valve 
displacement  x  =  OB'  is  laid  off  as  OB  along  OE.  The  locus 


276 


HEAT-POWER  ENGINEERING. 


of  point  B  is  OAMCORmK,  which  is  composed  of  two  circles. 
The  locus  for  displacements  to  the  right  is  shown  by  the  heavy 
line,  and  that  for  displacements  to  the  left  by  the  light  line. 
Given  any  eccentric  position  such  as  OE,  the  intercept  OB  is 
the  valve  displacement  (here  to  the  right) . 

Arc  AC  is  the  steam-lap  line,  and  is  struck  with  the  steam 
lap  as  radius.  Arc  RK  is  the  exhaust-lap  line,  with  radius 
equal  to  the  exhaust  lap. 

When  the  eccentric  is  at  Oq,  the  valve  is  central ;  when  it  ex- 
tends through  OA ,  the  valve  displacement  equals  the  steam  lap, 
and  admission  occurs ;  when  at  OM ,  the  displacement  and  steam 
opening  are  maximum;  when  through  OC,  cut-off  occurs;  at  OQ, 
the  valve  is  central;  when  through  OR,  release  takes  place;  at  Om, 
the  displacement  and  exhaust  opening  are  maximum;  and  at  OK, 
compression  begins.  The  lengths  of  the  radial  section  lines  show 
the  amounts  of  opening  of  the  steam  and  exhaust  edges. 


H.  E 


Fig-  i37- 


Fig.  136. 

(f)  Fig.  136  shows  a  double-end  D-valve 
such  as  is  used  on  double-acting  engines. 
The  crank-end  displacement  diagram  will 
be  similar  to  the  head-end  diagram  ro- 
tated through  1 80  degrees. 

145-  Relative  Valve  and  Piston  Posi- 
tions, (a)  Consider  the  piston  driven  by 
a  Scotch  yoke,  as  in  Fig.  132.  When  the 
crank  is  on  head-end  dead  center,  as  in 
Fig.  137,  the  valve  should  have  opened  a 
slight  amount,  called  the  lead,  principally 


L.HC  ivctU)  \Ji  liicipaliy 

in  order  to  furnish  steam  to  fill  the  clearance  space  and  replace  the 
vapor  lost  by  initial  condensation  before  the  stroke  starts.    Hence 


THE   VALVE  GEARS  OF  STEAM  ENGINES 


277 


the  eccentric  at  this  time  must  be  at  OB,  with  displacement  equal 
to  lap  plus  lead.  The  angle  a  =  gOB  is  called  the  angle  of 
advance,  and  it  is  seen  that,  for  the  valve  to  have  lead  and  the 


Fig.  138. 

proper  direction  of  motion  when  the  crank  is  on  dead  center,  the 
eccentric  must  precede  the  crank  by  an  angle  equal  to  90  degrees  plus 
angle  of  advance.  Thus  if  rotation 
were  counter-clockwise  the  eccentric 
would  be  at  OB '  when  crank  is 
at  OP. 

(b)  Fig.  138  shows  the  successive 
critical  crank  positions  during  one 
complete  revolution  of  the  crank. 
These  crank  positions  are  located 
90°  +  a  behind  the  corresponding 
eccentric  positions.  The  figure  also 
shows  the  development  of  the  indi- 
cator diagram  during  the  revolution.  J. 


146.  Elliptical  Diagram.  To  show 
at  a  glance  the  simultaneous  dis- 
placements of  the  valve  and  piston 
throughout  the  complete  revolution 

of  the  engine,  the  displacements  of     Fis-  139- -  Elliptical  Diagram, 
the  valve  may  be  plotted   as  ordinates  on  the  corresponding 
positions  of  the  piston  as  abscissas.      These  coordinates  can  be 


278 


HEAT-POWER  ENGINEERING. 


obtained  directly  from  the  corresponding  crank-pin  and  eccentric 
positions,  as  shown  in  Fig.  139  (a),  or  may  be  obtained  from  other 
valve  diagrams  which  will  be  discussed  later.  The  resulting 
figure  is  an  ellipse,  as  shown  in  Fig.  139  (6),  in  which  valve  dis- 
placements to  the  right  are  positive  ordinates  and  those  to  the 
left  negative. 

Lines  A  C  and  RK  are  the  head-end  steam  and  exhaust  lines 
and  are  drawn  at  distances  from  qQ  equal  to  these  respective 
laps.  (If  the  exhaust  lap  is  negative,  RK  will  be  above  qQ.) 
The  valve  events  are  lettered  in  accordance  with  the  notation 
adopted  in  Section  143  (k).  The  valve  openings  are  shown  by 
the  lengths  of  the  section  lines.  The  opening  at  the  beginning 
of  the  stroke  is  the  lead. 

If  an  indicator  diagram  for  the  head  end  were  drawn  just 
below  Fig.  139,  the  piston  positions  for  the  valve  events  could  be 
found  by  vertical  projection. 

As  both  ends  of  the  valve  have  the  same  displacement,  the 
same  ellipse  would  be  used  for  the  crank  end,  but  the  steam  lap 
would  be  located  below  and  the  exhaust  lap  above  qQ  (if  positive) . 

The  elliptical  diagram  shows  at  a  glance  the  complete  action 
of  the  valve,  and  shows  how  the  valve  opening  varies  with  the 
piston  positions.  The  part  of  the  diagram  above  the  steam-lap 
line  may  be  considered  as  a  Diagram  of  Steam  Openings.  Simi- 
larly, that  part  lying  below  RK  is  a  Diagram  of  Exhaust  Open- 
ings. 


Fig.  140.  —  Sweet  Diagram. 

147.   The  Sweet  Diagram.     In  Fig.  140  (a)  is  shown  a  diagram 
of  valve  and  eccentric  displacements  similar  to  Fig.   134,  and 


THE   VALVE  GEARS  OF  STEAM  ENGINES  279 

Fig.  140  (b)  shows  the  diagram  rotated  backward  (counter- 
clockwise) through  an  angle  of  90°  +  a,  which  is  the  angle  at 
which  the  crank  follows  the  eccentric.  When  the  crank  is  at  any 
location  OP  in  Fig.  140  (a)  and  eccentric  at  corresponding  posi- 
tion OB,  the  valve  displacement  is  oB  and  its  opening  is  DB. 
In  Fig.  140  (b),  with  crank  in  same  position  OP,  the  distance  oB, 
measured  perpendicularly  to  gQ,  gives  the  valve  displacement, 
and  DB  is  the  valve  opening.  Thus  the  valve  displacement  and 
opening  for  any  crank  position  can  be  obtained  directly  from 
Fig.  140  (b),  which  is  called  the  "  Sweet  Diagram,"  and  there  is 
no  necessity  of  finding  the  corresponding  eccentric  position. 

In  constructing  the  Sweet  diagram  a  circle  is  drawn  with 
radius  equal  to  the  eccentric  throw;  the  axis  gQ  is  at  angle  a 
with  OX ;  and  lap  lines  A  C  and  RK  are  drawn  at  distances  from 
gQ  equal  to  the  laps.  OP  A  is  the  crank  position  for  admission; 
OM,  for  maximum  displacement;  OPc,  for  cut-off;  OQ,  for  valve 
central;  OPR,  for  release;  OPR,  for  compression.  The  openings 
are  shown  by  the  lengths  of  the  section  lines,  and  when  the  crank 
is  on  head  dead  center  the  opening  is  the  lead.  The  foregoing  is 
for  the  head  end  of  a  valve  having  positive  exhaust  lap.  If  the 
exhaust  lap  is  negative  RK  would  be  above  gQ.  For  the  crank 
end  of  the  valve  the  steam  lap  would  be  located  below  gQ,  and 
the  exhaust  lap,  if  positive,  above  that  line.  The  little  "  Pilot 
Diagrams  "  show  the  relation  of  crank  and  eccentric  for  all  valve 
events. 

The  elliptical  diagram  can  be  obtained  from  Fig.  140  (b)  by 
using  distances  oB  as  ordinates  on  the  horizontal  projection  of 
the  crank  pin  P. 

148.  Zeuner  Diagram.  In  Fig.  141  (a)  is  shown  a  polar  dia- 
gram of  valve  and  eccentric  displacements  similar  to  Fig.  135, 
and  Fig.  141  (b)  shows  the  same  diagram  rotated  backward 
through  the  angle  90°  +  a.  In  Fig.  141  (a),  when  the  crank  is 
at  OP  and  eccentric  at  OE,  the  valve  displacement  is  OB  and 
its  opening  is  DB.  In  the  Zeuner  diagram,  Fig.  141  (b),  with 
crank  in  the  same  position  OP,  OB  is  the  displacement  and  DB 
is  the  opening.  The  crank  positions  for  all  events  (major  and 
minor)  are  shown  and  lettered  on  the  figure,  and  the  lengths  of 
the  radial  section  lines  show  the  valve  openings  for  the  different 
crank  positions.  The  lead  is  the  opening  when  the  crank  is  on 


28o 


HEAT-POWER  ENGINEERING 


dead  center.     The  Zeuner  diagram  for  the  crank  end  is  similar 
to  that  for  the  head  end  rotated  through  180  degrees.     In  Fig. 


(b) 


Fig.  141.  —  Zeuner  Diagram. 


141   (b)  the  "  Pilot  Diagrams  "  show  the  relative   positions  of 
crank  and  eccentric  at  all  valve  events. 

The  elliptical  diagram  can  be  easily  obtained  from  the 
Zeuner  diagram. 

149.  Bilgram  Diagram,  (a)  The  foregoing  diagrams  are  useful 
for  analyzing  the  action  of  a  valve  when  its  dimensions  and  those 
of  the  eccentric  are  known.  They  are  difficult  to  use,  however, 
in  designing  a  new  valve  gear,  that  is,  in  determining  the  valve 

laps   and    the    eccentric  throw  and 
angle  of  advance,  which  will  give  a 
P.^  proposed  steam   distribution  in  the 
Fom*>  cylinder,   with    specified    widths    of 


openings.       The    Bilgram    diagram 
°j^^j  has  the  advantage  that  it  can   be 

Fig.  142. -Bilgram  Diagram,     readily  used    either   for  analysis  or 

for  design. 

(b)  Fig.    142   shows  the  principle  of    the    Bilgram   diagram. 
/  On  it  the  line  OQ  is  made  equal  to  the  eccentric  throw  and  is  at 
'    angle  a  (the  angle  of  advance)  with  OX.     Q  is  a.  fixed  point  on 
this  diagram  and  is  called  the  Lap-Circle  Center.     The  Funda- 
mental Principle  on  which  the  construction  and  use  of  the  Bil- 
gram diagram  is  based  may  be  stated  thus:   The  length  of  the  per- 
pendicular (QD  in  Fig.  142)  from  the  lap-circle  center  (Q)  to  the  crank 
(OP),  produced  if  necessary,  is  the  valve  displacement  corresponding 


THE    VALVE  GEARS  OF  STEAM   ENGINES  281 

to  that  crank  position.  Proof.  —  When  the  crank  is  on  dead 
center  (at  OP'  in  Fig.  142)  the  eccentric  is  at  OE  and  angle 
EOY  =  a.  Now  if  the  crank  rotates  through  angle  0  to  OF, 
the  eccentric  moves  through  the  same  angle  to  B,  and  the  valve 
then  has  displacement  equal  to  D'B.  Now  angle  QOX  =  a 
and  XOD  =  0.  Then  if  QD  is  drawn  perpendicular  to  OP 
(produced),  it  is  evident  that  triangles  OQD  and  OBDf  are  equal 
and  that  QD  =  D'B ;  hence  the  perpendicular  QD  gives  the  valve 
displacement  when  crank  is  at  OP,  which  proves  the  "  funda- 
mental principle." 

The  term  "  perpendicular  "  used  in  connection  with  the  Bil- 
gram  diagram  will  hereafter  be  understood  to  refer  to  the  length 
of  perpendicular  dropped  from  Q  to  the  crank,  produced  if 
necessary. 

The  elliptical  diagram  can  of  course  be  constructed  by  using 
these  perpendiculars  as  ordinates  on  piston  positions  as  abscissas. 

(c)  Evidently  the  feet  of  the  perpendiculars  will  be  on  a  circle 
with  OQ  as  diameter,  as  in  Fig.  143.  By  subtracting  the  lap 
from  the  displacement  perpendiculars,  the  openings  of  the  valve 
are  obtained. 

In  Fig.  143,  with  Q  as  center  and  radius  equal  to  the  steam 
lap,  the  steam-lap  circle  BF  is  drawn;  hence  the  lengths  of 


Fig.  143- 

the  section  lines  (drawn  radially  from  Q)  in  this  figure  give  the 
steam  openings  for  the  head  end  of  the  valve.  Then  OA  (whose 
extension  is  tangent  to  the  lap  circle)  is  the  crank  position  for 
admission,  as  the  valve  displacement  (as  shown  by  the  length  of 
perpendicular)  just  equals  the  steam  lap.  At  OP  the  opening 


282 


HEA  T-POWER  ENGINEERING ' 


Fig.  144. 


is  FD  and  displacement  is  QD ;  at  OM  the  opening  is  maximum  and 
equal  to  OB ;  at  OC  the  opening  is  zero  and  cut-off  occurs.  When 
the  crank  is  on  head-end  dead  center  the  opening  L  is  the  lead. 

(d)  Fig.   144  shows  the   completed  Bilgram  diagram  for  the 
head  end  of  the  valve.     Compared  with  Fig.  143,  it  is  seen  that 

the  smaller  circle  about  Q,  and 
the  crank  positions  for  the  ex- 
haust events,  have  been  added. 
The  small  circle  is  the  Exhaust- 
Lap  Circle,  with  radius  equal 
to  the  exhaust  lap.  If  release 
is  to  occur  when  the  crank  is 
in  position  OR,  the  exhaust-lap 
circle  must  be  tangent  to  this 
line,  for  then  the  valve  displace- 
ment (as  shown  by  the  length 

of  the  perpendicular)  is  equal  to  the  exhaust  lap. 

When  the  crank  coincided  with  OQ  the  valve  was  central,  and, 

since  in  this  case  the  valve  does  not  open  until  the  crank  has 

rotated  clockwise  past  OQ,  the  valve  is  closed  when  central, 

therefore  the  exhaust  lap  is  positive. 

(e)  The  portions  of  the  perpendiculars  beyond  the  exhaust- 
lap  circle  represent  exhaust  openings.     Evidently  exhaust  closure, 
or  compression,  takes  place  when  the  extension  of  the  crank  is 
tangent  to  the  upper  side  of  the  lap  circle;  thus  OK  is  the  crank 
position  for  compression.     When  the  crank  coincides  with  Oq  the 
valve  is  central ;  and,  since  in  this  case  the  exhaust  lap  is  posi- 
tive,  the  exhaust   closure   must    take   place   before    the   valve 
reaches  central  position;  hence  OK  is  below  Oq  in  this  case,  as 
the  rotation  is  clockwise. 

If  the  exhaust  edge  has  negative  lap,  the  crank  position  OR 
would  be  tangent  to  the  upper  side  of  the  exhaust-lap  circle, 
and  the  extension  of  OK  would  be  tangent  to  the  under  side. 

(f)  The  application  to  design  problems  when  certain  definite 
cut-off,  lead  opening,  and  maximum  valve  opening  to  steam  are 
required,  is  as  follows:    In  Fig.  145,  for  the  H.E.  of  the  valve, 
starting  with  the  X  and  Y  axes,  draw  the  desired  crank  position 
OC  for  cut-off;  draw  a  line  (L)  parallel  to  OX  and  above  it  at  a 
distance  equal  to  the  specified  lead ;  and  with  O  as  center  and 
radius  equal  to  the  desired  maximum  valve  opening  strike  an 


THE   VALVE  GEARS  OF  STEAM  ENGINES 


283 


arc  B  in  the.  position  shown.  From  what  has  gone  before,  it  is 
evident  that  the  steam-lap  circle  must  be  tangent  to  these  three 
lines.  The  location  of  its 
center  Q  can  usually  be 
found  as  quickly  and  as 
accurately  by  trial  as 
by  geometrical  construction. 
Having  the  point  Q  deter- 
mined and  the  steam-lap  cir- 
cle drawn,  the  diagram  then 
shows  the  steam  lap  and  the 
throw  and  angle  of  advance 
of  the  eccentric,  which  must 
be  used  to  obtain  the  de- 
sired results. 

If  OK  in  Fig.  145   is  the 
desired    crank    position    for 


C.E. 


Fig.  145- 


compression,  the  exhaust-lap  circle  would  be  drawn  tangent  to 
the  extension  of  this  line,  with  center  at  Q  just  found,  and  its 
radius  will  equal  the  exhaust  lap.  Whether  the  exhaust  lap  is 
positive  or  negative  can  be  determined  in  accordance  with  (e) 
in  the  foregoing  discussion. 

(g)  For  the  crank  end  of  the  valve,  the  Bilgram  diagram  would 
be  similarly  constructed  but  rotated  180  degrees  with  respect 

to  the  diagram  for  the  head 
end.  Q  and  q  must  of  course 
be  diametrically  opposite 
each  other.  Fig.  146  shows 
the  crank-end  Bilgram  dia- 
gram separately;  *  it  is  usu- 
ally, however,  drawn  super- 
imposed on  the  diagram  of 
the  head  end. 

150.   Distortion    Due    to 
Angularity  of  the  Connecting 
Rod.     In  Fig.  147  o  is  the 
middle  of  the  stroke  and  the  distance  oO  is  equal  to  the  length 
of  the  rod  aP.     If  an  infinite  rod  is  used,   the  displacement 
of    the    piston    oa    will    of    course    be    equal    to   the  displace- 
*  With  negative  exhaust  lap  (shown  dotted). 


Fig.  146. 


284  HEAT-POWER  ENGINEERING  , 

ment  of  the  pin  P,  which  is  equal  to  OA.  If,  however,  a  finite 
rod  is  used  these  displacements  will  not  be  equal.  For,  if  the 
end  of  the  rod  a  is  kept  stationary  and  the  other  end  P  is 

uncoupled  and  swung  to  A', 
then  oa  will  be  equal  to  OA', 
which  is  seen  to  be  greater 
than  OA.  It  will  be  found 
that  no  matter  where  the 
crank  is,  A'  will  always  be 

Fig  I47  to  the  right  of  A.     It  is  evi- 

dent that,  owing  to  the 
"  angularity  "  of  the  connecting  rod,  if  one  of  finite  length  is 
used,  the  piston  is  always  nearer  the  crank  end  of  the  stroke  than 
it  would  be  ideally,  except  of  course  when  it  is  at  the  end  of  its 
stroke. 

It  follows  that:  The  valve  events  occur  later  with  respect  to  piston 
positions  during  the  forward  stroke  and  earlier  in  the  return  stroke 
than  they  would  with  the  Scotch  yoke,  but  their  mean  is  the 
same  as  this  latter  gives  if  the  laps  are  equal. 

The  distance  A  A'  is  the  "  distortion  due  to  the  angularity  of 
the  rod  "  and  is  equal  to  the  difference  between  the  length  of 
the  rod  and  its  horizontal  projection.  This  distortion  is  greatest 
when  the  crank  is  at  right  angles  to  the  center  line  of  the  engine, 
and  decreases  to  zero  at  the  ends  of  the  stroke.  The  shorter  the 
length  of  the  rod  when  compared  to  the  crank  radius,  the  greater 
is  this  relative  distortion. 

If  the  diameter  of  the  crank  circle  XX'  represents  the  stroke 
of  the  piston,  then,  having  any  position,  such  as  A' ,  the  corre- 
sponding position  of  the  crank  pin  P  may  of  course  be  found  by 
drawing  the  "  connecting-rod  arc  "  A'P-  or  if  P  is  known  at 
the  start,  A'  may  be  found  from  it  in  a  similar  manner. 

The  angularity  of  the  eccentric  rod  can  be  neglected  in  most 
cases,  as  the  rod  is  usually  very  long  when  compared  with  the 
eccentric  throw. 

151.  Valve  Diagrams  Considering  "  Angularity  "  of  the  Con- 
necting Rod.  (a)  All  the  valve  diagrams  discussed  show  the 
true  positions  of  the  crank;  therefore  if  the  positions  of  the  pis- 
ton are  not  being  considered,  but  only  those  of  the  crank,  the 
angularity  of  the  connecting  rod  would  not  affect  the  diagram. 


THE   VALVE  GEARS  OF  STEAM   ENGINES 


285 


If,  however,  after  the  crank  positions  have  been  found,  the  true 
positions  of  the  piston  are  desired,  it  will  then  be  necessary  to 
consider  the  angularity.  Having  already  determined  the  crank 
positions,  the  correspond irrg^true^  position  of  the  pistorT  would 
beTound  by  drawing  the  connecting-rod  arcs  in  the  manner 
shown  in  Fig.  148  (a),  (&),  (c)  for  the  Sweet,  Zeuner,  and  Bilgram 
diagrams.  Should  the  piston  positions  be  known  at  the  outset, 
then  by  drawing  similar  arcs  the  true  crank  positions  can  be 
found,  and  these  would  be  used  in  constructing  the  rest  of  the 
diagram. 

In  the  elliptical  diagram,  Fig.  148  (<f),  it  is  evident  that  the 
angularity  causes  all  points  on  the  ellipse  to  be  displaced  toward 


Fig.  148. 

the  crank  end  of  the  stroke.  The  resulting  figure  is  of  oval 
shape,  in  consequence  of  which  the  diagram  is  sometimes  called 
the  "  Oval  Diagram." 

(b)  Owing  to  the  effect  of  the  angularity  of  the  connecting 
rod,  the  piston  displacement  for  similar  events  in  the  two  strokes 
of  a  double-acting  engine  will  not  be  equal  if  the  laps  on  the 
two  ends  of  the  valves  are  the  same.  It  is  possible  to  "  equal- 
ize "  the  cut-offs  by  using  unequal  steam  laps,  but  in  that  case 
the  conjugate  events  (admissions)  are  unequal.  Similarly,  the 
compressions  can  be  "  equalized  "  by  using  unequal  exhaust 
laps,  but  then  the  releases  will  be  unequal.*  Equalization  may 
also  be  accomplished  by  using  special  arrangements  of  rockers 
between  eccentric  rod  and  valve  rod.  This  matter  is  discussed 
fully  in  most  books  especially  devoted  to  valve  gears,  and  will 
not  be  considered  further  here. 

152.  Valve  and  Port  Openings.  For  the  rate  at  which  the 
steam  is  supplied  to  the  cylinder  to  be  always  equal  to  the  rate 

*  Except  in  the  special  case  in  which  the  exhaust  lap  would  be  zero  if  the 
"  angularity  "  of  the  connecting  rod  were  neglected. 


286  HEAT-POWER  ENGINEERING  , 

at  which  volume  is  made  available  by  the  piston,  the  following 
expression  must  be  satisfied  : 

av  =  AV  ........     (273) 

in  which 

a  =  area  of  passage  (sq.  in.,  usually); 

A  =  area,  of  piston  (same  unit)  ; 
v  =  velocity  of  steam  (ft./min.,  usually); 
V  =  velocity  of  piston.  (same  unit). 

Then 

v  .......     (274) 


Valves  are  usually  designed  to  have  a  maximum  area  of 
opening  which  corresponds  to  a  velocity  (v)  of  steam  which  has 
been  found  by  experience  to  give  satisfactory  results.  The 
maximum  valve  opening  (a)  is  computed  by  using  Eq.  (274),  in 
which  V  is  the  mean  piston  velocity  (equal  to  2  X  stroke  in 
feet  X  r.p.m.),  and  v  has  a  value  which  in  practice  varies  from 
6000  to  10,000  feet  per  minute,  but  is  usually  about  8000  feet 
per  minute  in  simple  engines. 

In  designing  the  gear  with  single  valve,  it  is  generally  only 
necessary  to  see  that  the  steam  opening  of  the  valve  is  sufficiently 
large,  for  the  exhaust  opening  will  always  be  more  than  is  re- 
quired because  the  exhaust  lap  is  very  much  smaller  than  the 
steam  lap. 

The  width  of  the  valve  opening  (used  in  constructing  the  valve 
diagrams)  is  of  course  equal  to  the  area  of  opening  divided  by 
its  length.  This  length  is  nearly  always  equal  to  the  length  of 
port  across  the  cylinder. 

In  case  a  simple  valve  is  used,  the  area  of  the  port  in  the 
cylinder  should  be  sufficient  for  accommodating  the  exhaust 
steam,  as  the  same  passage  is  used  for  both  the  entering  and 
the  outgoing  vapor.  Its  area  may  be  determined  from  Eq. 
(274),  using  for  the  steam  velocity  (v)  from  4500  to  7000  feet 
per  minute,  but  about  6000  is  usual  in  simple  engines.  This 
area  is  then  more  than  is  needed  for  the  admission  of  steam. 

If  the  exhaust  passage  is  separate  from  the  steam  passage, 
this  latter  can  have  area  about  equal  to  the  maximum  valve 
opening  to  steam. 

153.  Cushioning  the  Reciprocating  Parts,  (a)  First  suppose 
there  is  no  compression.  Then  when  the  piston  approaches  the 
end  of  its  stroke  the  effective  steam  pressure  and  the  inertia  of 


THE    VALVE  GEARS  OF  STEAM  ENGINES  287 

the  reciprocating  parts  are  both  acting  towards  that  end  of  the 
stroke,  taking  up  the  slack  in  the  bearings  of  the  reciprocating 
parts.  Now,  when  the  steam  is  admitted  on  the  other  side  of 
the  piston,  the  pressure  on  the  bearings  is  reversed  more  or  less 
suddenly.  With  reciprocating  parts  of  small  weight,  and  with 
high  steam  pressure,  this  reversal  will  be  very  sudden,  and  if 
there  is  much  "  play  "  in  the  bearings  (and  there  must  always 
be  a  little)  the  consequent  impact  or  "  hammering  "  will  cause 
excessive  stresses  in  the  impinging  parts,  and  will  render  the 
operation  of  the  engine  noisy. 

(b)  One  method  of  preventing  the  occurrence  of  these  unde- 
sirable features  is  to  make  the  weight  of  the  reciprocating  parts 
so  great  that  their  inertia  will  oppose  the  pressure  of  the  enter- 
ing steam  sufficiently  to  cause  the  play  in  the  bearings  to  be 
taken  up  gradually,  thus  preventing  impact.     But  as  the  inertia 
forces  are  free  forces  which  tend  to  move  the  engine  on  its  founda- 
tion, it  is  usually  desirable  to  have  them  small,  even  when  counter- 
balancing is  attempted ;  so  this  method  is  usually  unsatisfactory. 

(c)  Another  method   is  to  arrange   the  valve    to  open  grad- 
ually, but  this  is  accompanied  by  a  more  gradual  cut-off,  which  is 
undesirable. 

(d)  The  best  method  is  to  gradually  reverse  the  pressure  on 
the  bearings  by  introducing  compression;  then,  when  admission 
takes  place,  there  is  no  play  to  be  taken  up  and  consequently  no 
impact. 

It  is  possible  to  compute  the  inertia  force  of  the  reciprocating 
parts  at  the  end  of  the  stroke.  Then  in  order  to  reverse  the 
pressure  on  the  bearings  the  steam  pressure  at  the  end  of  com- 
pression should  equal  or  be  greater  than  this  inertia  force  plus 
the  steam  pressure  on  the  other  side  of  the  piston. 

154.  Early  Valve  Opening,  (a)  If  steam  is  admitted  just  as 
the  new  stroke  begins,  the  pressure  will  not  rise  immediately  to 
the  value  in  the  steam  pipe  because  (i)  the  valve  opens  grad- 
ually, (2)  the  clearance  space  must  be  filled,  and  (3)  a  large 
proportion  of  the  entering  steam  is  liquefied  by  cylinder  conden- 
sation. Hence  it  is  necessary  to  have  the  valve  open  before  the 
commencement  of  the  stroke;  that  is,  the  valve  is  given  "lead." 
As  the  clearance  volume  is  constant,  the  lead  and  crank  angle  at 
which  opening  occurs  should  be  constant  regardless  of  variations 


288  HEAT-POWER  ENGINEERING 

in  cut-off,  if  the  speed  of  the  engine  is  uniform.  The  higher  the 
speed  and  the  less  the  compression,  the  earlier  should  the  opening 
of  the  valve  occur. 

(b)  In  order  to  have  the  steam  pressure  drop  to  that  of  ex- 
haust by  the  time  the  end  of  the  stroke  is  reached,  the  exhaust 
edge  of  the  valve  is  given  lead,  causing  "  early  release."  As  re- 
lease and  compression  are  conjugate  events,  the  fixing  of  one  of 
these  events  determines  the  other.  Often  it  is  not  possible  tc 
have  both  occur  as  desired,  in  which  case  a  compromise  must 
be  made. 

155.  Limitations  of  the  Simple  Valve.     It  is  impracticable  to 
have  cut-off  occur  early  in  the  stroke  with  the  simple  D-valve 

because,  in  order  to  obtain  a  satisfactory 
width  of  opening  in  such  cases,  it  is  found 
(i)  that  the  valve  and  eccentric  are  ex- 
cessively large  (and  consequently  the 
valve  gear  must  work  against  great  fric- 
tion and  inertia  forces),  and  (2)  that  the 
release  and  compression  occur  too  early 
in  the  stroke. 

Fig.  149  is  a  Bilgram   diagram    for  a 
valve  cutting  off   at  one-fourth  stroke, 
p.  If  the  scale  is  such  that  the  maximum 

opening  to  steam  is  one  inch,  it  is  seen 

that  all  of  the  foregoing  statements  are  true.  The  simple  D-valve 
is  not  used  with  cut-offs  much  earlier  than  five-eighths  stroke. 

Ordinarily,  the  best  economy  in  a  simple  engine  is  obtained 
when  cut-off  is  at  about  one-fourth  stroke;  .hence  the  simple 
slide  valve  should  not  be  used  when  economy  is  important. 

156.  Special  Types  of  Single  Valves,     (a)  By  increasing  the 
length  of  the  steam  edge  of  the  valve  a  reduction  can  be  made 
in  the  port  width,  laps,  travel,  and  eccentric  throw;  but  there  are 
practical  limitations  to  increasing  the  length  of  this  edge  in  the 
simple  flat  valve. 

(b)  Piston  Valves,  Fig.  150,  which  may  be  looked  upon  as 
flat  valves  rolled  into  cylindrical  shape,  may  have  greater  length 
of  edge  (equal  to  the  circumference)  than  the  simple  flat  valve, 
without  having  prohibitive  size.  Fig.  150  (a)  shows  an  "exter- 
nal "  piston  valve;  Fig.  150  (b)  shows  an  "  internal  "  one. 


THE    VALVE  GEARS  OF  STEAM  ENGINES 


289 


EX.L. 


I/'          SECTION 
THROUGH  X-X 

Fig.  150.  —  External  and  Internal  Piston  Valves. 

(c)  Multiported  Valves,  in  which  there  are  two  or  more  work- 
ing edges,  are  frequently  used.     Fig.    151    shows  a  "Double- 


SECTION  B-B;  SECTION  C-C 

Fig.  151. —  Double-ported  Marine  Valves. 

ported  Marine  Valve,"  each  end  of  which  has  two  steam  edges 
and  two  exhaust  edges. 

(d)  Some  valves  have  auxiliary  ports  in  them  so  arranged  as 
to  give  multiported  action.     An  example  of  this  is  the  Allen  or 
Trick  Valve  shown  in  Fig.  1 52 .    This  valve 
has  an  auxiliary  passage  aar  and  valve  seat  steam 
so  arranged  that,  as  the  valve  moves  to 
the  right  in  the  figure,  the  edge  /  opens 
simultaneously  with  the  main  steam  edge  y. 
The  exhaust  is  single- ported. 

Considering  the  valve  as  moving  to  the 
right,  the  phases  of  opening  of  the  steam 
edge  are:  (i)  "Double-ported"  action  while  *  ^  ^ 

edges  /  and  y  open   at   the    same  rate.     Fig.  152.  — Allen  Valve. 
This  continues  until  the  auxiliary  port  a 

is  wide  open.     (2)  With  movement  continuing,  Fig.  152  (&),  the 
opening  at  y  increases  but  that  through  a  remains  constant, 


290  HEAT-POWER  ENGINEERING, 

i.e.,  the  opening  is  "single-ported  plus  a  constant."  This  con- 
tinues until  a'  in  Fig.  152  (c)  becomes  throttled  by  the  exhaust 
edge  of  the  valve  seat.  (3)  As  the  opening  at  a'  is  then 
decreasing  (as  the  valve  continues  to  the  right)  at  the  same 
rate  as  that  at  edge  y  is  increasing,  the  effective  area'  remains 
"  constant:'  (4)  If  the  movement  is  sufficient  to  completely 
close  a',  the  valve  becomes  "  single-ported:'  Now  if  the  valve 
returns  to  the  left  to  close,  the  effective  openings  will  decrease 
in  the  reverse  order. 

The  openings  of  the  steam  edge  of  an  ordinary  valve  are 
shown  by  the  sectioned  part  above  the  steam-lap  line  of  the 

elliptical  diagram  in  Fig.  139. 
This  is  also  shown  (somewhat 
distorted)  by  the  light  line  in 
Fig-  J53-  The  heavy  lines  in 
this  figure  show  the  character 

„  of  the  openings  when  an  Allen 

valve,  like  that  just  described, 

is  used.  Note  that  the  smaller  openings  are  affected  more  than 
the  larger  ones. 

Piston  valves  similarly  arranged  have  been  used  (Armington- 
Sims  valve). 

(e)  The  Sweet  Valve  shown  in  Fig.  154  is  another  valve  hav- 
ing an  auxiliary  port.  This  valve  is  a  rectangular  piston  valve 
which  slides  be'tween  the  valve  seat  and  a  "balance  plate," 
which  latter  is  supported  by  distance  pieces  so  as  to  just  clear 
the  valve.  The  face  of  the  balance  plate  is  similar  to  the  face 
of  the  valve  seat.  All  sliding  surfaces  are  scraped  to  give 
sufficient  clearance  for  free  movement  of  valve  but  not  enough 
to  permit  of  appreciable  leakage  of  steam.  The  valve  has 
separate  auxiliary  ports  a  at  each  end,  which  causes  double- 
ported  action  through  at  least  part  of  the .  opening  of  the 
valve. 

Referring  to  Fig.  155,  it  is  seen  that  as  the  valve  moves  to 
the  right  the  phases  of  opening  of  the  steam  edge  are  the  same 
as  those  of  the  Allen  valve;  thus  there  is  (i)  "  double  opening" 
withy  and /opening  together;  (2)  "  single-ported  plus  a  constant" 
when  /  becomes  greater  than  a;  (3)  "  constant"  when  a  is  being 
closed  by  the  exhaust  edge  of  the  valve  seat  at  same  rate  that  y 
is  opening;  and  (4)  "  single-ported"  when  a  is  entirely  closed  by 


THE    VALVE  GEARS  OF  STEAM   ENGINES 


291 


the  exhaust  edge.  The  areas  during  closure  decrease  in  the 
reverse  order. 

The  auxiliary  port,  or  another  one,  may  be  so  arranged  as  to 
assist  during  the  exhaust. 

(f)  A  combination  of  the  Allen  and  Sweet  arrangements 
gives  quadruple  openings  (Woodbury  valve) ,  and  there  are  many 


Fig.  154.  —  Cylinder  with  Sweet  Valve. 


Fig- 


other  forms  of  such  valves.     For  further  discussion  see  text- 
books on  Valve  Gears. 

(g)  Valve  Friction  is  undesirable,  not  only  because  of  the 
waste  of  power  it  causes,  but  because  it  may  disturb  the  action 
of  the  governor,  if  one  is  used.  The  whole  back  of  the  simple 
D-valve  is  subject  to  full  steam  pressure,  while  the  larger  part 
of  the  under  side  is  exposed  to  the  exhaust  pressure.  The  un- 
balanced pressure  causes  excessive  wear  and  friction  loss  at  the 
rubbing  surfaces.  To  reduce  this  unbalanced  pressure,  various 
schemes  of  "  balancing  "  are  used.  The  simplest  is  the  use  of 


292 


SEAT-POWER  ENGINEERING 


Spring 


Balance  Ring 


a  piston  valve  which  is  perfectly  balanced  except  for  its  weight. 
The  Sweet  type  of  valve  is  practically  the  equivalent  of  the  piston 
valve  in  this  respect.  Some  valves  have  "  balance  or  equilibrium 
rings  "  on  their  backs  (like  that  shown  in  Fig.  156)  so  arranged 
that  the  area  within  the  ring  is  subject  to  exhaust  pressure  and 
is  about  equal  to  the  area  subjected  to  exhaust  pressure  on  the 
under  side.  However,  in  such  cases  there 
should  always  be  enough  unbalanced  pres- 
sure to  maintain  steam-tightness  between 
valve  and  .seat. 

(h)  In  case  there  should  be  entrapped 
in  the  cylinder  a  quantity  of  water  more 
than  sufficient  to  fill  the  clearance  space, 
some  part  of  the  engine  would  break  dur- 
ing compression  unless  some  means  of 
relief  were  provided.  Sometimes  "Relief 
Valves,"  which  are  somewhat  similar  to 
boiler  safety  valves,  are  attached  to  the 
cylinder  ends.  Sometimes  the  slide  valve 
itself  offers  this  relief;  for  example,  the 
simple  slide  valve,  with  or  without  balance 

rings,  and  valves  (like  the  Sweet)  with  pressure  plates  can  lift 
from  their  seats  and  thus  give  relief.  In  such  cases  there 
should  be  springs  or  other  devices  to  return  the  valve  and  bal- 
ance ring,  or  plate,  to  its  proper  position  after  the  cylinder  has 
been  relieved  of  the  water.  Piston  valves  offer  no  such  relief 
themselves,  and  engines  with  this  type  of  valve  should  be  pro- 
vided with  special  relief  valves  or  other  similar  device. 

157-  Valve  Gears  for  High-Speed  Engines,  (a)  The  high- 
speed engine  was  briefly  described  on  page  245.  It  is  fitted  with 
a  "shaft  governor,"  which  controls  the  point  of  cut-off  by  vary- 
ing the  position  of  the  eccentric  with  respect  to  the  crank. 

(b)  Simple  engines  of  this  type  usually  have  cut-off  occur  at 
about  one-fourth  stroke  when  operating  under  "  normal  load." 
The  "  range  of  cut-off"  is  generally  from  zero  to  five-eighths  or 
three-fourths  stroke,  and  the  "  range  of  load  "  is  from  "friction 
load  "  to  50  or  even  100  per  cent  overload. 

It  was  shown  on  page  288  that  if  a  simple  slide  valve  is  used 
to  give  cut-off  as  early  as  one-fourth  stroke,  certain  features  will 


Fig.  156.  —  Valve  with 
Balance  Ring. 


THE    VALVE  GEARS  OF  STEAM  ENGINES  293 

be  introduced  which  are  undesirable  in  the  ordinary  case.     Two 
of  these  are  early  release  and  early  compression. 

(c)  It  so  happens,  however,  that  these  phenomena  are  de- 
sirable in  a  high-speed   engine.     The  early  release  is  advanta- 
geous, as  it  allows  more  perfect  drop  to  back  pressure  in  the 
short  time  available.    The  early  compression  assists  in- causing  a 
gradual  absorption  of  the  inertia  forces;  and  an  excessive  ter- 
minal pressure  can  be  prevented  by  increasing  the  ratio  between 
clearance    volume    and    piston    displacement.     With    a    given 
clearance  volume  and  piston  area,  this  ratio  can  be  made  large 
by  using  a  short  stroke,  and  with  high  rotative  speed  a  short 
stroke  is  desirable  in  order  to  keep  the  piston  speed  down  to 
safe  limits;  hence  what  are  faults  in  the  ordinary  case  make  the 
short-stroke  high-speed  engine  possible. 

(d)  The  excessive  size  of  the  valve-gear  parts,  which  ordinarily 
occurs  when  a  valve  is  designed  for  an  early  cut-off,  as  was 
shown  in  Section  155,  may  be  overcome  by  increasing  the  length 
of  port,  which  calls  for  a  narrower  valve  opening  and  a  cor- 
responding reduction  of  the  laps,  travel,  and  size  of  the  eccen- 
tric;  and  these  in  turn  are   accompanied  by  a  decrease  in  the 
friction  and  wear  of  the  valve  gear.     The  greater  length  of  port 
may  be  obtained  by  using  a  wide  valve,  a  piston  valve,  or  a 
multiported  valve. 

With  the  type  of  valve  gear  which  is  used  on  this  class  of 
engine,  the  travel  of  the  valve  varies  with  the  cut-offs,  and 
the  earlier  the  cut-offs  the  more  restricted  are  the  openings 
of  the  valve.  The  valves  may  be  designed  to  have  open- 
ings ample  for  the  latest  cut-offs,  and  to  have  auxiliary  ports 
added  in  such  a  manner  as  to  assist  during  the  early  openings 
only,  and  to  have  little  or  no  effect  on  the  wider  openings. 
Examples  of  these  various  types  of  valves  have  already  been 
given. 

Sometimes  special  arrangements  of  linkage  are  employed  to 
give  wide  openings  with  small  travel,  as  in  the  case  of  the 
"High-Speed  Corliss  "  engine  to  be  considered  later. 

(e)  The  friction  of  the  valve  is  undesirable,  not  only  because 
it  decreases  the  mechanical  efficiency  of  the  engine  and  causes 
wear,  but  also  because  it  disturbs  the  action  of  the  shaft  gover- 
nor.    This   latter  is  especially  true  if   the  governor  is  of   the 
[nertia  type.     The  governor  is  also  affected  by  the  inertia  of 


294 


HEAT-POWER  ENGINEERING  "' 


the  valve  gear;  hence  high-speed  engines  use  valves  that  are 
balanced  and  are  of  light  weight. 

(f)  In  Fig.  157,  which  is  a  diagram  of  positions,  i-J  is  one 
path,  with  respect  to  crank  OP,  over  which  the  eccentric  might 
be  shifted  by  a  shaft  governor  in  adjusting  the  cut-off  to  meet 
the  power  demanded  of  the  engine.  When,  in  Fig.  157  (a),  the 
eccentric  is  at  i  (with  throw  O-i  and  angle  of  advance  «i)  the 
cut-off  is  at  about  three-fourths  stroke,  for  when  the  eccentric 
has  rotated  in  the  direction  of  the  arrow  to  Ci  (displacement 


Fig.  157. —  Diagram  of  Positions. 

equal  to  steam  lap)  the  crank  pin  is  at  Ci;  when,  in  Fig.  157  (b), 
the  eccentric  is  at  2  (with  throw  0-2  and  angle  of  advance  az) 
the  cut-off  is  about  one-half  stroke,  for  when  the  eccentric  is 
at  C-L  the  crank  pin  is  at  Cz',  and  when  the  eccentric  is  at  J, 
diametrically  opposite  the  crank,  the  cut-off  is  at  Ca.  In  this  case 
the  path  1-3  is  so  selected  that  it  will  coincide  with  Lai  when 
the  crank  is  in  position  OA i;  hence  the  crank-pin  positions 
(Ait  At,  and  AS)  for  the  admissions  corresponding  to  all  cut-offs 
will  coincide,  that  is,  the  admission  is  constant. 

With  crank  at  OP,  the  horizontal  distance  between  the  eccen- 
tric and  the  steam-lap  line  a^  is  the  lead.  From  the  figure  it 
is  seen  that  Lead2  is  less  than  Leadi,  and  that  as  the  eccentric 
is  shifted  to  give  earlier  cut-off  the  lead  becomes  less. 

The  figure  also  shows  that  when  the  eccentric  throw  is  O-i 
the  maximum  valve  opening  is  LAfi,  when  the  throw  is  0-2  the 
maximum  opening  is  LM2,  and  with  0-j  this  opening  is  L-j. 
Thus  the  maximum  openings  decrease  as  the  cut-off  is  made  to 


THE    VALVE  GEARS  OF  STEAM   ENGINES 


295 


occur  earlier.  The  valves  are  therefore  usually  designed  to 
have  proper  opening  at  latest  cut-off  when  operating  as  a  single- 
ported  valve  and  to  be  multiported  when  early  cut-offs  occur. 

If  the  exhaust-lap  line  is  added  to  the  diagram  of  positions, 
Fig.  157,  and  the  crank  positions  are  determined  for  exhaust 
events  corresponding  to  the  different  points  of  cut-offrit  will  be 
found  that  as  cut-off  is  made  to  occur  earlier  the  release  and 
compression  are  also  made  earlier.  Thus  with  early  cut-off 


Fig.  158. 


Fig.  159- 


there  is  greater  compression  than  with  late  cut-off.  Fig.  158 
shows  how  these  events  vary  and  affect  the  form  of  the  ideal 
indicator  diagram,  and  Fig.  159  is  an  actual  diagram  obtained 
from  a  high-speed  engine. 

From  the  foregoing  it  is  seen  that  the  following  general  state- 
ment can  be  made:  As  the  eccentric  is  shifted  from  the  outer  to 
the  inner  position,  cut-off,  release,  and  compression  are  made  to 
occur  earlier  and  the  maximum  opening  is  decreased. 


Fig.  160.          Paths  of  Swinging  Eccentric.         Fig.  161. 

Instead  of  shifting  the  eccentric  over  a  straight  path,  it  can  be 
swung  about  a  pivot  in  the  governor  case  or  flywheel.  When  an 
inertia  governor  (Fig.  130)  is  used  with  external  valve,  the  eccen- 
tric center  will  be  moved  over  a  circular  path,  as  in  Fig.  160,  with 


§96 


HEAT-POWER  ENGINEERING  , 


pivot  opposite  the  crank.  When  the  ordinary  centrifugal  gover- 
nor is  used,  the  eccentric  may  be  pivoted  on  either  side  of  the 
shaft  with  respect  to  crank,  hence  its  path  may  be  that  in  Fig. 
1 60  or  that  in  Fig.  161.  These  curved  paths  approximate  the 
straight  one  in  Fig.  157.  The  admission  will  vary  as  the  eccen- 
tric position  is  changed,  and  the  character  of  the  variation  depends 
on  the  curvature  of  the  path. 

(g)  The  various  valve-gear  diagrams  can  be  constructed  in 
the  usual  manner,  taking  each  position  of  the  eccentric  inde- 


Fig.  162.  —  Valve  Diagrams  for  Variable  Eccentric  Valve  Gear. 


pendently.  The  diagrams  for  the  different  eccentric  positions 
may  be  drawn  separately,  but  usually  they  are  superimposed  on 
one  another,  as  in  Fig.  162,  which  corresponds  to  Fig.  160. 

(h)  At  any  one  cut-off  the  valve  events  can  be  equalized  in 
the  manner  mentioned  in  Section  151  (b).      In  some  cases  it  is 


THE   VALVE  GEARS  OF  STEAM  ENGINES  297 

possible  to  approximate  the  equalization  in  all  positions  of  the 
eccentric  by  using  a  special  arrangement  of  rocker  arm  or  guide 
for  the  eccentric-rod  pin. 

158.   General  Characteristics  of  Independent  Cut-off  Gears. 

(a)  If  an  engine  operates  at  a  constant  speed,  as  most  engines  do, 
it  is  desirable  to  have  the  admission,  compression,  and  release 
remain  constant,  no  matter  how  the  cut-off  varies.  It  has  been 
seen  that  the  simple  valve  with  shifting  eccentric  does  not  give 
this  desired  constancy  of  all  these  events,  nor  does  it  give  suf- 
ficient opening  and  sharp  closure  when  cut-off  is  early  in  the 
stroke.  If,  however,  instead  of  a  single  valve,  two  or  more  are 
used,  with  two  independent  sets  of  valve  gear,  it  is  possible  to 
avoid  some  or  all  of  these  difficulties.  Owing  to  the  complications 
and  extra  expense  involved  with  such  arrangements,  they  are  not 
often  used  on  the  small  high-speed  types  of  engines.  They  are 
quite  common  on  larger  and  longer  stroke,  medium  speed  engines. 
(b)  In  general  the  gear  having  the  two  valves  may  be  ar- 
ranged in  either  of  two  ways:  (i)  Each  valve  may  control  one 
pair  of  conjugate  events;  thus,  one  valve,  having  a  fixed  eccen- 
tric, may  operate  the  release  and  compression,  while  the  other 
valve  takes  care  of  the  admission  and  cut-off,  the  latter  event 
being  changed  by  shifting  the  eccentric  by  a  shaft  governor,  as 
in  the  case  of  the  valve  gear  used  on  high-speed  engines.  In 
this  case,  separate  valve  diagrams  would  be  drawn  for  each  pair 
of  conjugate  events;  that  for  the  steam  events  would  be  con- 
structed the  same  as  for  the  simple-shifting  eccentric  gear;  that 
for  the  exhaust  events  would  be  constructed  the  same  as  for 
any  case  in  which  the  crank  positions  for  the  opening  and  clos- 
ing of  the  exhaust  edge  are  given,  together  with  the  maximum 
width  of  opening  desired.  This  arrangement  will  not  be  con- 
sidered further.  (2)  In  the  other  arrangement  of  the  gear,  one 
valve,  which  will  be  termed  the  main  valve,  controls  the  admis- 
sion, compression,  and  release,  and  is  driven  by  a  fixed  eccentric 
("  main  eccentric  ").  The  other  valve  operates  the  cut-off  only, 
and  will  be  called  the  cut-off  valve.  It  is  an  intercepting  valve, 
being  located  between  the  main  valve  and  the  source  of  steam 
supply.  It  may  slide  on  a  separate  valve  seat,  or  it  may  ride  on 
the  back  of  the  main  valve,  in  which  case  it  is  called  a  "  riding  " 
cut-off  valve. 


298 


HEAT-POWER  ENGINEERING' 


The  variation  in  cut-off  may  be  accomplished  in  three  ways: 
(a)  by  changing  the  lap  of  the  cut-off  valve,  (6)  by  changing  the 
position  of  the  cut-off  eccentric  with  respect  to  the  crank,  and 
(c)  by  a  combination  of  (a)  and  (b). 

The  range  of  cut-off  on  medium-speed  engines  is  usually  from 
zero  to  five-eighths  or  three-fourths  stroke.  Under  normal  load 
simple  engines  usually  cut-off  at  about  one-fourth  stroke. 

(c)  In  all  the  gears  having  a  cut-off  valve  of  the  intercepting 
type,  the  main  valve  or  valves  (operated  by  the  main  eccentric) 
control  the  admission,  release,  and  compression. 

Referring  to  Fig.  144  it  is  seen  that  the  line  OQ  bisects  the 
angle  formed  between  OR  and  OK  produced;  hence,  in  order  to 
determine  [the  proportions  of  the  main  valve  and  its  eccentric, 
proceed  as  follows: 

The  two  conjugate  events  (R  and  K),  which  can  be  decided 
upon  initially,  fix  the  angle  of  advance  of  the  main  eccentric,  for, 
in  the  Bilgram  diagram,  Fig.  163,  OQi  must  bisect  the  angle 


Diagram  of  openings 


Fig.  163. 


Fig.  164. 


between  R  and  K  (produced).  After  drawing  the  lead  line  L,  and 
the  arc  W  for  maximum  opening,  the  steam  lap  is  determined 
by  drawing  the  lap  circle  tangent  to  W  and  L  in  the  figure,  the 
center,  Q,  being  on  OQ,.  Having  located  Q,  the  exhaust-lap  cir- 
cles can  then  be  drawn.  The  diagram  is  now  complete  and  all 
dimensions  for  the  valve  and  eccentric  have  been  found.  The 
cut-off  of  the  main  valve  is  unimportant,  provided  it  is  at  least 
as  great  as  the  latest  given  by  the  cut-off  valve.  Compression, 
of  course,  can  be  equalized  by  using  unequal  exhaust  laps. 

The  diagram  of  openings  of  the  main  valve,  which  is  that 
part  of  the  elliptical  diagram  which  lies  above  the  stearn  lap, 
S.L.,  (for  the  H.E.  of  the  valve),  is  shown  in  Fig.  164. 

(d)  In  all  valve  gears  in  which  there  is  a  separate  cut-off 


THE    VALVE  GEARS  OF  STEAM  ENGINES 


299 


valve  it  is  necessary  that  this  valve  open  before  the  main  valve 
does,  as  the  latter  controls  the  admission.  To  provide  for  this,  it 
is  necessary  in  many  instances  to  have  negative  lap  on  the  cut-off 
valve  and  large  angle  of  advance,  a,  of  the  cut-off  eccentric  (a' 
may  even  be  greater  than  180  degrees  in  some  instances). 

In  the  general  case  the  constructions  of  the  various  valve 
diagrams  for  negative  lap  and  large  angle  of  advance  are  identical 


(a) 


ZEUNER 


Fig.  165. 

with  those  previously  described;  in  each  case  the  angle  of  ad- 
vance is  located  in  exactly  the  same  manner,  and  the  negative 
lap  is  laid  off  opposite  the  positive  lap;  the  openings  are  then 
equal  to  the  displacement  plus  the  negative  lap,  and  the  closures 
equal  the  displacement  minus  this  lap.  With  negative  lap  the 
valve  when  central  is  open,  hence  closure  must  occur  after  the 
central  position  has  been  passed,  and  opening  takes  place  before 
that  position  is  reached.  Figs.  165  (b)  to  (e)  show  the  various 
valve  diagrams  for  angle  of  advance  greater  than  90  degrees, 
and  Fig.  165  (a)  gives  the  actual  position  of  the  eccentric  with 


-00  HEAT-POWER  ENGINEERING   , 

respect  to  the  crank  when  the  latter  is  on  dead  center.  The 
lengths  of  the  section  lines  show  the  widths  of  valve  openings. 

The  generating  point  in  the  elliptical  diagram  will  move 
around  the  ellipse  in  a  counter-clockwise  direction  if  the  angle 
of  advance  is  greater  than  90  degrees,  as  it  is  in  Fig.  165.  As 
before,  the  part  of  the  elliptical  diagram  lying  above  the  steam- 
lap  line  constitutes  a  diagram  of  openings. 

The  cut-offs  at  one  point  in  the  stroke  can  be  equalized  by 
using  unequal  laps. 

(e)  Referring  to  Fig.  165  (e),  it  is  seen  that  the  cut-off  can  be 
varied  either  (i)  by  altering  the  size  of  the  lap  circle  (which  may 
even  be  made  positive),  or  (2)  by  changing  the  angle  of  advance, 
a.  Both  methods  are  used  in  practice. 

A  shaft  governor  may  be  used  to  automatically  change  the 
angle  of  advance  by  turning  the  cut-off  eccentric  about  the 
center  of  the  shaft  on  which  it  is  loosely  mounted. 

159.  Independent  Cut-off  Valve  with  Stationary  Seat.     Fig. 
166  shows  diagrammatically  an  arrangement  with  cut-off  valve 
C  riding  on   an   independent  valve  seat 
between  the  main  valve  M  and  the  steam 
pipe.     The  main  valve  is  driven  by  a  fixed 
eccentric.     It  controls  the  admission,  re- 
lease, and  compression,  and  is  designed  in 
the  manner  outlined  in  Section  158  (c). 
Fig.  166.  The  cut-off  valve  is  driven  by  an  inde- 

pendent eccentric  and  controls  only  the 

one  event.  The  cut-off  can  be  changed  in  either  of  two  ways 
already  mentioned. 

Case  I.  —  The  lap  of  the  cut-off  valve  may  be  altered  by  any 
of  the* following  methods: 

(i)  The  valve  may  be  in  two  parts,  mounted  on  the  valve 
stem  with  R.H.  and  L.H.  threads  respectively.  By  turning  the 
stem,  the  distance  between  the  ends,  and  consequently  the  laps, 
can  be  varied.  With  this 'arrangement,  as  in  Fig.  167,  the  ad- 
justment is  made  by  hand,  and  the  point  of  cut-off  for  the  setting 
can  be  read  on  the  indicator,  which  is  moved  by  a  nonrotating  nut 
on  the  valve  stem.  It  is  difficult  to  arrange  a  governor  to  make 
the  adjustment  with  this  arrangement,  as  several  revolutions  of  the 
valve  stem  are  required  to  accomplish  the  full  range  of  cut-off. 


THE    VALVE  GEARS  OF  STEAM  ENGINES 


301 


Indicator 


Fig.  167. 

(2)  Fig.  1 68  shows  the  back  of  another  arrangement  in  which 
the  edges  of  the  valve  and  ports  are  oblique.  On  the  back  of 
the  valve  is  a  rack  with  which  a  pinion,  on  the  valve  stem, 
engages.  By  turning  the  stem  the  valve  may  be  raised  or 
lowered  (as  viewed  in  the  figure),  thus  changing  the  distance  be- 
tween its  edge  and  that  of  the  port. 


k- Valve >} 


:Neg.  Lap 

Fig."  168. 


Fig.  169. 


(3)  Fig.  169  shows  a  somewhat  similar  arrangement,  except 
that  the  valve  face  and  seat  are  cylindrical  surfaces.  The  valve 
is  fastened  to  the  stem,  so  that  by  turning  the  latter  the  lap  is 
changed. 

The  arrangements  shown  in  Figs.  168  and  169  can  be  controlled 
by  a  fly-ball  governor,  which  can  be  connected  to  an  arm  on  the 
valve  stem. 

Case  II.  —  The  angle  of  advance  may  be  changed,  as  in  Fig. 
170,  in  which  M  is  the  main  eccentric,  o,  \  and  f  are  the  positions 
of  the  cut-off  eccentric  for  those  cut-offs,  X  is  the  "  range  angle  " 
through  which  the  governor  has  to  turn  the  eccentric  on  the 
shaft,  a0'  is  the  maximum  angle  of  advance  of  the  cut-off  eccentric, 
and  a\  is  that  for  three-fourths  cut-off. 

Fig.  171  shows  for  this  case  the  diagram  of  openings  of  the 
cut-off  valve  (dotted  lines)  superimposed  on  that  for  the  main 
valve  (heavy  lines),  and  the  sectioning  shows  the  effective  open- 
ing from  the  time  of  admission  of  the  main  valve  to  the  closure 
of  the  cut-off  valve  at  one-fourth  stroke. 

The  arrangement  of  valves  shown  in  Fig.  166  is  not  satisfac- 
tory, as  with  early  cut-offs  the  space  beyond  the  end  of  the  main 


302 


HEAT-POWER  ENGINEERING 

-0" 


D1AGRAM  OF  OPENINGS 


Fig.  170. 


Fig.  171. 


valve  is  clearance  space  during  the  part  of  the  expansion  preced- 
ing the  closure  of  the  main  valve.  • 

160.  Riding  Cut-off  Valves,  (a)  Instead  of  having  a  separate 
seat  for  the  cut-off  valve,  this  valve  may  ride  directly  on  the 
back  of  the  main  valve  (or  within  it,  if  piston  valves  are  used)  and 
perform  its  functions  with  respect  to  a  port  in  that  valve.  There 
are  several  such  arrangements  possible.  One,  the  Buckeye 
Gear,  is  in  effect  the  exact  equivalent  of  the  arrangement  de- 
scribed as  Case  II  above. 

The  arrangement  of  valves  in  this  gear  is  given  in  Fig.  172, 
both  valves  being  shown  central  with  respect  to  the  ports.  The 


Cylinder- 


I72. 


cut-off  valve  has  negative  lap  equal  to  the  amount  it  is  open  in 
the  figure  with  respect  to  the  main  valve.  The  main  valve  is  a 
box  filled  with  live  steam,  practically  a  reciprocating  steam 
chest.  It  is  an  "  internal  "  valve,  taking  steam  from  the  inside 
and  exhausting  at  the  ends.  The  cut-off  valve  rides  inside  the 


THE    VALVE  GEARS  OF  STEAM   ENGINES  303 

main  valve  and  is  "external";  its  negative  lap  is  of  constant 
amount.  Its  valve  stem  passes  through  that  for  the  main  valve, 
the  latter  being  hollow. 

The  main  valve  is  driven  by  a  fixed  eccentric,  and  controls 
admission,  release,  and  compression.  The  cut-off  valve  is  driven 
by  an  eccentric  which  is  controlled  by  a  shaft  governor  which 
turns  the  eccentric  about  the  center  of  the  shaft,  thus  varying 
the  angle  of  advance,  a',  as  in  Fig.  170. 

(b)  The  arrangement  of  the  rockers  which  guide  the  eccentric- 
rod  ends  is  shown  in  Fig.  173.  The  main  rocker  ab  is  pivoted  at  b 

JsU 

i  To  M.  Ecc 


Fig.  173- 

to  the  frame  of  the  engine.  The  cut-off  rocker  cd  is  pivoted  at 
its  middle  e  to  the  middle  of  the  main  rocker.  With  this  special 
arrangement  of  rockers,  it  is  seen  that  the  displacement  (5)  of  the 
center  of  the  cut-off  valve  with  respect  to  the  center  of  the 
main  valve  is  given  by  the  distance  between  a  and  c,  which  is 
the  same  as  that  between  b  and  d.  Evidently,  then,  the  motion 
of  the  cut-off  valve  with  respect  to  the  main  valve  is  the  same 
as  that  of  c  with  respect  to  a,  or  opposite  to  that  of  d  with  re- 
spect to  b.  Since  b  is  a  fixed  point,  it  follows  that  the  motion  of 
the  cut-off  valve  with  respect  to  the  main  valve  is  the  same  as  that 
of  a  simple  valve  with  respect  to  a  fixed  seat.  The  distance  the 
cut-off  valve  travels  with  respect  to  the  main  valve  remains 
constant,  no  matter  how  the  cut-off  and  phase  relations  of  the 
two  valves  are  altered  by  changing  the  angle  of  advance  of 
the  cut-off  eccentric. 

Thus  this  arrangement  is  equivalent  to  Case  II  of  Section  159, 
but  avoids  its  faults. 

(c)  In  other  "  riding  cut-off  "  gears,  this  peculiar  arrange- 
ment of  rockers  of  the  Buckeye  gear  is  not  used,  but  both 
valves  receive  motion  direct  from  their  respective  eccentrics. 
The  general  arrangement  of  the  valves  is  shown  in  Fig.  174,  in 
which  both  valves  are  external.  The  main  valve  has  a  false 


HE  A  T-POWER  ENGINEERING  • 

end  B,  the  only  purpose  of  which  is  to  provide  an  edge  F,  with 
respect  to  which  the  cut-off  valve  opens  or  closes.  Each  valve 
is  driven  by  its  own  eccentric,  the  location  of  which  is  shown  in 


Crank 


Fig.  175.  The  main  valve  controls  the  admission,  release,  and 
compression,  and  is  designed  as  in  (c)  of  Section  158.  To 
analyze  the  action  of  the  cut-off  valve,  its  motion  with  respect 
to  the  main  valve  must  be  considered. 

(d)  As  the  crank  revolves,  not  only  do  the  eccentrics  rotate 
about  the  center  of  the  shaft,  but  they  rotate  about  each  other. 
That  this  last  statement  is  true  can  be  seen  by  turning  Fig. 
175  about  0,  and  it  will  be  noticed  that,  at  the  same  time,  the 
cut-off  eccentric  rotates  about  the  main  eccentric  and  in  the 
same  direction  as  that  in  which  the  crank  turns.     Evidently, 
then,  the  motion  of  the  cut-off  valve  with  respect  to  the  main  valve 
is  produced  by  the  rotation  of  the  cut-off  eccentric  about  the  main 
eccentric;  hence,  this  motion  is  equivalent  to  that  which  a  simple 
valve  would  have,  with  respect  to  a  fixed  seat,  if  driven  by  an  eccen- 
tric having  throw  equal  to  the  distance  between  the  eccentric  centers 
(Fig.  175)  and  with  angle  of  advance  equal  to  6.     This  imaginary 
eccentric  will  be  called  the  "  relative  eccentric  "  R.     Thus,  to 
analyze  the  action  of  the  cut-off  valve  with  respect  to  the  main 
valve  (its  moving  seat),  the  position  of  the  relative  eccentric 
must  first  be  determined,  after  which  the  valve  diagrams  would 
be  constructed  in  the  usual  manner,  but  using  the  throw  and 
angle  of  advance  of  this  eccentric. 

(e)  The  Meyer  Valve   Gear   has  the   same   arrangement   of 
valves  as  that  shown  in  Fig  174.     The  cut-off  eccentric  usually 
has  a  90-degree  angle  of  advance,  that  is,  it  is  located  opposite 
the  crank.     The  cut-off  is  varied  by  changing  the  lap  of  the 
valve  by  the  method  shown  in  Fig.  167. 

(f)  The  Russell  Valve  Gear  is  similar  in  character  to  Figs. 
174  and  175,  but  the  cut-off  is  altered  by  changing  the  position 


THE   VALVE  GEARS  OF  STEAM  ENGINES 


305 


of  the  cut-off  eccentric.  This  adjustment  is  made  by  a  shaft 
governor  which  turns  the  eccentric  on  the  shaft  to  vary  the  angle 
of  advance. 


Fig.  176. 


Fig.  177. 

The  valves  are  shown  in  Figs.  176  and  177.  The  main  valve 
operates  the  admission  only.  The  exhaust  is  controlled  by  sepa- 
rate triple-ported  valves  of  the  Corliss  type  shown  in  Fig.  177. 


306  HEAT-POWER  ENGINEERING- 

The  cut-off  valve  is  made  triple-ported,  as  is  its  seat  on  the  back 
of  the  main  valve.  The  arrangement  of  eccentrics  is  similar  to 
that  shown  in  Fig.  170. 

(g)  The  Mclntosh-Seymour  Gear  has  separate  main,  cut-off, 
and  exhaust  valves,  of  the  "gridiron"  type,  working  across 
the  cylinder,  as  shown  in  the  section  in  Fig.  178.  These  six 


.Closed 


Fig.  178. 

valves  are  driven  by  arrangements  of  rockers  and  toggles  in  the 
linkage,  which  distort  the  movements,  so  that  after  the  valves 
are  closed  they  have  little  motion;  hence  the  friction  and  wear 
are  reduced  to  a  minimum. 

The  main  valve  receives  its  motion  from  a  fixed  eccentric, 
and  the  cut-off  valve  is  driven  by  an  eccentric  which  is  turned 
about  the  shaft  by  a  shaft  governor  to  adjust  the  cut-off.  Fig. 
100  (p.  247)  shows  the  general  arrangement  of  the  valve  gear 
and  the  rocker  shafts,  which  latter  are  given  an  oscillatory 
motion  by  the  eccentrics  acting  through  bell  cranks.  The 
arrangement  of  eccentrics  is  similar  to  Fig.  170. 


1.2          4  T\  10      12 


Fig.  179. 


Fig.  180. 


Fig.  179  is  the  distorted  elliptical  diagram  for  the  main  valve, 
with  the  opening  diagram  shown  by  bold  lines,     Superimposed  on 


THE   VALVE  GEARS  OF  STEAM  ENGINES 


307 


the  latter  are  lines  showing  the  closure  of  the  cut-off  valve.  Fig. 
1 80  gives  the  distorted  elliptical  diagram  for  the  exhaust  valve. 
It  is  seen  that  the  valve  movements  after  closure  are  much  less 
than  with  ordinary  valve  gears. 

(h)  There  are  many  other  possible  arrangements  of  riding 
cut-off  gears,  a  great  number  of  which  are  in  actual  use. 

161.  Gears  with  Oscillating  Valves,  (a)  Instead  of  having 
the  slide  valve  flat,  it  may  have  a  curved  face,  as  in  Fig.  181,  in 
which  case  the  valve  oscillates  about  center  0'.  The  displace- 
ment x  of  the  eccentric-rod  pin  U  from  the  Y-axis  is  always 
equal  to  that  of  the  eccentric  with  respect  to  the  vertical  axis 
through  the  shaft.  This  valve  is  substantially  equivalent  to 
the  ordinary  flat  D- valve,  and  would  be  designed  or  analyzed  in 


Exhaust 


Fig.  181.  — Oscillating  Valve.  Fig.  182. 

the  same  manner,  using  the  same  valve  diagrams.  These  dia- 
grams show  the  true  positions  of  the  crank  for  all  events;  but 
the  laps,  displacements,  and  openings  are  chordal,  that  is,  would 
be  measured  as  chords  instead  of  as  arcs. 

(b)  This  arrangement  of  valve  introduces  very  long  steam 
passages,  extending  from  the  center  to  the  ends  of  the  cylinder, 
and  this  is  not  conducive  to  economical  performance,  as  has 
already  been  seen. 

(c)  A   better  arrangement  is  one  in  which   there  are   four 
oscillating  valves,  as  in  Fig.   182,  each  of  which  performs  the 
single  function  of  one  of  the  four  edges  of  the  single  valve.     In 
the  figure  the  outer  edges  of  the  two  upper  valves  control  the 
steam  events,  and  the  inner  edges  of  the  lower  valves  operate 
the  exhaust  events.     The  other  edges  of  the  valves  perform  no 
function.     The  chordal  laps  would  be  the  same  as  in  the  case  of 
the  single  valve  of  Fig.  181.     The  valves  shown  in  Fig.  182  are 
of  the  "  Corliss  "  type.     With  this  arrangement  the  steam  and 
exhaust  passages  are  very  short  and  direct,  thus  the  clearance 
volume  and  surfaces  are  relatively  small. 


3o8 


HEAT-POWER  ENGINEERING  ,- 


(d)  All  four  valves  may  be  driven  by  the  single  variable  eccen- 
tric with  shaft  governor,  as  is  common  with  high-speed  engines. 
It  is  better,  however,  to  connect  the  steam  valves  in  this  manner, 
and  to  drive  the  exhaust  valves  by  a  separate  fixed  eccentric,  so 
that  release  and  compression  will  remain  constant. 

(e)  One  fault  of  most  valve  gears  is  that  the  valve  has  large 
movement  after  it  has  closed.     To  reduce  wear  and  friction,  the 
movement  should  cease  as  soon  as  the  overlapping  is  sufficient 
to  prevent  leakage.     Also,   it  is  desirable  to  have  more  rapid 
movement  of  the  valve  after  it  opens  than  is  obtained  with  the 


Imaginary 
Equivalent  Eccentric 


Reach  Rod 


Open 


Fig.  183. 


simple  gear.  Both  results  can  be  effected  by  using  links  and 
rockers  so  arranged  as  to  give  the  valve  the  desired  motion. 
One  such  arrangement  is  shown  in  the  upper  right-hand  corner 
of  Fig.  183.  Engines  using  this  type  of  gear  may  be  called  High- 
Speed  Corliss  Valve  Engines,  or  positive  cut-off  Corliss  engines. 

(f)  At  the  left  of  Fig.  183,  the  edge  s  of  the  steam  valve  is 
shown  even  with  the  port  edge  with  which  it  opens  or  closes. 
Let  gf  be  the  desired  (small)  angular  movement  after  closure, 
and  /'  be  the  (large)  angle  after  opening.  The  steam  arm  oaa', 
which  moves  the  valve,  will  swing  through  the  same  angles  as 
the  valve;  thus  g  and  /  are  respectively  equal  g'  and  /'.  The 


THE    VALVE  GEARS  OF  STEAM  ENGINES  309 

pin  position  a!  for  admission  (motion  to  right)  of  course  coin- 
cides with  c'  for  cut-off  (motion  to  left). 

Starting  at  the  right  of  the  figure,  Ea  is  the  eccentric  position 
for  admission;  Em,  that  for  maximum  opening;  Ec  that  for  cut- 
off; and  En  is  for  extreme  closure.  The  similarly  subscripted 
positions  of  pins  H  and  /  on  the  rocker  arm,  the  positions  A , 
M,  C,  and  N  of  the  reach-rod  pin,  and  a,  m,  c,  and  n  of  the  steam 
pin,  all  respectively  correspond  with  these  eccentric  positions. 
In  each  case  the  position  for  admission  (motion  to  the  right) 
coincides  with  the  position  for  cut-off  (motion  to  the  left).  It 
will  be  seen  that  the  angular  movement  am  of  the  steam  pin 
for  opening  is  smaller  than  that  for  closure  en,  which  is  just 
contrary  to  what  is  desired  for  the  valve  movement.  However, 
it  is  possible  to  locate  the  steam  pin  on  the  wrist  plate  in  such 
position,  and  to  use  such  a  length  of  steam  rod,  that  the  steam 
arm  moves  through  angles  n'c'  and  a'm'  respectively  when  the 
steam  pin  moves  through  angles  nc  and  am,  and  thus  to  ac- 
complish the  desired  result.  With  such  arrangement  the  dis- 
tances nn' ,  aaf,  and  mm'  must  of  course  all  be  equal,  since  they 
represent  the  length  of  the  steam  rod. 

The  exhaust  valve  motion  can  be  similarly  distorted  so  as  to 
be  small  after  closure  and  large  after  release.  The  arrangement 
for  the  crank  end  of  the  cylinder  is  identical  except  reversed. 

(g)  There  are  many  other  arrangements  of  linkage  used  for 
high-speed  Corliss  valve  engines.  Some  involve  the  use  of  a 
separate  fixed  eccentric  to  drive  the  exhaust  valves  and  thus 
obtain  constant  release  and  compression. 


Steam  "Edge) 


Fig.  184.  Fig.  186. 

(h)  In  Fig.  184  is  given  the  distorted  elliptical  diagram  for  the 
steam  valve  of  one  gear  of  this  high-speed  Corliss  type. 

(i)  The  Trip-Cut-off  Corliss  Engine  with  Single  Eccentric. 
Fig.  185  is  similar  to  the  arrangement  just  discussed >  except  that 
the  eccentric  is  fixed  and  the  cut-off  is  operated  by  a  tripping 


310 


HEAT-POWER  ENGINEERING 


THE    VALVE  GEARS  OF  STEAM  ENGINES 


311 


device  positioned  by  a  governor  of  the  fly-ball  type.  The  type 
of  steam  valve  used  is  shown  in  Fig.  186;  and  the  bonnet  for  the 
head-end  steam  valve,  and  the  part  of  the  gear  which  it  supports, 
are  illustrated  in  Fig.  187  (a) .  The  names  of  these  parts  are  given 
in  Fig.  187  (b) .  The  left  arm  A  of  the  bell  crank  carries  a  hook  C 


Latest  C.O 
Earliest  C.O: 
Knock  otf 


SprSng 


Cam. 


Fig.  187.  —  Steam  Gear —  Corliss  Engine. 

which  engages  with  the  steam  arm  on  the  valve  stem.  If  the 
hook  remains  latched,  the  motion  which  the  bell-crank  arm  B 
obtains  from  the  wrist  plate  by  means  of  the  steam  rod  is 
transmitted  directly  to  the  valve,  and  the  case  is  identical  with 
that  discussed  in  (f )  of  this  section.  In  these  engines,  however, 
the  governor  controls  the  position  of  the  knock-off  cam  E,  which 
has  a  definite  position  corresponding  to  each  different  cut-off. 
As  the  bell  crank  is  moved  clockwise,  the  hook  turns  the  steam 
arm  and  opens  the  valve  (as  in  Fig.  183).  This  continues  until 
the  part  D  of  the  hook  comes  in  contact 
with  the  stationary  knock-off  cam  E, 
when  the  hook  becomes  disengaged  from 
the  steam  arm,  which  is  then  returned 
to  its  lowest  position  by  the  dash  pot, 
thus  closing  the  valve. 

(j)  The  simple  elements  of  the  dash  pot 
are  shown  in  Fig.  188.  When  the  steam 
valve  is  opened  the  plunger  is  raised  and 
a  vacuum  is  formed  at  V.  After  the  hook 
has  been  tripped  this  vacuum  causes  the 
descent  of  the  plunger  and  closure  of  the 

steam  valve.   The  fall  is  stopped  by  the  air  cushion  which  is  formed 
between  C  and  C  and  which  is  adjusted  by  the  cushion  valve, 


3I2 


HEAT-POWER  ENGINEERING. 


(k)  Fig.  189  shows  the  distorted  elliptical  diagram  for  the 
steam  valve.  With  the  trip  occurring  at  /,  the  cut-off  is  at  c. 
As  the  valve  cannot  close  instantaneously,  tc  will  slope  somewhat. 
A  similar  diagram  for  the  exhaust  valve  is  given  in  Fig.  190. 


Pull  Back 


'^^^l^arp^ 

Fig.  190. 

In  connection  with  Fig.  187,  it  will  be  noticed  that  the  trip  of 
the  head-end  steam  valve  occurs  when  the  hook  end  D  comes 
in  contact  with  the  stationary  cam  E,  while  the  hook  and  bell 
crank  are  still  moving  to  the  right  (that  is,  before  the  eccentric  has 
reached  the  R.H.  dead  center)',  and  that  if,  when  the  eccentric 
arrives  at  this  position,  the  trip  has  not  taken  place  (E  being 
too  far  to  the  right),  it  will  not  take  place  at  all,  and  cut-off  will 
occur  at  C'  in  Fig.  189  instead  of  at  C. 

(1)  The  angle  of  advance  is  fixed  by  the  release  and  com- 
pression, as  in  the  case  of  the  main  valve  of  the  riding  cut-off 
gears  (Fig.  163).  It  is  in  no  way  dependent  on  the  other  events, 
for,  with  crank  on  dead  center,  the  steam  rod  can  be  adjusted  to 

give  the  valve  the  proper  lead,  and  cut- 
off is  controlled  by  the  knock-off  cam 
independently  of  the  eccentric. 

If  £  in  Fig.  191  is  the  eccentric  po- 
sition for  latest  trip,  the  crank  pin  is 
then  at  T  and  the  piston  at  C.  As, 
however,  some  time  must  elapse  before 
the  valve  is  closed,  cut-off  will  occur 
when  the  piston  has  reached  some  po- 


Fig.  191. 


sition  D,  which  is  usually  at  about  0.4  stroke.  Thus  with  an 
(  rdinary  single  eccentric  Corliss  gear  the  latest  cut-off  possible  is 
about  04  stroke,  and  this  is  accomplished  only  by  using  the 
smallest  angle  of  advance  that  will  give  the  proper  release  and 
compression. 

(m)  There  are  many  other  arrangements  of  va,lves,  of  trip 
gear,  of  wrist-plate  linkage,  and  of  dash  pot,  but  all  operate  in 


THE    VALVE  GEARS  OF  STEAM  ENGINES 


313 


a  manner  similar  to  that  described.     The  valves  are  frequently 
double-  or  multiple-ported. 

(n)  One  of  the  faults  of  this  gear  is  that  a  failure  of  governor 
belt  stops  the  governor  and  lets  the  weights  drop  to  the  lowest 
position,  thus  advancing  the  cut-off  to  the  latest  point.  The 
power  then  developed  is  greater  than  that  absorbed,  ^and  the 
engine  will  ''run  away"  and  be  demolished,  unless  stopped  by 
hand  or  by  some  safety  device. 

One  safety  device  consists  of  a  "  safety  cam  "  S  in  Fig.  187 
which  prevents  the  hook  engaging  with  the  steam  arm  when 
the  governor  occupies  its  lowest  position.  Some  engines  have 
auxiliary  fly-ball  governors  which  will  close  the  throttle  valve 
when  the  speed  becomes  unsafe.  There  are  many  other  forms 
of  safety  devices  in  use. 

(o)  The  limitation  of  the  latest  cut-off  can  be  avoided  by 
using  the  Two-Eccentric  Corliss  Gearf  in  which  one  eccentric 
drives  a  wrist  plate  for  the  exhaust 
valves,  and  another  one  actuates  the 
steam  wrist  plate.  Fig.  192  shows  the 
arrangement  of  eccentrics,  with  crank 
on  dead  center.  The  angle  ft  between 
the  crank  and  steam  eccentric  fixes  the 
latest  cut-off,  but  with  this  arrangement, 
since  the  exhaust  valves  are  driven  in- 
dependently, it  may  be  made  any  value 
within  limits.  The  angle  used  in  the 
figure  permits  of  cut-off  as  late  as  three-fourths  stroke  as  is  seen 
from  the  extreme  (dotted)  position. 

Late  cut-off  can  also  be  obtained  by  using  a  moving  knock-off 
cam  which  may  be  oscillated  either  by  a  separate  small  eccentric  at 
about  90  degrees  with  the  main  eccentric,  or  by  the  sidewise  motion 
of  the  eccentric  rod,  which  is  90  degrees  out  of  phase  with  the  longi- 
tudinal movement.  With  such  arrangement  the  knock-off  cam 
overtakes  the  hook  and  releases  it  even  after  the  main  eccentric 
has  rotated  a  considerable  angle  beyond  the  dead-center  position. 

(p)  The  rotative  speed  of  trip-cut-off  Corliss  gears  must  be 
relatively  low,  for  otherwise  the  hook  gear  becomes  uncertain  in 
action.  Speeds  above  120  r.p.m.  are  seldom  used,  and  generally 
they  are  considerably  less.  Hence  engines  using  this  type  of 
gear  are  commonly  classified  as  "  low-speed." 


Fig.  192. 


314 


HEAT-POWER  ENGINEERING 


(q)  There  are  several  trip-cut-off  gears  which  have  gridiron 
valves  working  across  the  cylinder  either  horizontally  (some- 
what similar  in  arrangement  to  Fig.  178)  or  vertically.  Trip- 
cut-off  gears  are  also  used  with  poppet  valves  (Section  164). 

162.  Link  Gears,  (a)  The  valve  gear  most  commonly  used 
on  engines  which  are  reversed  is  the  Stephenson  Link  Gear,  one 

arrangement  of  which  is  shown 
semi-diagrammatically  in  Fig. 
193.  The  illustration  is  for  a 
vertical  engine  with  cylinder 
above,  but  the  arrangement  for 
a  horizontal  engine  would  be 
identical  except  for  the  position 
of  the  longitudinal  axis. 

(b)  The  eccentrics  are  ar- 
ranged as  in  Fig.  194,  with  the 
"forward  eccentric,"  /,  placed 
90  degrees  plus  angle  of  advance 


Fig.  193.  —  Stephenson  Link  Gear. 


ahead  of  the  crank  in  the  forward  direction  of  rotation,  and  the 
"  backing  eccentric,"  b,  at  the  same  angle  in  the  opposite  direction. 
If  the  valve  receives  all  its  motion  from  eccentric  /,  the  rotation 
will  be  forward  (clockwise  in  this  case) ;  if  from  b,  it  will  be  back- 
ward (counter-clockwise) . 

In  Fig.  193  it  is  seen  that  the  forks  at  the  ends  of  the  two 
eccentric  rods  are  connected  by  a  "  link  "  (whence  the  name  of 
this  type  of  gear),  different  points  of  which  may  be  brought 
opposite  the  "  link  block  "  on  the  end  of  the  valve  stem,  by 
turning  the  "  reverse  "  shaft.  The  illustration  shows  the  for- 
ward end  opposite  (in  "full  gear"  forward),  hence  the  valve  is 
receiving  all  its  motion  from  the  forward  eccentric  and  conse- 


THE    VALVE  GEARS  OF  STEAM  ENGINES  315 

quently  rotates  forward  with  latest  cut-off  possible.  If  the  other 
end  of  the  link  is  brought  opposite  the  link  block  ("full  gear"  back- 
ing) ,  the  engine  would  operate  backward  at  maximum  cut-off. 

With  the  middle  of  the  link  opposite  ("  mid-gear  "),  the  valve 
receives  motion  equally  from  both  eccentrics;  and  the  valve 
will  open  an  amount  equal  to  the  lead  and  close  immediately, 
the  cut-off  being  practically  at  zero  stroke. 

If  the  link  is  shifted  from  mid-gear  toward  the  forward  end, 
the  valve  will  still  receive  motion  from  both  eccentrics,  but  the 
major  part  will  be  from  the  forward  eccentric.  As  the  forward 
end  of  the  link  is  shifted  nearer  the  link  block,  the  width  of 
valve  opening  is  increased  and  the  cut-off  is  advanced  in  a  man- 
ner quite  similar  to  that  in  the  gear  with  single  variable  eccentric, 
Figs.  160  and  161,  when  the  eccentric  is  moved  from  inner  posi- 
tion J  outward  towards  /.  In  fact,  an  approximate  analysis  of 
the  Stephenson  link  gear  can  be  made  by  considering  the  valve 
as  driven  by  a  single  swinging  eccentric  with  a  radius  of  path  R 
which  can  be  computed  by  McFarlane-Gray's  formula: 

o  _  distance  between  eccentric  centers  X  length  of  ecc.  rod     ,       >. 
2  X  distance  between  eccentric-rod  pins 

(c)  If,  with  the  crank  P  pointing  away  from  the  cylinder,  the 
rods  are  not  crossed,  as  in  Figs.  193  and  195  (a),  the  arrangement 
is  termed  "  open  rod."  In  this  case  the  path  of  the  equivalent 
single  eccentric  'isfeb  with  radius  R.  If,  with  crank  in  the  same 
position,  the  rods  are  crossed,  as  in  Fig.  195  (b),  it  is  a  "cross- 
rod  "  linkage,  and  the  path  of  the  equivalent  eccentric  isfeb  * 

For  any  link  position,  the  equivalent  eccentric  occupies  the  same 
relative  position  on  its  path/6  as  the  link  block  on  the  link  FB. 
It  is  seen  that  the  open-rod  linkage  gives  increasing  lead  as  the 
cut-off  is  decreased,  whereas  the  reverse  occurs  with  crossed 
rods.  From  Eq.  (275)  it  is  seen  that  using  longer  eccentric 
rods  increases  R,  thus  making  the  path  straighter  and  the  lead 
less  variable.  To  have  the  lead  vary  equally  at  the  two  ends  of 
the  valve,  the  radius  of  the  link  arc  must  equal  the  length  from 
eccentric  center  to  eccentric-rod  pin,  in  the  arrangement  shown. 

*  Note  that  when  the  crank  has  rotated  180  degrees  the  rods  are  crossed  in  the 
"  open-rod  "  arrangement  and  open  in  the  "  crossed-rod  "  gear.  In  classifying  the 
arrangement  the  crank  must  point  away  from  the  cylinder. 


3i6 


HEAT-POWER  ENGINEERING 


(6) 


Fig.  195- 


(d)  The  link  shown  in  Fig.  193  is  of  the  "  double-bar  "  type. 
There  are  many  other  arrangements:  some  have  the  eccentric- 
rod  pins  offset  from  the  link;  on  some  the  suspension-rod  pin  is 
located  at  the  middle  of  the  link  arc;  on  others,  between  the 
middle  and  the  end.     The  modifications  introduced  in  such  cases 
cannot  be  considered  here. 

(e)  For  the  method  of  making  an  exact  analysis  of  the  action 
of  the  valve  operated  by  a  Stephenson  link  see  textbooks  on 
valve  gears. 

(f)  In    the  Gooch   Link    Gear,  Fig.   196,  the  "radius   rod," 
instead  of  the  link,  is  shifted  to  change  the  cut-off.     As  the  link 
radius  equals  the  length  of  the  radius  rod,  there  is  no  move- 
ment of  the  valve  if  the  adjustment  is  made  when  the  crank  is 
on  dead  center,  as  in  the  figure;  hence   the  lead  is  constant. 
Line  b'f  is  the  path  of  the  equivalent  single  variable  eccentric, 
and  b'bO  is  a  right  angle. 

(g)  The  Allan  Link  Gear  shown  in  Fig.   197  has  a  straight 
link.     The  link  and  the  radius  rod  are  shifted  in  opposite  direc- 
tions in  such  manner  that  the  valve  is  not  moved  when  crank 
is  on  dead  center,  hence  the  lead  is  constant.     The  path  of  the 


THE    VALVE  GEARS  OF  STEAM  ENGINES 


317 


Fig.  196.  —  Gooch  Link  Gear. 


Fig.  197.  —  Allan  Link  Gear. 


equivalent  single  eccentric  is  similar  to  that  in  the  Gooch  link- 
age. 

(h)  The  Porter- Allen  Gear  shown  in  Fig.  198  has  a  link  which 
is  consolidated  with  the  eccentric  strap  and  is  guided  at  A  along 


Val 


(a) 
Fig.  198.  — Porter- Allen  Gear. 

the  center  line  of  the  engine.  The  throw  OM  of  the  eccentric 
equals  lap  plus  lead,  thus,  in  the  position  shown,  the  head  end  of 
the  valve  is  open  to  lead.  As  the  eccentric  rotates  from  this 
position  the  tilting  of  the  link  increases  the  opening,  which  later 
is  decreased  by  the  translatory  motion  of  the  link.  At  (a)  in 
the  figure,  with  link  block  at  V,  maximum  opening  occurs  at 
crank  position  2  and  cut-off  at  j.  With  link  block  in  a  lower 
position,  there  would  be  less  opening  and  earlier  closure,  the 
lead  remaining  the  same,  however. 

Motion  satisfactory  for  exhaust  valves  can  be  obtained  from 
some  point  such  as  E. 

163.   Radial  Valve  Gears,     (a)  In  vertical  multicylinder  ma- 
rine engines  using  link  gears,  the  valves  are  usually  located  per- 


\ 


3*8 


HEAT-POWER  ENGINEERING 


pendicularly  over  the  shaft,  and  some  or  all  of  them  lie  between 
the  cylinders  and  thus  lengthen  the  engine.  It  is  true  that  by 
using  rocker  arms  the  valves  might  be  placed  at  the  side,  but  that 
arrangement  of  mechanism  has  certain  disadvantages,  and  even 
then  the  eccentrics  prevent,  to  a  certain  extent,  the  shortening  of 
the  engine. 

Using  the  type  of  valve  gears  known  as  "  radial  gears  "  necessi- 
tates placing  the  valves  on  the  side  of  the  engine.  In  most  of  the 
gears  of  this  type  a  single  eccentric  is  used  and  in  some  the  eccen- 
trics are  dispensed  with  altogether.  With  this  type  of  gear  the 
engine  can  be  made  to  occupy  less  space  than  with  link  gears. 

There  are  a  great  many  kinds  of  radial  gears;  only  the  most 
important  will  be  described. 

(b)  The  Marshall  Type  of  Gear,  which  is  shown  in  Fig.  199, 
uses  a  single  eccentric,  either  at  o°  or  180°  with  the  crank. 


Head  En* 


Fig.  199.  —  Marshall  Type  of  Radial  Gear. 

The  point  a  on  the  eccentric  rod  Eab  is  guided  along  path  Gg* 
The  end  b  traces  the  oval  figure  shown,  and  its  positions  are 
numbered  to  correspond  with  those  of  the  eccentric  and  crank. 
The  motion  which  the  valve  receives  through  the  rod  be  is  prac- 
tically the  same  as  that  obtained  from  an  eccentric.  By  chang- 
ing the  inclination  of  the  guide  Gg  the  oval  is  changed,  the 
*  The  Hackworth  gear  has  a  straight  guide. 


THE   VALVE  GEARS   OF  STEAM   ENGINES 


3*9 


amount  of  opening  is  altered,  and  the  cut-off  is  varied.  A  re- 
versal of  the  inclination,  as  G'g'  reverses  the  engine.  The  pin  b 
may  either  be  located  as  shown  or  it  may  be  between  E  and  a. 

(c)  If  any  point  in  a  linkage  moves  in  phase  with  the  crank 
and  describes  a  path  that  is  approximately  circular,  a  pin  located 
at  that  point  can  be  used  instead  of  the  eccentric  to^give  the 
valve  the  motion  equivalent  to  that  obtained  with  the  Marshall 
gear. 


v  f 


Vi<  —  /- 


Fig.  200.  —  Joy  Radial  Gear 

In  the  Joy  Gear,  shown  in  Fig.  200,  ac 
is  a  link  with  one  end  attached  to  the  con- 
necting rod  and  the  other  end  to  the  sus- 
pension link  fc.  The  point  E  moves  in 
a  path  which  may  be  substituted  for  the  p 
eccentric  circle.  The  rest  of  the  linkage 
resembles  the  Marshall  in  character  and 
performance. 

(d)  If,  in  Fig.  201,  the  harmonic  motion 
received  from  an  eccentric  H  opposite  the 
crank  is  combined  with  that  from  another  FiS-  201- 

eccentric  V  at  right  angles  to  the  first,  the  resultant  motion  is 
equivalent  to  that  which  would  be  obtained  from  an  eccentric 
located  at  EQ  (found  by  constructing  the  parallelogram  OVEaH), 


320  HEAT-POWER  ENGINEERING 

and  a  valve  receiving  this  combined  motion  would  operate  satis- 
factorily. OH  is  made  equal  to  the  lap  plus  lead,  and  0V  may 
be  varied  to  change  the  angle  of  advance  and  throw  of  the  equiv- 
alent eccentric  E0,  which  has  HE0  as  its  path  and  resembles  the 
single  variable  eccentric  previously  discussed. 

The  Walschaert  Valve  Gear  shown  in  Fig.  202  uses  this  prin- 
ciple. If  the  link  block  d  is  shifted  to  the  middle  e  of  the  link, 
point  c  will  remain  practically  stationary.  Then  the  lever  ab, 


Fig.  202.  —  Walschaert  Radial  Gear. 

which  is  pivoted  at  c  and  receives  motion  at  a  from  the  cross- 
head,  will  vibrate  in  such  manner  that  the  end  b  will  displace 
the  valve  a  distance  equal  to  lap  plus  lead  when  the  crosshead 
reaches  the  end  of  its  stroke,  and  that  the  valve  motion  will 
equal  that  received  from  eccentric  OH  in  Fig.  201.  The  link/g 
receives  motion  from  an  eccentric  E,  which  is  90  degrees  out  of 
phase  with  the  other  motion.  With  link  block  in  any  position 
d  (other  than  central)  on  the  link,  point  c,  and  consequently  b, 
will  receive  this  motion,  which  is  equivalent  to  that  obtained 
from  eccentric  0V  in  Fig.  201.  The  resultant  motion  of  the 
valve  is  that  which  would  be  given  by  the  eccentric  OE0. 

By  shifting  the  link  block  d  the  amplitude  of  its  motion  can 
be  varied,  and  this  is  accompanied  with  corresponding  change 
in  the  width  of  valve  opening  and  time  of  cut-off.  If  shifted 
above  the  pivot  e,  the  engine  would  be  reversed. 

The  Walschaert  gear  is  widely  used  on  locomotives  of  the 
largest  sizes.  Being  located  on  the  outer  side  of  the  engine,  it 
olaces  no  limitation  on  the  size  of  the  boiler,  as  does  the  Stephen- 


THE    VALVE   GEARS   OF  STEAM  ENGINES 


32I 


son  link  gear,  which  is  located  directly  below  the  boiler  and  re- 
quires considerable  room  for  shifting  from  one  full-gear  position 
to  the  other. 

164.  Poppet  Valves  and  Their  Gears,     (a)  Poppet-lift  valves 
(Figs.   203   and  204)   have  no  friction   nor  wear  from  sliding. 


Fig.  203  Fig.  204. 

They  require  no  lubrication,  and  being  symmetrical  do  not  warp 
with  temperature  changes;  hence  they  are  suitable  for  use  with 


Cam  '**Ji' 


Fig.  205. 

highly    superheated    steam.     The    ordinary    single    poppet    or 
mushroom  valve,  Fig.  203,  is  hard  to  open  because  of  the  un- 


322  HEA  f -POWER  ENGINEERING, 

balanced  pressure  on  its  back;  therefore,  the  double-seated  type 
of  valve,  one  form  of  which  is  shown  in  Fig.  204,  is  commonly 
used  instead,  since  the  steam  pressures  on  upper  and  lower  sides 
are  about  equal.* 

There  is  a  great  variety  of  arrangements  of  such  valves  and 
of  their  gears. 

(b)  The  valve  may  be  operated  by  a  continuously  rotating 
cam;  and  there  may  be  a  sleeve  with  variable  cam  surface  which 
may  be  moved  endways  to  change  the  valve  events. 

(c)  An  oscillating  cam,  as  a  in  Fig.  205,  may  be  used,  and  it 
may  be  driven  by  an  eccentric  which  is  shifted  by  a  shaft  type 
of  governor,  as  in  the  figure ;  or  it  may  be  driven  by  a  fixed  eccen- 
tric, in  which  case  the  cut-off  may  be  operated  by  trip  or  by 
shifting  the  cam,  or  by  changing  some  intermediate  linkage  to 
distort  the  motion;  or  closure  may  be  brought  about  by  some 
other  means. 

(d)  The  valve  may  be  operated  by  a  floating  lever  which  ful- 
crums  on  a  cam  surface,  as  b  in  Fig.  205,  and  which  is  driven  by 
an  eccentric,  which  may  be  variable  or  stationary.     The  cut-off 
can  be  changed  by  any  of  the  methods  given  in  (c). 

(e)  Cams  are  also  used  to  operate  other  types  of  valves,  such 
as  piston  valves  and  gridiron  valves. 

*  Allowance  must  be  made  for  the  area  of  the  valve  stem. 


CHAPTER   XX. 

CONVENTIONAL  INDICATOR  UlAGRAM. 

165.  Conventional  Diagram  for  Simple  Engines,  (a)  If  the 
actual  indicator  diagram  has  been  obtained  from  an  engine,  the 
m.e.p.  may  be  determined  by  any  of  the  methods  discussed  in 
Section  102,  and  the  i.h.p.  of  the  engine  may  be  obtained  by 
using  Eq.  210.  In  making  such  computation  for  a  double-act- 
ing engine,  however,  the  area  of  the  piston  rod  must  be  deducted 
from  the  area  of  the  piston  on  one  side,  and  the  average  of  the 
areas  on  the  two  sides  of  the  piston  must  be  used  in  the  formula ; 
or  else  the  i.h.p.  for  each  side  of  the  piston  must  be  computed 
separately. 

(b)  When  actual  indicator  diagrams  are  not  available,  it  is 
customary  to  use  a  conventional  diagram,  with  proper  correc- 
tion factor,  for  estimating  the  probable  m.e.p. 

(c)  Before  the  conventional  diagrams  can  be  drawn,  however, 
the  clearance  volume  in  the  cylinder  must  be  known.     This  vol- 
ume can  be  determined  by  pouring     ^  ^ 

a  measured  quantity  of  water  into  P!  ' 
the  clearance  space.  It  can  also  be 
found  approximately  from  the  actual 
indicator  diagram  in  the  following 
manner  (shown  in  Fig.  206):  Select 
two  points  1  and  2  on  the  expansion  °"^  Fi  ^ 

line  and  draw  a  rectangle  with  these 

points  as  corners  and  with  the  sides  parallel  to  the  respective 
PV-axes.  Then,  the  diagonal  through  the  other  corners  will  cut 
the  V-axis  at  the  origin  O,  assuming  that  the  expansion  equation 
is  py  =  constant.  Then  Cl  in  the  figure  is  the  clearance  vol- 
ume to  scale.  The  compression  curve  may  be  used  in  a  similar 
manner  to  find  0.  This  makes  application  of  the  construction 
shown  in  Fig.  n. 

The  clearance  volumes  used  in  practice  are  about  as  follows: 

Single- valve  engine 5  to  15% 

Multi- valve  engines 2  to    8% 

323 


Atm, 


3  24 


HEAT-POWER  ENGINEERING 


(d)  In  constructing  conventional  diagrams  for  estimating  the 
probable  power  of  an  engine,  it  is  customary  to  assume  that 
expansion  follows  the  equation  PV  =  P\V\  =  PzV2  =  constant, 
instead  of  being  adiabatic.  This  is  because  the  "  equilateral 
hyperbola  "  is  easier  to  construct  than  the  adiabatic  curve,  and 
because  the  actual  expansion  line  follows  it  as  closely  as  it  does 
the  latter.  The  expansion  line  may  be  constructed  by  the 
methods  shown  in  Figs.  II  and  12. 

The  foot-pounds  of  work  (^4)  represented  by  the  area  (Fig. 
207)  under  such  an  expansion  line  is  found  in  the  manner  already 
discussed  in  Section  29  (c)  to  be 


Xy2 


(276) 
(277) 


where  r  is  the  ratio  of  expansion  [•=£ 


208  r  is  =?> 


(e)  In  the  case  of  an  engine  without  clearance  the  conven- 
tional diagram  is  abode  of  Fig.  208.     The  work  shown  by  area 


Fig.  207.  Fig.  208. 

Ai  is  PiVi  foot-pounds,  and  that  represented  by  A2  is  PiVi 
loge  r.  Hence  if  the  back  pressure  is  P2,  the  work  shown  by 
the  conventional  diagram  abode  is 

PM  +  Ptfi  loge  r  -  P2V2  =  PmV2, 

in  which  Pm  is  the  mean  effective  pressure.  Solving  this  equa- 
tion for  Pm  gives 

Pm  =  Pi 


As  the  m.e.p.  is  generally  used  in  pounds  per  square  inch,  it  is 

*   Loge  =  2.302  logic. 


CONVENTIONAL  INDICATOR  DIAGRAM 


325 


more  convenient  to  divide  both  sides  of  this  equation  by  144, 
giving 


The  values  of  the  bracketed  quantity  for  different  values  of 
r  are  given  in  Table  V. 

TABLE  V. 


I  +  log,  r 

i  +  log«  r 

i  +  log.  r 

r 

r 

r 

I.O 

1.  00 

6.0 

0.465 

16.0 

0.236 

1.5 

0.937 

70 

0.421 

17-0 

0.226 

2.0 

0.847 

8.0 

0.385 

18.0 

0.216 

2.5 

0.766 

9.0 

0.355 

19.0 

0.208 

3.0 

0.700 

10.  0 

0.330 

20.0 

0.200 

3.5 

0.644 

II.  O 

0.309 

21.0 

0.192 

4.0 

0.597 

12.0 

0.290 

22.0 

0.186 

4-5 

0.556 

13  o 

0.274 

23.0 

0.180 

SO 

0.522 

14.0 

0.260 

24.0 

0.174 

5-5 

0.492 

15.0 

0.247 

25-0 

0.169 

'(f)  The  actual  indicator  diagram  of  course  differs  from  the 
computed  one  drawn  by  this  method.  The  ratio  of  the  area 
of  the  actual  to  that  of  the  conventional  diagram  is  called  the 
"  Diagram  Factor  "  (DF).  Then  if  the  diagram  factor  is  known 
for  engines  similar  to  that  which  is  being  considered,  the  prob- 
able m.e.p.  for  the  new  engine  is 

pmf  =  DF  X  pm.  .     .     .     .     .     .     (279) 

It  is  a  common  practice  to  use  Eq.   (278)  even  for  engines 

which  have  clearance,  and  to  substitute  ( -= — TT-  )  for  r,  thus 

\cut-off  ratio/ 

ignoring  the  clearance. 

The  diagram  factors  to  be  used  for  different  types  of  engines 
in  such  cases  are  given  in  the  following  table: 

TABLE  VI.  —  DIAGRAM  FACTORS. 

Simple  slide-valve  engine 55  to  9°% 

Simple  Corliss  engine 85  to  90 

Compound  slide-valve  engine 55  to  80 

Compound  Corliss  engine 75  to  85 

Triple-expansion  engines.  t 55  to  70 

(g)  The  conventional  diagram  for  an  engine  with  clearance 
is  shown  by  abode  in  Fig.  209.  Here  the  ratio  of  expansion  is 

r  =  (L  +  le)  -*-  (/  +  /«),  .     .     .,,..".     (280) 
using  scalar  distances  to  represent  volumes. 


HEAT-POWER  ENGINEERING,- 

The  net  work  shown  by  the  area  is 

A  =  Ai  +  A2  -  A, 

=  Pi/  +  Pi  (lc  +  /)  log*  r  -  P2L.    .     .     .     (281) 

Dividing  by  L  and  by  144  gives  the  mean  effective  pressure  for 
this  case  as  follows: 


To  simplify  this  expression,  let  C  =  -^  =  cut-off  ratio,  and  •£  =  c 
=  clearance  ratio  ;  then 

An=M£+(£  +  Ologed-£2.      .     .     .     (283) 

The  diagram  factors  for  this  case  are  3  or  4  per  cent  larger 
than  those  given  in  Table  VI. 


P-- 


Fig.  209. 

(h)  With  compression,  the  diagram  of  Fig.  209  is  reduced  by 
the  area  D  in  Fig.  210. 

If  pf  is  the  pressure  at  the  end  of  compression,  the  reduction 
of  the  m.e.p.  caused  by  this  small  area  is  evidently 


from  which,  since          p/  = 


+ 


Subtracting  this  from  Eq.  282  and  -letting  k  represent  the 
compression  ratio  (y),  gives  the  m.e.p.  of  diagram  abcdef  as 


\C+(C+c)  logcrS  - 


e  .     (284) 

c 


CONVENTIONAL  INDICATOR  DIAGRAM 


327 


In  this  case  the  diagram  factors  are  4  to  6  per  cent  larger 
than  the  values  given  in  Table  VI. 

(i)  A  conventional  diagram  that  approaches  closer  to  the 
actual  diagram  than  any  that  have  been  discussed  is  shown  in 
Fig.  211.  This  has  the  sloping  admission  line.  The  area  is 
made  up  of  the  triangle  A  and  the  area  B,  similar  to  that  for 


Fig.  210. 


Fig.  211. 


which  Eq.  284  was  developed,  and  much  less  correction  is  nec- 
essary for  obtaining  the  probable  m.e.p.  than  in  the  previous 
cases. 

(j)  For  noncondensing  simple  slide-valve  engines  operating 
under  ordinary  conditions,  with  steam  pressure  about  100  pounds 
gauge,  the  m.e.p.  at  the  most  economical  cut-off  is  about  one- 
half  the  initial  gauge  pressure.  For  simple  Corliss  engines  the 
m.e.p.  is  about  four-tenths  the  initial  gauge  pressure,  under  the 
same  conditions. 

These  values  may  be  used  only  when  the  estimates  are  very 
approximate. 

1 66.  Conventional  Diagrams  for  Multiple-Expansion  En- 
gines, (a)  By  referring  to  Fig.  93,  on  which  diagrams  of  both 
the  high -pressure  and  the  low-pressure  cylinders  of  a  compound 
engine  are  drawn  to  the  same  scale,  it  will  be  seen  that  if 
the  dividing  line  at  TR  is  omitted,  there  results  a  single  indi- 
cator diagram  of  area  equal  to  the  sum  of  the  areas  H.P.  and 
L.P. ;  thus,  theoretically,  a  simple  engine  of  the  same  size  as 
the  lower-pressure  cylinder  (total  volume  =  V%)  would  give  the 
same  amount  of  power  with  this  single  diagram  as  is  obtained 
with  the  two  cylinders  of  the  compound  engine. 

Evidently,  then,  to  calculate  the  i.h.p.  of  the  compound  en- 
gine, it  is  only  necessary  to  consider  the  m.e.p.  of  this  simple 


328  HEAT-POWER  ENGINEERING  ,• 

(or  "combined")  diagram  as  acting  on  the  low-pressure  piston. 
The  i.h.p.  of  triple-  and  quadruple-expansion  engines  can  be 
computed  in  a  similar  manner. 

The  m.e.p.  of  the  combined  diagram  is  usually  called  the 
"m.e.p.  referred  to  the  low-pressure  cylinder,"  or  more  briefly 
the  "  referred  m.e.p."  Its  theoretical  value  can  be  computed 
by  Eqs.  (278),  (283),  or  (284),  and  the  probable  m.e.p.  is  found 
by  correcting  with  the  diagram  factor.  Values  of  the  latter  are 
given  in  Table  VI  for  use  with  Eq.  (278).  Modified  values 
should  be  used  with  Eqs.  (283)  and  (284). 

(b)  If  it  is  desired  to  estimate  the  size  of  a  compound  engine 
that  will  give  a  specified  amount  of  power,  the  referred  m.e.p. 
is  first  computed;  then  with  the  stroke,  L  (feet),  and  number  n 
of  cycles  per  minute  selected,  the  area  of  the  low-pressure  piston 
(square  inches)  to  give  any  i.h.p.  can  be  computed  from 

i.h.p.  X  33,000  ,  _  N 

aL  =  pmRXDFxLXn' (285) 

in  which  DF  is  the  diagram  factor  (see  Table  VI). 

Then  with  the  ratio  R  of  low-pressure  cylinder  volume  to 
that  of  the  high-pressure  cylinder  known,  the  area  of  the  high- 
pressure  piston  is  of  course  l/R  th  of  the  low-pressure  area  if  the 
strokes  are  equal. 

The  size  of  the  cylinders  in  triple-  and  quadruple-expansion 
engines  is  found  in  similar  manner.  The  cylinder  ratios  to  be 
used  are  found  in  Section  170. 

(c)  The  diagrams  of  multiple-expansion  engines  will  now  be 
considered  more  in  detail,  and  to  facilitate  the  discussion  the 
engines  will  be  divided  into  two   groups:    (i)  the  Woolf   type, 
without  receivers;  and  (2)  engines  with  receivers. 

167.  Diagrams  of  Woolf  Type  of  Engine,  (a)  The  com- 
pound engine  was  patented  in  1781  by  Jonathan  Hornblower, 
but  Watt's  broad  patents  on  expansion  steam  engines  delayed 
its  use.  In  1804,  Woolf  reintroduced  the  compound  engine  and 
used  an  arrangement  in  which  the  steam  was  exhausted  from 
the  high-pressure  cylinder,  directly  through  very  short  passages 
to  the  low-pressure  cylinder.  Because  there  is  little  or  no  re- 
ceiver volume  or  storage  volume  between  the  cylinders  in  such 
an  engine,  it  is  necessary  for  the  pistons  to  start  and  finish  their 
strokes  together,  and  the  low-pressure  cylinder  must  receive  steam 


CONVENTIONAL  INDICATOR  DIAGRAM 


329 


throughout  its  entire  stroke  from  the  high-pressure  cylinder.  If  the 
steam  were  cut  off  in  the  low-pressure  cylinder,  there  would  be 
no  place  into  which  the  high-pressure  steam  could  be  exhausted 
during  the  remainder  of  the  stroke  after  this  cut-off  had  occurred. 
The  pistons  may  move  together  or  in  opposite  directions. 

(b)  Fig.  212  (a)  shows  a  Woolf  engine  whose  pistons  move 
synchronously  and  in  the  same  direction.  This  motion  would 
result  if  both  piston  rods  were  connected  to  the  same  end  of  a 
"  walking  beam  "  or  to  cranks  set  together.  In  Fig.  212  (b) 
the  indicator  diagram  H  is  for 
the  headend  of  the  high-pressure 
cylinder  and  L  is  for  the  crank 
end  of  the  low-pressure  cylin- 
der, clearance  volume  being 
neglected  in  both  cases.  In 
operation,  steam  is  admitted  to 
the  high-pressure  cylinder  ac- 
cording to  line  abc\  it  is  cut  off 
at  c\  is  expanded  along  cd\  and 
it  is  exhausted  from  the  high- 
pressure  cylinder  along  line  da. 
This  steam  exhausted  from  the 
high-pressure  cylinder  is  re- 
ceived by  the  low-pressure  Fig.  212. 
cylinder  along  the  line  ABC  and 

is  then  exhausted  along  line  CD  A.  BC  and  da  will  be  called 
hereafter  the  line  of  transference  or  receiver  line.  In  Fig.  212 
(b)  the  indicator  cards  of  both  cylinders  have  the  same  length, 
that  is,  the  abscissas  are  piston  positions,  and  are  numbered  to 
correspond  with  the  positions  shown  in  Fig.  212  (a). 

In  Fig.  212  (c)  the  diagrams  have  been  "  combined,"  with 
abscissas  representing  the  respective  volumes  in  the  two  cyl- 
inders. In  Fig.  212  (d)  the  diagrams  have  been  combined  in 
such  a  way  that  the  volume  of  the  steam  during  transference 
from  the  first  to  the  second  cylinder  can  be  scaled  directly. 
Thus,  when  the  pistons  have  reached  simultaneous  positions  2 
and  2'  the  distance  o'-2'  (=  ox)  is  the  volume  of  steam  in  the 
high-pressure  cylinder,  the  distance  4-2  ( =  oX)  is  the  volume  it 
occupies  in  the  low-pressure  cylinder,  and  distance  2 '-2  ( =  Xx) 
is  the  total  volume  of  the  steam  between  the  two  pistons  for 


330  HEAT-POWER  ENGINEERING 

this  position  in  the  stroke.  Obviously,  the  distances  between 
piston  positions  bearing  like  numbers  in  this  figure  represent 
the  volumes  of  steam  during  the  period  of  transference.  After 
these  volumes  have  been  determined  (by  scaling),  the  pressures 
at  the  corresponding  piston  positions  can  be  found  if  the  expan- 
sion is  assumed  to  be  hyperbolic,  for  during  expansions  cd,  da, 
and  BC  the  product  PV  remains  constant,  since  there  is  no 
change  in  the  quantity  of  steam  involved  during  these  processes. 
Thus  the  high-  and  low-pressure  PV-diagrams  can  be  readily 
constructed. 

1 68.  Diagrams  for  Engines  with  Infinite  Receivers  and  No 
Clearance  (General),  (a)  If  a  receiver  of  infinite  volume  is 
placed  between  the  cylinders  of  the  Woolf  engine  the  curves  da 
and  BC,  in  Fig.  212,  would  become  horizontal  straight  lines,  and 
the  low-pressure  indicator  diagram  would  be  a  rectangle.  Evi- 
dently, with  finite  receiver,  the  larger  the  receiver  volume  the 
more  nearly  horizontal  and  straight  will  the  line  of  transference 
become. 

With  a  receiver  of  considerable  volume  into  which  the  high- 
pressure  cylinder  can  exhaust,  it  is  possible  to  "  cut  off  "  in 
the  low-pressure  cylinder  and  thus  to  expand  the  steam  inde- 
pendently in  this  cylinder.  The  pressure  of  the  receiver  will 
vary,  because  part  of  the  time  steam  is  being  received  from  the 
high-pressure  cylinder,  at  other  times  steam  is  being  delivered 
to  the  low-pressure  cylinder,  and  during  part  of  the  cycle  both 
of  these  operations  may  occur  simultaneously.  Consequently 
the  back-pressure  line  on  the  H.P.  indicator  diagram  and  the 
admission  line  of  the  L.P.  diagram  will  be  irregular.  The 
character  of  the  line  of  transference  will  be  discussed  in  detail 
later. 

(b)  When  a  receiver  of  considerable  volume  is  used  it  is  pos- 
sible  to   have'  any  angle   between    the 
cranks  of  the  two  cylinders,  whereas  in 
the  Woolf  engine  this  angle  is  limited  to 
zero  degrees  or  1 80  degrees  in  cases  where 
there  is  a  separate  crank  for  each  cylinder, 
(c)  In  Fig.  213,  AbcD  is  a  conventional 
2I3-  "  combined  "  diagram  for  a  compound 

engine  with  receiver  of  infinite  volume.    In  it,  AD  is  the  volume 


CONVENTIONAL  INDICATOR  DIAGRAM  331 

of  the  low-pressure  cylinder,  ad  is  that  of  the  high-pressure  cyl- 
inder, be  is  the  volume  of  steam  admitted  to  the  high-pressure 
cylinder,  and  BC  is  that  at  the  time  of  cut-off  in  the  low-pressure 
cylinder.  Then 

—  =rH  =  ratio  of  expansion  in  the  high-pressure  cylinder; 

AD 

=  TL=  ratio  of  expansion  in  the  low-pressure  cylinder  ; 


AD 

-——  =  rT=  total  ratio  of  expansion. 

Since,  if  hyperbolic  expansion  is  assumed, 

PC  (be}  =  pd(ad), 
the  receiver  pressure  is  evidently 


for  the  case  in  which  the  expansion  is  complete  in  both  cylinders. 

(d)  It  is  evident  that  the  horizontal  transfer  line  obtained 
with  a  receiver  of  infinite  volume  would  correspond  to  the  mean 
transfer  pressure  if  a,  receiver  of  finite  volume  is  used,  and  that 
indicator  diagrams  drawn  with  this  horizontal  transfer  line  would 
have  practically  the  same  areas  as  with  the  variable  line  of  the 
small  receiver.     Hence  these  diagrams  may  not  only  be  used 
for  the  engine  as  a  whole  but  also  when  each  cylinder  is  con- 
sidered separately. 

(e)  Changing  the  low-pressure  cut-off  to  make  it  occur  earlier 
results  (i)  in  raising  the  receiver  line,  as  shown  dotted  in  Fig.  213; 
it  also  results  (2)  in  a  reduction  of  the  area  of  the  high-pressure 
diagram  and  (3)  an  increase  in  the  area  of  the  low-pressure  dia- 
gram.    Making  the  low-pressure  cut-off  later  reverses  these  re- 
sults.    Thus  the  cut-off  in  the  low-pressure  cylinder  influences  the 
receiver  pressure  and  distribution  of  work  between  the  cylinders, 
but  does  not  affect  the  total  work  done  by  the  engine. 

(f)  The  selection  of  the  receiver  pressure  is  based  on  the  fol- 
lowing considerations: 

(i)  For  greatest  economy  in  the  use  of  steam  the  temperature 
ranges  in  the  two  cylinders  should  probably  be  equal,  although 
this  is  not  certain.  Hence  the  receiver  pressure  should  probably 
be  such  that  the  corresponding  temperature  of  the  steam  is 


332  HEAT-POWER  ENGINEERING 

midway  between  the  initial  and  final  temperatures  of  the  work- 
ing fluid.  Other  considerations  may  be  more  important  than 
this,  however. 

(2)  It  is  sometimes  desirable  to  have  the  same  cut-off  (that  is, 
the  same  expansion   ratios)   in   both  cylinders.     For  example, 
in  the  tandem  compound  engine  shown  in  Fig.   107,  the  two 
valves  are  on  the  same  rod,  hence  the  cut-offs  in  the  two  cylin- 
ders must  change  together. 

(3)  Usually  it  is  desirable  to  have  equal  work  done  in  the  two 
cylinders.     In   this  case  the  receiver  line  should  be  so  drawn 
that  the  areas  of  the  high-pressure  and  low-pressure  diagrams 
are  equal.     This  is  especially  desirable  when  the  engine  is  a 
cross  compound. 

(4)  In   some  special   cases,   equal   maximum   thrusts  on   the 
piston  rods  are  desirable,  and  these  thrusts  are  dependent  on  the 
receiver  pressure. 

(5)  The  uniformity  of  turning  effort  is  dependent  on  the  shape 
and  relative  proportions  of  the  indicator  diagrams  of  the  two 
cylinders,  and  hence  is  dependent  on  the  receiver  pressure. 

Usually  compound  engines  are  operated  to  perform  equal  work 
in  the  two  cylinders,  and  this  gives  about  as  uniform  a  crank  effort 
as  is  possible,  and  hence,  considerations  (3)  and  (5)  are  satisfied 
together  with  sufficient  accuracy  for  ordinary  purposes. 

169.  Receiver  Pressures  in  Compound  Engines  with  Infinite 
Receivers  and  No  Clearance,  (a)  It  has  just  been  seen  that 
the  distribution  of  work  among  the  cylinders  depends  on  the 
receiver  pressures,  hence  the  problem  is  one  of  determining  the 
mean  receiver  pressures  which  will  give  the  desired  distribution. 
The  receiver  pressure  may  be  determined  either  graphically  or 
analytically,  using  the  conventional  diagram.  The  receiver  vol- 
ume will  be  considered  infinite  and  the  clearance  zero. 

(b)  The  graphical  method  will  be  considered  first. 

Let  plt  p2,  and  V2  in  Fig.  214  be  given,  and  assume  a  terminal 
pressure  PD  such  as  will  give  the  drop  (DE)  in  pressure  in  ac- 
cordance with  Section  in.  With  this  data  available,  the  com- 
bined PV-diagram,  AbcDE,  can  be  easily  drawn  and  its  work 
area  can  be  determined.  If  the  high-pressure  cylinder  is  to  do 
1/wth  of  the  total  work,  the  area  H  will  be  I/ nth  of  the  total 
area.  The  problem  then  is  to  find  the  location  of  line  ad  which 


CONVENTIONAL  INDICATOR  DIAGRAM 


333 


will  give  this  distribution  of  work.  The  line  ad  can  be  drawn 
tentatively  and  then  the  area  above  it  can  be  integrated  by 
planimeter  to  see  if  it  has  the  proper  value.  If  it  is  not  correct, 
another  position  of  ad  can  be  tested,  and  by  repeated  trials  a 
proper  receiver  line  can  be  obtained  by  this  "  cut  and  try  " 
method.  This  same  method  can  be  used  when  the  H,P.  expan- 
sion is  incomplete  (i.e.,  when  the  toe  of  the  H.P.  diagram  is 
removed)  as  in  Fig.  215,  and  can  also  be  applied  to  multiple- 
expansion  engines  with  any  number  of  expansion  cylinders. 


Fig.  214. 

In  Figs.  214  and  215,  VH  is  the  volume  of  the  high-pressure 
cylinder;  and  the  corresponding  mean  effective  pressure  acting 
in  the  high-pressure  cylinder  is 

area  H 


pmH  = 


X  scale  of  ordinates.   . 


length  VH 

Similarly  the  L.P.  mean  effective  pressure  is 
area  L 


(287) 


PmL  = 


X  scale  of  ordinates. 


length  VL 
The  total  m.e.p.  "  referred  "  to  the  low-pressure  cylinder  is 


(288) 


PmR  = 


area  (H  +  L) 


X  scale  of  ordinates.  . 


(289) 


length  VL 

(c)  By  removing  the  toe  from  the  H.P.  diagram,  as  in  Fig. 
215,  the  high-pressure  cylinder  is  decreased  in  volume  in  the 


fl  P 


ratio  ^^   and  the  cost  of  the  engine  is  consequently  reduced. 


On  account  of  this  saving,  and  because  the  expansion  should  not 
be  to  a  pressure  lower  than  that  which  is  sufficient  to  overcome 
the  engine  friction,  most  compound  engines  are  operated  with 
the  drop  de  at  release  in  the  high-pressure  cylinder. 


334  HEAT-POWER  ENGINEERING, 

Hence,  only  that  case  will  be  considered  in  the  analytical 
method  which  follows: 

It  will  be  assumed  that  the  expansion  is  hyperbolic,  that  the 
receiver  volume  is  infinite,  and  that  the  clearance  volumes  are 
zero. 

(d)  In  Fig.  215,  let 
pi  =  Initial  pressure  (Ibs.  sq.  in.)  ; 
pz  =  L.P.  back  pressure  (Ibs.  sq.  in.)  ; 
PR=  Receiver  pressure  (Ibs.  sq.  in.); 
PD=  Release  pressure  in  low-pressure  cylinder; 
R  =  Cylinder   ratio  =  (vol.    low-pressure    cylinder)  -5-  (vol 

high-pressure  cylinder)  =  VL/VH 

=  (area  low-pressure  piston)  -f-  (area  high-pressure  piston) 
when  the  piston  strokes  are  equal,  as  they  usually  are. 

rT  =  Total  ratio  of  expansion  =  —  =  ~  ; 

PD       "i 

y 
rH  =  Ratio  of  expansion  in  high-pressure  cylinder  =  •—-  ; 

rL  =  Ratio  of  expansion  in  the  low-pressure  cylinder  =  ^  ; 

pmH  =  M.e.p.  of  the  steam  in  high-pressure  cylinder  (pounds 

square  inch)  ; 
pmL  =  M.e.p.  of  the  steam  in  low-pressure  cylinder  (pounds 

square  inch)  ; 
pmR  =  Total  m.e.p.  "referred"  to  the  low-pressure  cylinder 

(pounds  square  inch). 

Since 

_  VH  _  VL      VH 


and  since 

g-r,  and   £  =  *,  '    • 

it  is  evident  that  the  ratio  of  expansion  in  the  high-pressure 
cylinder  is 

rH  =  rT+  R.  .  .     .    ,.     ,     .  V  (290) 

(e)  As  the  L.P.  piston  is  R  times  as  large  as  the  H.P.  piston 
(the  strokes  being  assumed  equal),  the  intensity  of  pressure  on 
the  L.P.  piston  that  would  do  work  equal  that  due  to  the  H.P. 
mean  effective  pressure  is  evidently  pmH/R.  Then  if  the  high- 


CONVENTIONAL  INDICATOR  DIAGRAM 


335 


pressure  cylinder  is  to  do  l/n  th  of  the  total  work,  it  must  follow 
that  the  H.P.  m.e.p.  referred  to  the  L.P.  piston  will  be  equal  to 


*t  hence 


Now,  from  Eq.  (278), 
and 


•pmH         pmR 

= 


.  •  (292) 
(293) 


in  which  K  is  a  factor  introduced  to  correct  for  the  loss  due  to 
the  omission  of  the  toe  of  the  H.P.-diagram.  It  ranges  from 
0.9  to  i.o,  the  latter  value  being  for  the  complete  expansion  in 
the  high-pressure  cylinder. 

Substituting  for  pmn  and  pmR  in  Eq.  (291)  and  solving  for  pRj 
results  in  the  following  expression  for  the  receiver  pressure  which 
will  give  the  desired  distribution  of  work: 


(f)  With  pR  known  the  ratio  of  expansion  in  the  low-pressure 
cylinder  can  then  be  found.     Since  rL  =  —•  =  —  (see  Fig.  215) 

and  since  po  =  — ,  it  follows  that 
rT 


fP_n\ 
\pj 


rT. 


(295) 


(g)  This  analytical  method  not  only  applies 
to  two-stage  compound  engines  but  also  to 
multiple-expansion  engines  having  any 
number  of  expansion  cylinders.  Thus,  if 
the  work  is  equally  distributed  among  x 
cylinders  (for  example,  x  =  3  in  Fig.  216), 
the  work  in  the  first  cylinder  is  1/x  th  of 
the  total.  Then  the  pressure  (pR^)  in  the  first 


Fig.  216. 


receiver  can  be  found  from  Eq.  (294),  with  x  substituted  for  n. 
second  cylinder  receives  steam  at  this  same  receiver  pres- 


336  HEAT-POWER  ENGINEERING 

sure  (pR^'j  and  this  cylinder  and  the  succeeding  ones  can  be 
considered  as  constituting  another  engine  with  initial  pressure 
equal  to  pRt  and  with  (x  —  1)  cylinders.  This  engine  will  do 

-  parts  of  the  work  of  the  whole  engine,  and  this  second 
cylinder  (considered  now  as  a  high-pressure  cylinder)  will  do 
-. — ^7y\th  °f  tm's  work.  Then  the  pressure  (pR2)  in  the  second 

receiver  can  be  found  by  again  using  Eq.  (294)  with  (x  —  1)  sub- 
stituted for  n  and  by  making  such  other  changes  as  will  be 
apparent.  Pressures  in  succeeding  receivers  (if  any)  can  be 
found  in  like  manner. 

(h)  In  a  triple-expansion  engine,  after  the  ratio  R  of  low- 
pressure  cylinder  to  high-pressure  and  ratio  RIH  of  I. P.  to  H.P. 
have  been  selected,  it  is  evident  (since  VL=  F^^and  Vi—  VHRin) 
that  the  cylinder  ratio  RLI  of  L.P.  to  I. P.  is 

•••-     (296) 


(i)  Following  (f)  of  this  section,  the  ratio  of  expansion  in  the 
low-pressure  cylinder  is 

/pjf\ 

i*  »i i  /       \ 

rL  =        -]rT (2Q7» 

\pi  / 

Also,  by  analogy,  rL  =  (^]  rTs,  in  which  rT  is  the  total  expansion 

\PR\/ 

in  the  intermediate-pressure  and  the  low-pressure  cylinders  com- 
bined.   After  rL  is  known,  rTz  can  be  computed  from  rTz  =  rL  ( — 1Y 

Then  by  comparison  with  Eq.  (290)  it  is  seen  that  the  ratio 
of  expansion  in  the  intermediate-pressure  cylinder  is 


The  ratios  of  expansion  in  a  quadruple-expansion  engine  would 
be  determined  in  a  similar  manner. 

170.  Cylinder  and  Expansion  Ratios  Used  in  Multiple-Ex- 
pansion Engines,  (a)  In  general  the  greater  the  total  range  of 
pressures  in  the  engine  the  larger  should  be  the  cylinder  ratio 
and  the  expansion  ratio.  Thus  high-pressure  engines  have 


CONVENTIONAL  INDICATOR  DIAGRAM  337 

larger  ratios  than  low-pressure  engines,  and  those  condensing 
have  greater  ratios  than  those  which  operate  noncondensing. 
Practice  varies  widely  and  only  the  average  values  can  be 
given  here. 

(b)  Modern   compound   engines   usually   operate   with   steam 
pressures  between  125  pounds  and  150  pounds  gauge.     In  many 
instances,  however,  much  higher  and  lower  values  have  been 
used.     Stationary  engines  of  this  type  usually  have  cut-offs  in 
the  high-pressure  cylinders  between  0.25  and  0.4  of  the  stroke 
under  normal  load.     With  late  cut-off  a  smaller  engine  can  be 
used  for  a  given  power  than  with  early  cut-off;  but  the  conse- 
quent  saving   in    "  first   cost  "   of   engine   may   be   more  than 
balanced  by  loss  in   efficiency   and   greater  cost  of  operation. 
Cylinder  ratios  customarily  used  are  about  as  follows: 

CYLINDER  RATIOS  FOR  COMPOUND  ENGINES. 

Cylinder  ratio 2\  3!          4            4^ 

Gauge  pressure,  noncondensing 100        120         

Gauge  pressure,  condensing 100        120        150 

Dividing  the  cylinder  ratio  by  the  H.P.  cut-off  fraction  (0.25 
to  0.4)  gives  the  total  ratio  of  expansion.  What  the  best  cyl- 
inder and  expansion  ratios  are,  is  still  under  discussion.  Some 
advocate  cylinder  ratios  even  as  large  as  6  or  7  and  remarkable 
economies  have  been  obtained  with  such.* 

(c)  The  ratio  of  expansion  is  sometimes  fixed  by  first  assum- 
ing the  pressure  drop  at  release.     If  this  drop  is  added  to  the 
L.P.  exhaust  pressure,  the  pressure  (pD  in  Fig.  215)  at  release 
is  obtained.     Then,  considering  the  expansion  to  be  hyperbolic, 
the  total  ratio  of  expansion  on  the  conventional  diagram  is 

rr=£, (299) 

PD 

which  is  approximated  more  or  less  closely  in  the  actual  case. 
If  the  expansion  ratio  (ru)  in  the  high-pressure  cylinder  is  then 
selected,  the  cylinder  ratio  is 

R  =  '-£ (300) 

fu 

*  r    =  6. 25  Cross  Compound  Corliss.     Am.  Electrician,  June,  1903. 
T  =  7-3    Fleming  Four-valve.     Trans.  A.  S.  M.  E.,  Vol.  XXV,  page  212. 
rT  =  6  .4    Tandem  Compound  Corliss  —  Barrus'  Engine  Tests,  page  185. 
rT  =  6 . 2    Edison  Waterside  Station,  New  York.   Power,  July,  1904,  page  424. 
Also  see  papers  in  Trans.  A.  S.  M.  E. 


338  HEAT-POWER  ENGINEERING 

After  the  receiver  pressure,  which  will  give  the  proper  distri- 
bution of  work  between  the  cylinders,  has  been  determined,  the 
drop  in  pressure  at  H.P.  release  should  be  checked. 

(d)  Modern  triple-expansion  engines  usually  operate  with 
steam  pressures  from  150  pounds  to  180  pounds  gauge  or  even 
higher.  The  pressure  at  L.P.  release  in  condensing  marine  en- 
gines is  commonly  about  15  pounds  per  square  inch  absolute  under 
normal  load,  and  in  stationary  engines  it  is  about  half  this  value. 
As  before,  the  total  expansion  ratio  (rT)  can  be  found  approx- 
imately by  dividing  the  initial  pressure  by  the  L.P.  release  pres- 
sure (considering  the  expansion  to  be  hyperbolic) ;  or  it  can  be 
obtained  from  economy  curves  of  similar  engines  operating  under 
similar  conditions,  when  ratios  have  been  used  as  abscissas. 

The  H.P.  cut-off  in  marine  engines  is  usually  from  0.55  to  0.7 
of  the  stroke  and  in  stationary  engines  is  much  earlier.  The 
H.P.  expansion  ratio  (rH)  is  the  reciprocal  of  this  cut-off  ratio 
(neglecting  clearance).  With  rT  and  rH  known,  the  volume 

ratio  of  high-pressure  to  low-pressure  cylinder  is  R  =  — .     If 

rH 

the  strokes  are  equal,  as  is  almost  invariably  the  case,  the  ratio 
of  piston  areas  will  be  the  same  as  the  volume  ratio. 

If  the  conventional  diagrams  of  the  various  cylinders  have 
sharp  toes,  the  work  will  be  equally  distributed  among  the  cylin- 
ders if  the  cylinder  volumes  (or  piston  areas)  are  such  that 

TT  T 

-j  =  -£  (in  which  the  letters  refer  to   the   high-,   intermediate, 

and  low-pressure  cylinder  volumes,  or  areas).     In  such  a  case  the 
intermediate  cylinder  volume  (or  piston  area)  is  found  from 

/=  VHX  L. 

In  the  actual  case,  because  of  departure  of  the  real  indicator 
diagrams  from  the  theoretical  and  because  of  cylinder  conden- 
sation, cushion  steam,  etc.,  the  intermediate-pressure  cylinder  is 
made  a  little  smaller  than  this  equation  would  give.  Seaton  * 
states  that  in  marine  practice  the  intermediate  cylinder  volume 
(or  piston  area)  is  about  as  given  by  the  following  equation  : 

rVJTxT, 

~lj — (301) 

*Seaton's  "Manual  of  Marine  Engineering";  or  Seaton  and  Rounthwaite's 
"Pocket  Book  of  Marine  Engineering." 


CONVENTIONAL  INDICATOR  DIAGRAM  339 

Marine  triple-expansion  engines  are  proportioned  about  as 
follows  : 

Initial  pressure,  abs 165  175                195 

Ratio I  to  H 2.33  2.4  2.54 

Ratio  L  to  H 6.6  7.0  7.8 

Total  expansion  ratio n .  n  •  7  13. 

(e)  Quadruple- expansion  engines  usually  operate  with  pressures 
from  175  to  225  pounds  gauge.  The  L.P.  terminal  pressures 
and  H.P.  cut-off  percentages  are  about  the  same  as  for  triple- 
expansion  engines.  Thus  the  total  expansion  ratios  are  some- 
what larger  than  in  the  latter  engines.  If  the  ratios  of  adjacent 
cylinders  are  made  equal,  then 

Ji  _  **  -  L  -7? 
H  ~  7i  "  72  "  "*' 

in  which  7i  and  72  refer  to  the  first  and  second  intermediate 
cylinders.     From  which  it  follows  that 

/i  =  RXH (302) 

72  =  RJi  =  R**H (303) 

L  =  RJ2  =  RJH (304) 

Hence  the  ratio  of  adjacent  cylinders  (assuming  -=y  known)  is 

-TZ 


**  =  Vf (305) 

or  the  ratio  of  low-pressure  to  high-pressure  cylinder  (assuming 
Rx  known)  is 

R=±=R/ (306) 

After  Rx,  H,  and  L  are  known,  7i  and  72  follow  from  Eqs. 
(302),  (303).  These  values  of  7i  and  72  should  be  reduced  some- 
what, for  the  same  reasons  that  were  given  in  the  case  of  the 
triple-expansion  engine. 

In  quadruple-expansion  marine  engines  the  cylinders  are  about 
in  the  following  proportions: —  i  :  1.8  :  3-6  :  7-8-  A  study*  of 
14  different  quadruple-expansion  engines,  with  pressures  about 

*  H.  H.  Suplee.     Trans.  A.  S.  M.  E.,  Vol.  X,  page  583. 


340 


HEAT-POWER  ENGINEERING 


i8o  pounds  per  square  inch,  showed  the  average  cylinder  propor- 
tions to  be  1 :  2  :  3.78  :  7-7° ;  or  nearly  1:2:4:8.* 

171.  The  Theoretical  Indicator  Diagram  of  Multiple-Expan- 
sion Engines  with  Clearance.  In  the  foregoing  discussion 
clearance  was  neglected.  If  clearance  is 
considered,  the  results  will  be  changed 
somewhat.  In  such  cases  the  analytical 
method  is  a  little  complicated,  hence  the 
graphical  method  is  generally  the  best  one 
to  use.  This  method  needs  no  explanation. 


£ 


;  -          In   the   theoretical    cards  of   a  compound 
engine  with  clearance,  as  shown  in  Fig.  217, 


the  total  ratio  of  expansion  is 

_LL+CIL 
=  la 

the  H.P.  ratio  of  expansion  is 

LH 


the  cylinder  ratio  is 


and  the  H.P.  and  L.P.  cut-off  ratios  are  respectively  -^-  and  -~^— 

LH          LL 

172.  Effects  of  Changing  the  Cut-offs  in  the  Respective 
Cylinders  of  Multiple-Expansion  Engines,  (a)  In  "  regulating  " 
the  engine  to  make  the  power  output  equal  to  the  demand,  the 
steam  distribution  to  the  cylinders  can  be  varied  in  several  ways. 

(b)  It  has  already  been  shown  that  the  effect  of  making  the 
L.P.  cut-off  occur  later  in  the  stroke  (other  things  remaining  the 
same)  is  (i)  to  lower  the  receiver  pressure,  (2)  to  increase  the 
H.P.  work,  (3)  to  decrease  the  L.P.  work;  and  vice  versa.     But 
(4)  such  change  does  not  affect  the  total  work  of  the  engine  if 
the  toes  of  the  diagrams  are  not  lost,  hence  the  engine  cannot 
be  regulated  by  changing  merely  the  L.P.  cut-off. 

(c)  If  the  L.P.  cut-off  is  fixed,  and  the  H.P.  cut-off  is  made  to 

*  For  data  relating  to  multiple-expansion  marine  engines,  see  Seaton's  "  Manual 
of  Marine  Engineering,"  Robertson's  "Translation  of  Bauer's  Marine  Engines  and 
Boilers."  For  all  types  of  multiple-expansion  engines,  see  Heck's  "The  Steam 
Engine,"  Vol.  II,  pages  506-9,  and  Gebhardt's  "Steam  Power  Plant  Engineering." 


CONVENTIONAL  INDICATOR  DIAGRAM 


341 


occur  later,  there  results  (i)  an  increase  in  the  receiver  pressure 
(Fig.  218),  (2)  a  greater  increase  in  the  L.P.  work  than  in 
the  H.P.  work.  Making  H.P.  cut-off  occur 
earlier  produces  the  reverse  effects.  Com- 
pound engines  can  be  regulated  by  having  an 
automatic  governor  control  only  the  cut-off 
in  the  high-pressure  cylinder.  But  in  such 
case,  if  there  is  much  change  in  the  load  on 
the  engine,  the  L.P.  cut-off  should  be  ad- 
justed by  hand  to  equalize  the  distribution 
of  the  load  between  the  cylinders. 

(d)  If  the  initial,  receiver,  and  exhaust  pressure  lines  on  a 
PV-diagram  for  a  compound  engine  are  extended  from  one  hy- 
perbolic expansion  line  to  another,  as  from  cD  to  c'D'  in  Fig.  219 
(a),  it  will  be  found  (i)  that  the  expansion  ratios  in  the  cylinders 


Fig.  218. 


remain  unchanged;  and  that,  in  consequence,  (2)  the  propor- 
tionate distribution  of  work  between  the  cylinders  also  remains 
the  same. 

In  Fig.  219  (6)  it  is  seen  that  the  high  and  low  cylinder  volumes 
(VH  and  VL)  are  such  that  the  expansion  lines  cd  and  CD  in 
the  two  cylinders  are  complete  and  continuous.  If  the  cylinder 
volumes  are  related  thus,  and  if  the  cut-offs  are  advanced  pro- 
portionately (so  that  c'd!  and  C'D'  in  Fig.  219  (b)  are  on  the  same 
hyperbola),  the  distribution  of  work  can  be  shown  to  be  in  the 
same  proportion  as  in  the  case  of  complete  expansion  just  dis- 
cussed; and  further  (from  this),  that  (3)  the  toe  areas  (XH  and 
XL)  lost  will  be  in  this  same  proportion.  These  same  state- 
ments are  also  true  in  case  the  cut-offs  are  decreased  propor- 
tionately as  in  Fig.  220.  In  this  figure,  however,  it  is  seen  that 
the  diagrams  have  "  loops  "  XH  and  XL,  which  represent  nega- 


342 


H  EA  T -POWER  ENGINEERIl\  G . 


Fig.  220. 


tive  work.     Evidently  the  cut-off  should  not  be  earlier  than  c, 
if  good  economy  is  important. 

With  such  arrangement  the  automatic  governor  can  be  made 
to  change  the  cut-off  equally  in  the  two  cylinders  and  the  proper 
balance  of  work  will  be  always  auto- 
matically maintained.  The  tandem  com- 
pound engine  in  Fig.  107  is  an  example 
of  this  case. 

If  the  L.P.  toe  loss  is  greater  than  the 
similar  H.P.  loss,  it  can  be  shown  that 
to  maintain  the  same  relative  balance  of 
power  between  the  cylinders,  the  L.P. 
cut-off  must  vary  more  rapidly  than  the 
H.P.  cut-off;  thus  as  the  power  is  in- 
creased the  receiver  pressure  must  be  raised. 

(e)  If  the  cut-offs  (or  expansion  ratios)  in  the  two  cylinders 
remain  constant,  the  power  of  the  engine   may  be  decreased 
by  throttling  the  steam,  and   in   this   case   the  distribution  of 
power   between    the    cylinders    remains    in    substantially   the 
same  proportion.     That  this  is  true  may  be  seen  from  inspec- 
tion of  Eq.  (294),  in  which  PR  is  seen  to  be  practically  propor- 
tional to  pi   (since  all  other  quantities  are  constants   in   this 
case,  except  the  ratio  p2/pi,  which  is  so  small  a  quantity  that 
its  change  is  negligible).     This  shows  that  the  effect  of  throt- 
tling is  substantially  equivalent  to  changing  the  pressure  scale 
of  the  diagram. 

(f)  Because  of  the  effect  of  clearance,   "  wire  drawing,"  cyl- 
inder condensation,  etc.,  the    real 

diagrams   differ   greatly  from   the 
theoretical  ones,  hence  the  conclu-    Y 
sions  just  given  can  be  used  only 
in  a  very  general  sense  in  actual 
cases. 

173.   Theoretical     PV-Diagrams 

of  a   Tandem   Compound   Engine  _^C,LU_  stroke  ->bi'r-    v« 
with  Receiver  of    Finite  Volume, 
and  having    Clearance,     (a)    Fig.  Fig.  221. 

221   shows  the    PV-diagrams   for  a    tandem   compound    engine 
which  has  clearance  volume  and  finite  receiver  volume.     The 


CONVENTIONAL  INDICATOR  DIAGRAM  343 

abscissas  of  both  the  H.P.  and  L.P.  diagrams  are  the  strokes 
(same  for  both  cylinders).  OF  is  the  line  of  absolute  zero  for 
volumes  in  the  low-pressure  cylinder,  and  oy  is  the  similar  line 
for  the  high-pressure  cylinder.  In  the  latter  cylinder  abc  is 
the  admission  line,  cd  is  the  expansion  line  (with  respect  to  axes 
oy  and  00),  ddi  is  the  drop  in  pressure  when  the  H.P.  steam 
is  released  to  the  receiver,  d\e\  is  the  period  when  the  high-pres- 
sure cylinder  is  exhausting  into  the  receiver  alone,  and  e\ej  is 
the  period  during  which  the  high-pressure  cylinder  is  exhausting 
into  both  the  receiver  and  the  low-pressure  cylinder;  fg  shows 
the  period  when  the  high-pressure  cylinder  is  exhausting  into 
the  receiver,  after  cut-off  has  taken  place  (at  C)  in  the  low-pressure 
cylinder;  and  ga  is  the  compression  into  the  H.P.  clearance 
space  (and  is  therefore  asymptotic  to  oy).  Evidently  if  O'Y'  is 
drawn  to  the  right  of  oy  at  a  distance  (F#)  equal  to  the  receiver 
volume  (measured  to  the  same  scale  that  is  used  for  the  H.P. 
volumes) ,  fg  will  be  a  hyperbola  with  axes  0'  Yf  and  O'O.  Dur- 
ing the  period  ef  of  the  H.P.  exhaust  the  low-pressure  cylinder 
is  receiving  steam  along  the  coincident  line  BC.  After  L.P. 
cut-off  at  C,  the  steam  in  the  low-pressure  cylinder  expands 
according  to  CD,  is  exhausted  along  DEF,  compressed  along 
FA,  and  admitted  along  ABC  from  the  high-pressure  cylinder 
and  from  the  receiver.  Evidently  CD  and  FA  are  hyperbolas 
with  respect  to  axes  Oo  and  0  Y. 

(b)  These  diagrams  can  also  be  constructed  by  the  method 
given  in  the  next  section. 

174.  Theoretical  PV-Diagrams  of  a  Cross  Compound  Engine 
with  Receiver  of  Finite  Volume,  and  having  Clearance,  (a)  In 
Fig.  222  (a)  the  H.P.  and  L.P.  diagrams  of  opposite  strokes  are 
shown  with  true  volumes  as  abscissas,  and  with  the  clearance 
and  receiver  volumes  in  proper  proportion  and  relation  for  a 
single-acting  cross  compound  engine  with  L.P.  cut-off  less  than 
one-half  stroke.  It  will  be  seen  that  the  arrangement  of  dia- 
grams is  similar  to  that  in  Fig.  212  (d),  but  with  clearance  and 
receiver  volumes  added. 

If  the  points  in  the  stroke  at  which  the  valve  events  occur  are 
known,  the  lines  abed  and  EFA  are  easily  drawn,  but  the  points 
on  the  H.P.  exhaust  line  and  L.P.  admission  line  are  harder  to 
find.  The  method  of  determining  these  will  now  be  considered. 


344 


HEAT-POWER  ENGINEERING 


(b)  It  will  be  convenient  to  have  an  auxiliary  diagram,  such 
as  Fig.  222  (b),  called  a  steam-distribution  chart,  which  will 


Fig.   222. 


show  for  each  crank  angle  (ordinate)  the  volumes  (abscissas)  of 
steam  in  both  the  cylinders  and  in  the  receiver.  If  the  motion 
of  the  piston  is  harmonic  (as  it  is  approximately),  the  curves  of 


CONVENTIONAL  INDICATOR  DIAGRAM  345 

volumes  displaced  by  the  pistons  are  of  course  sinusoids,  and 
can  be  easily  constructed  in  the  manner  shown  in  the  lower 
part  of  the  figure.  In  the  case  under  consideration,  as  the 
cranks  are  at  right  angles  these  sinusoids  must  differ  in  phase  by 
90°.  The  clearance  lines  (oyf  and  OF')  are  added  to  the  chart; 
thus  the  distance  from  a  point  on  a  sinusoid  to  the^  clearance 
line  gives  the  volume  of  steam  in  the  cylinder  for  the  corre- 
sponding crank  angle. 

The  percentages  of  stroke  for  all  "  valve  events  "  are  sup- 
posed to  be  known,  thus  the  abscissas  of  all  events  can  be  laid 
off  on  the  PV-diagrams  in  Fig.  222  (a).  Lines  abed  and  EFA 
can  be  drawn  at  once,  and  efgha  and  BB±C  can  be  drawn  ten- 
tatively to  show  roughly  the  general  shape  of  the  diagrams. 
The  exact  lines  will  be  found  later.  Then  on  the  sinusoids,  in 
Fig.  222  (6),  the  points  for  the  valve  events  can  be  found  by 
projecting  downward  from  the  PV-diagrams,  or  may  be  located 
more  accurately  by  using  the  crank  angles  corresponding  to  the 
valve  events.  The  points  thus  found  are  lettered  the  same  as 
the  corresponding  points  on  the  PV-diagrams,  but  are  primed. 

(c)  From  bf  to  c'  in  Fig.  222  (b)  is  H.P.  admission,  and  from 
cr  to  df  is  H.P.  expansion,  with  volumes  varying  according  to 
the  heavy  abscissas  to  the  right  of  the  sinusoid  between  these 
points.      The   product   PV  is   constant   during   this   expansion 
(and  its  value  can  be  found  since  Pc  and  Vc  are  known),  hence 
the  "  PV-quantity  "    (PV)C  niay  be  taken  as  representing  the 
whole    process    of    expansion.     Evidently  the    following    broad 
statement  can  be  made: 

General  Proposition  A:  Between  valve  events  (not  neces- 
sarily in  the  same  cylinders)  controlling  the  weight  of  steam 
involved,  the  "  PV-quantity  "  is  constant;  and  when  its  value  is 
known  the  expansion  curve  can  be  constructed.  Thus,  in  this 
instance,  dividing  the  PV-quantity  (PV)C  by  different  values 
of  V  gives  the  pressures  to  be  used  in  plotting  the  expansion 
curves  cd. 

(d)  At  d  (and  d')  the  steam  with  PV-quantity  equal  to  (PV)C 
is  released  from  the  high-pressure  cylinder  and  mixes  with  the 
receiver   steam   which   has  a  PV-value  equal   to  mn(PV)g,   in 
which  m  and  n  are  unknown  coefficients,  the  value  of  which  will 
be  determined  later.     In  such  cases  the  following  assumption  is 
made: 


246  HEAT-POWER  ENGINEERING  ''' 

General   Proposition   B:   The    PV  -quantity  resulting  from  a 
Mixture  is  ......     (307) 


Thus,  after  point  e  is  passed 

[PV]e  =  (PV)e  +  rnn  [PV]a,  -  .-  .  .  (308) 
from  which  [PV]e  can  be  found  when  mn  [PV]g  has  been  deter- 
mined, since  (PV)C  is  already  known. 

(e)  The  L.P.  compression  occurs  from  F  to  A  (and  Fr  to  A') 
with  PV-quantity  constant  and  equal  to  (PV)p,  —  the  value  of 
which  can  be  easily  found,  since  PF  and  VF,  are  given,  —  and 
with  volumes  varying.  as  shown  by  the  heavy  dotted  abscissas 
to  the  left  of  sinusoidal  arc  F'A'.  At  A  (and  at  A'  and  /') 
this  L.P.  cushion  steam  mixes  with  that  in  the  receiver  and  high- 
pressure  cylinder;  hence  the  PV-  value  of  the  mixture  is,  from 
Proposition  B, 

[PV\Q  =  [PV],+  (PV)F.     .    '.     .     .     (309) 


Thus  during  phase  gh  and  BBi  the  pressures  may  be  found  by 
dividing  [PV]g  by  the  volumes  which  are  shown  by  the  dotted 
abscissas  between  arcs  gfhr  and  AfB\. 

(f)  After  the  H.P.  exhaust  valve  has  closed  at  h  there  remain 
in  the  receiver  and  low-pressure  cylinder  n  parts  of  the  steam  that 
has  been  represented  by  [PF]ff,  and  the  rest,  (i  —  ri)  parts,  is 
used  for  compression  in  the  high-pressure  cylinder.  Between  BI 
and  C  (and  BI  and  C')  the  PV-quantity  of  the  steam  in  the 
low-pressure  cylinder  and  receiver  is  n  [PV]a  in  accordance  with 
the  following  assumption: 

General  Proposition  C:  If  a  weight  of  steam,  having  a  cer- 
tain PV-quantity,  is  divided  without  change  in  pressure,  the  PV- 
quantity  of  the  part  is  the  same  fraction  of  the  original  PV-quantity 
that  its  weight  is  of  the  original  weight.  For  example,  if  one-half 
the  steam  involved  is  left  in  the  cylinder  and  receiver,  when  the 
H.P.  exhaust  closure  occurs  at  h  or  BI  (hf  or  BI),  then  n  =  \,  and 
the  PV-quantity  of  this  remaining  steam  has  the  value  \  \PV\Q. 
Thus,  between  points  BI  and  C  the  PV-value  is  n  [PV]a  and  the 
volumes  are  shown  by  the  abscissas  to  the  left  of  the  sinusoidal 
arc  between  points  BI  and  C'  '. 

After  the  L.P.  valve  has  cut  off  at  C  (and  C')  there  are  left 
in  the  receiver  m  parts  of  the  steam  which  was  represented  by 
n  [PV]a\  hence,  this  receiver  steam  has  a  PV-value  of  mn  [PV]at 


CONVENTIONAL  INDICATOR  DIAGRAM 


347 


which  continues  constant  until  point  a  in  the  next  cycle  is 
reached. 

(g)  In  the  simultaneous  equations  (308)  and  (309)  all  quan- 
tities are  either  known  or  can  be  determinable  directly,  except 
the  bracketed  quantities  [PV]e  and  [PV]g ;  but  these  latter  can  be 
found  by  elimination.  When  these  are  known,  the  PV-diagrams 
can  easily  be  completed. 

(h)  If  the  engine  is  double-acting,  and  if  it  has  equal  PV-dia- 
grams at  both  ends  of  the  cylinders,  the  solution  of  only  one  end  is 
necessary.  But  if  the  diagrams  are  not  equal,  it  is  necessary  to 
draw  the  steam-distribution  chart  for  both  ends  of  the  cylinders. 
Then  there  will  be  four  unknown  PV-quantities,  but  there  will 
be  the  following  four  simultaneous  equations,  from  which  the 
unknowns  can  be  determined: 

[PV}0  =  (PV)e  +  m'n'  [PV]'a  .     .     . 
[PV]g  =  [PV\.   +  (PV)F      .... 
[PV]'e  =  (PVYc  +  mn(PV}0      .     .     .     (312) 

iPVY,  =  iPVY.*(pvyf  ....  (313) 

in  which  the  primed  quantities  are  those  for  the  cylinder  ends 
not  considered  in  the  previous  discussion. 


Fig.  223.  —  Effect  of  Early  Release. 


(i)  In  the  foregoing  it  has  been  assumed  that  release  and 
admission  occur  at  the  ends  of  the  stroke.  If  the  engine  is 
double-acting  and  if  the  steam  is  released  before  the  end  of  the 
stroke  in  the  high-pressure  cylinder,  the  L.P.  admission  line  will 
suddenly  rise,  in  case  the  L.P.  cut-off  has  not  already  occurred; 
for  this  release  suddenly  increases  the  steam  pressure  in  the  re- 
ceiver from  which  steam  is  still  being  supplied  to  one  end  of  the 
low-pressure  cylinder.  This  is  shown  in  Fig.  223,  from  which  it 


348 


HEAT-POWER  ENGINEERING 


is  seen  that,  when  the  steam  is  released  at  di,  there  is  a  drop  of 
pressure  in  the  high-pressure  cylinder  accompanied  by  a  simul- 
taneous rise  at  X  in  the  low-pressure  cylinder,  until  the  pres- 
sures at  X'  and  d\  are  equal.  This  case  can  be  analyzed  by 
the  method  already  given. 

(j)  The  case  with  cut-off  later  than  half-stroke  is  somewhat 
similar  to  that  discussed  in  (i)  of  this  section  and  is  illustrated 
in  Fig.  224.  Even  if  the  H.P.  release  occurs  at  the  end  of  the 
stroke  (at  di),  there  will  be  the  sudden  rise  XX'  on  the  L.P. 
admission  line,  as  the  low-pressure  cylinder  has  not  previously 


Fig.  224.  —  Low-pressure  Cut-off  later  than  Half-stroke. 

/ 

been  cut  off  from  the  receiver.  From  X'  to  cut-off  at  C  the  low- 
pressure  cylinder  continues  to  receive  steam  from  the  receiver, 
while  simultaneously  the  high-pressure  cylinder  is  discharging 
steam  into  the  receiver  according  to  line  e\e\  .  Evidently  the 
pressures  at  points  e\  and  X'  are  equal;  and  the  same  is  true  of 
points  e\  and  C.  This  case  can  be  analyzed  with  the  aid  of  a 
steam-distribution  chart,  in  the  same  manner  as  that  which  has 
just  been  discussed  in  connection  with  the  other  cases. 

175.  Theoretical  PV-Diagrams  of  Multiple-Expansion  En- 
gines with  Finite  Receiver  and  Clearance  Volumes,  with  Any 
Number  of  Cylinders  and  with  Any  Angles  between  Cranks 
(General  Case).  The  methods  just  discussed  in  connection  with 
the  construction  of  PV-diagrams  for  compound  engines  can  be 
extended  to  this  perfectly  general  case.  It  is  assumed  that  the 
initial  and  exhaust  pressures  are  known,  together  with  the  vol- 
ume ratios  of  cylinders,  receivers,  and  clearances,  and  that  the 


CONVENTIONAL  INDICATOR  DIAGRAM 


349 


percentages  of   stroke   (or  crank  angles)   of   the  various  valve 
events  are  given.     The  procedure  is  as  follows: 

1 i )  Draw  the  cylinder,  clearance,  and  receiver  volumes  in  proper 
relative  positions  on  the  PV-diagrams. 

(2)  Sketch  as  much  of  the  H.P.  and  L.P.  PV-diagrams  as 
can  be  done  initially. 

(3)  Draw  the  sinusoids  on  the  steam-distribution  chart  in  a 
proper  phase  relation   (considering  the  crank  angles  and   "  se- 
quence "  of  cranks);  locate  the  valve  events;  and  by  a  system 
of -section  lining  show  the  volumes  connected  between  events 
(remembering  that  these  volumes  are  not  necessarily  confined 
to  those  in  one  cylinder). 

(4)  On  the  distribution  chart: —  (a)    give  the  PV-quantities 
initially  known,  such  as  (PV)C  and  (PV)p  in  the  previous  cases; 
(b)  in  accordance  with   General   Proposition   C  state  the  PV- 
quantities  resulting  from  a  separation  of  volumes   (when  not 
accompanied  by  change  in  pressure)  as  fractional  parts  of  the 
quantity  which  is  divided,  as  mn  (PV)g\  and  (c)  in  accordance 
with  General  Proposition  B,  write  equations  for  the  PV-quan- 
tities resulting  from  mixtures. 

(5)  Obtain  the  values  of  the  fractional  coefficients,  m,  n,  etc. 

(6)  Find  the  unknown  PV-quantities  by  solving  the  simul- 
taneous equations,  of  which  there  should  be  the  same  number  as 
there  are  unknowns. 

(7)  Complete  the  construction  of  the  PV-diagram,  which  can 
be  done  now  that  the  PV-quantities  are  all  known. 

The  heavy  lines  in  Fig.  225 
show  the  PV-diagrams  for  a  * 
triple-expansion  engine.  The  in- 
dividual diagrams  were  first  ob- 
tained in  the  manner  just  outlined 
and  then  were  combined  with 
respect  to  a  common  axis  of 
volumes  as  shown  in  this  figure. 

176.   The  Actual  Combined  In- 
dicator   Diagrams    of    Multiple-    a 
Expansion  Engines,     (a)   In  Fig. 
225  it  is  seen  that  the  theoretical 
PV-diagrams    (in    heavy   lines)    overlap,    that    their   expansion 


Fig.  225. 


350 


HEAT-POWER  ENGINEERING  •' 


lines  do  not  fall  on  the  same  hyperbola,  and  that  the  sum 
of  their  areas  is  much  less  than  that  of  the  simple  diagram 
abode.  The  overlapping  parts  of  the  diagrams  do  not  occur 
simultaneously.  The  lack  of  continuity  of  the  expansion  lines 
is  largely  due  to  the  difference  in  the  amounts  of  cushion  steam 
in  the  various  cylinders;  it  is  also  due  to  the  sloping  and  irregu- 
larity of  the  I. P.  and  L.P.  admission  lines,  and  to  earliness  of 
the  I. P.  and  L.P.  cut-offs  compared  with  that  in  the  high- 
pressure  cylinder.  The  ratio  of  the  sum  of  areas  H,  I,  and  L 
to  area  abcde  is  the  theoretical  diagram  factor  in  this  case,  and 
it  is  evidently  much  less  than  unity. 

flb)  The  actual  indicator  diagrams  depart  considerably  from 
the  theoretical.  This  is  partly  because  of  wire  drawing  during 
flow  of  steam  through  valves,  receivers,  and  piping,  partly  be- 
cause of  condensation  or  reevaporation  in  cylinders,  receiver, 
and  piping,  partly  from  radiation  and  similar  losses,  partly  be- 
cause the  real  expansion  line  is  not  hyperbolic,  and  may  also  be 
partly  due  to  the  withdrawal  of  the  condensate  collecting  in 
"  separating  "  receivers.  In  Fig.  225  the  probable  diagrams  are 
shown  dotted. 

(c)  Given  the  actual  indicator  cards  obtained  from  the  en- 


Fig.  226. 

gine,  as  h  and  /  in  Fig.  226,  they  can  be  readily  "  combined," 
as  shown  by  H  and  L,  if  the  cylinder  and  clearance  volumes  are 
known. 


CONVENTIONAL  INDICATOR  DIAGRAM  351 

The  areas  of  diagrams  H  and  L  can  then  be  found  and  the 
"  referred  m.e.p."  determined  in  the  usual  manner. 

After  this,  the  actual  diagram  factor  can  be  obtained  by 
getting  the  ratio  of  these  quantities  to  the  area  of  the  conven- 
tional diagram.* 

(d)  On  Fig.  226  the  saturation  curves,  55  and  S£S',  have 
been  drawn.  As  the  weights  of  cushion  steam  in  the  two  cyl- 
inders are  not  the  same,  and  because  the  condensate  has  been 
removed  from  the  receiver  in  this  case,  there  are  unequal  weights 
of  steam  in  the  two  cylinders  during  the  respective  expansions, 
consequently  saturation  line  S'S'  lies  to  the  left  of  SS. 

Fig.  226  also  shows  the  quality  curves  XH  and  xi,  which  are 
obtained,  after  the  saturation  lines  have  been  drawn,  by  the  same 
method  that  was  described  for  simple  engines. 

I76A.  Clayton's  Analysis  of  Expansion  Lines,  (a)  By  re- 
plotting  indicator  cards  on  logarithmic  coordinates  Clay  ton  f 
has  determined  the  expansion  coefficients  n  for  many  engines. 
He  found  that  such  expansion  lines  were  substantially  straight 
(except  when  modified  by  leakage  or  faulty  indicator  practice 
which,  if  present,  were  revealed  by  the  curvature);  that  the 
points  of  cut-off  and  other  valve  events  could  be  accurately 
determined;  and  that,  as  in  the  ideal  case  (see  (d),  page  207), 
there  appeared  to  be  a  definite  relation  between  the  quality  (xc) 
at  cut-off  and  the  exponent  of  expansion  (n)  for  each  type  of 
engine  and  condition  of  operation. 

For  a  Corliss  non-condensing  engine,  without  leakage,  he  found 
xc  =  1.245  n  -  0.576 (3i3a) 

There  was  some  variation  with  change  of  speed  and  pressure;  but 
cylinder  size  and  point  of  cut-off  had  little  influence.  Having 
determined  n  for  the  engine  xc  can  be  computed,  after  which  the 
water  rate  can  be  found. 

With  the  logarithmic  coordinates  the  clearance  volume  can 
be  determined  quite  closely,  when  there  are  no  abnormal  dis- 
turbances, by  finding  the  origin  which  will  give  a  straight  line. 

*  There  are  several  different  kinds  of  diagram  factors,  each  of  which  may  be 
used  to  best  advantage  for  some  particular  purpose.  When  the  engine  is  consid- 
ered by  itself,  the  definition  previously  used  in  the  text  is  the  one  most  commonly 
given.  The  A.  S.  M.  E.  Report  of  Committee  on  Standardizing  Engine  Tests 
defines  the  card  factor  in  such  manner  as  to  include  the  cylinder-feed  losses  be- 
tween engine  and  boiler.  See  Trans.  A.  S.  M.  E.,  Vol.  XXIV,  page  751. 

t  Trans.  A.  S.  M.  E.  34,  p.  17.    Bulletin  58  and  65,  U.  of  111.  Exp.  Sta. 


CHAPTER   XXI. 

PERFORMANCE  OF  STEAM  ENGINES. 

177.  Steam  Consumption,  (a)  Steam  engines  are  governed 
by  (i)  throttling  the  steam,  (2)  by  varying  the  cut-off,  and 
(3)  by  combining  (i)  and  (2). 

When  the  engine  is  governed  by  throttling  (the  cut-off  re- 
maining constant),  the  available  energy  AE  per  pound  of  steam 
theoretically  decreases  as  the  pressure  is  reduced.  This  is  shown 
in  the  Mollier  diagram,  Fig.  227.  Starting  with  initial  pressure 

pi,  the  associated  heat  Aft,  and  back 
MOLLIER  CHART  pressure  pb,  the  available  energy  is 

AEi.  In  throttling  to  pressure  p2  the 
associated  heat  remains  unchanged, 
but  the  available  energy  per  pound 
is  reduced  to  AE2,  and  consequently 

/  A    7U1    \ 

Fig.  227.  more  steam,  in  the  ratio  [TT5~/»  must 

be  used  to  develop  one  i.h.p.-hour.  Evidently  the  actual  throt- 
tling engine  gives  the  best  economy  only  under  maximum  load, 
hence  the  water-rate  curve  will  resemble  cd  in  Fig.  228. 

It  is  found  that  with  this  type  of  governing,  the  curve  of 
total  consumption  (ab)  is  practically  a  straight  line,  and  this 
relation  is  commonly  called  Willans'  Law.  When  two  points 
on  this  line,  or  one  point  and  the  slope,  are  given,  the  line  can 
at  once  be  drawn.  Then  dividing  ordinates  by  corresponding 
abscissas  gives  the  simultaneous  values  of  the  water  rate,  and 
these  values  can  be  used  for  plotting  the  water  curve. 

With  greater  ratio  of  expansion,  less  steam  is  used  for  a  given 
output,  hence  for  such  cases  the  curves  a'b'  and  c'd'  in  Fig.  228 
would  lie  below  the  others. 

(b)  When  the  engine  is  governed  by  varying  the  cut-off,  the 
water-rate  curve  resembles  efg  in  Fig.  229,  the  reasons  for  which 
were  made  clear  in  Section  125.  To  this  figure  has  been  added 

352 


PERFORMANCE  OF  STEAM  ENGINES 


353 


the  curve  cd  of  Fig.  228,  the  point  d  of  course  coinciding  with  g. 
Thus  it  is  seen  that  cut-off  governing  gives  better  results  than 
throttle  governing  except  at  the  maximum  load. 

The  product  of  abscissas  by  ordinates  gives  the  total  steam 
consumption,  plotting  which  gives  the  curved  line  hij  as  the 
Curve  of  Total  Water  Consumption  for  cut-off  governing.  Evi- 
dently point  i,  where  a  line  drawn  from  O  becomes  tangent  to 
hij,  determines  the  abscissa  for  the  lowest  water  rate,  for  that 
point  has  the  smallest  ratio  of  ordinate  to  abscissa. 

(c)  The  y  intercept  Oy  of  the  T.C.  curve  represents  the  weight 
of  steam  used  when  no  i.h.p.  is  being  developed.  It  is  the  weight 
which  furnishes  heat  equivalent  to  the  losses  from  condensation, 
leakage,  and  radiation. 

Curves  similar  to  Figs.  228  and  229  might  have  B.t.u.  as  ordi- 
nates; and  m.e.p's,  cut-offs,  ratios  of  expansion,  or  d.h.p's  may  be 


Fig.  228.  " 

used  as  abscissas.  When  abscissas  are  d.h.p.,  then  the  y  inter- 
cept represents  the  consumption  due  to  engine  friction  in  addi- 
tion to  the  other  losses  mentioned  in  the  preceding  paragraph. 

(d)  If,  in  Fig.  229,  00'  is  the  i.h.p.  used  in  overcoming  the 
engine  friction,  then  O'Y'  is  the  axis  from  which  the  d.h.p.  are 
measured.  If  the  engine  friction  is  assumed  constant  for  all 
loads  (which  is  not  strictly  true),  the  curve  TC  in  the  figure, 
with  origin  at  O ',  gives  the  total  consumption  for  the  d.h.p.  de- 
veloped. The  curve  e'fg'  of  water  rate  per  d.h.p. -hour  will  of 
course  lie  above  efg,  and  the  lowest  point  f  will  lie  farther  from 
0  than  /.  Evidently,  on  the  basis  of  delivered  power,  the  best 
economy  in  this  case  occurs  when  the  i.h.p.  equals  Okr  (corre- 
sponding to  a  d.h.p.  of  0'&'),  and  this  should  be  the  power  which 
the  engine  normally  develops  ("  Normal  Power  ")  if  steam  econ- 
omy is  of  prime  importance.  This  should  then  be  the  "  rated 


354 


HEAT-POWER  ENGINEERING 


power,"  or  power  at  which  the  engine  is  rated  to  operate  nor- 
mally. When  the  i.h.p.  developed  is  either  more  or  less  than 
this,  the  engine  has  poorer  economy. 

(e)  The  load  factor   is   the   ratio  of  the  actual  load  to  the 
rated  load.     There  are  instantaneous  load  factors,  and  average 
load  factors.     For  best  steam  economy  the  load  factor  should  be 
unity;  and,  since   it  is  better  to  overload  than  to  underload  a 
steam  engine  (see  Fig.  229) ,  a  load  factor  a  certain  amount  above 
unity  is  preferable  to  one  the  same  amount  below.     There  are, 
however,  other  considerations  which  may  make  it  financially  more 
profitable  to  rate  the  engine  at  output  other  than  that  giving 
best  steam  economy,  and  to  operate  with  some  load  factor  other 
than  unity. 

In  many  instances,  the  average  load  factor  of  the  power  plant 
as  a  whole  is  low,  but  in  such  cases  it  is  customary,  when  pos- 
sible, to  have  several  engines  and  to  place  in  operation  such  a 
number  as  will  cause  those  in  service  to  operate  under  the  most 
economical  conditions;  that  is,  the  load  factors  of  the  individual 
engines  are  maintained  near  unity. 

The  instantaneous  load  factor  may  vary  widely,  as  in  a  street- 
railroad  power  plant,  and  the  fluctuations  may  be  of  such  rapid 
character  as  to  prohibit  changing  the  number  of  engines.  In 
such  a  case  a  small  average  load  factor  may  be  unavoidable. 

(f)  Curves  of  steam  consumption  for  an  engine  are  useful  in 
determining  the  best  conditions  of  operation  for  that  particular 
engine  and  for  comparing  it  with  others  that  operate   under 
similar  conditions.     When  the  conditions  are  widely  different 
the  water  rates  should  not  be  compared  directly. 

To  reduce  water  rates  to  a  comparable  basis,  when  the  differ- 
ence in  conditions  of  operation  is  not  great,  the  following  cor- 
rections may  be  made :  * 

0.4  to  0.6  per  cent  per  I  inch  change  in  vacuum  (between  25 
and  28  inches). 

i  per  cent  per  8  to  n  degrees  of  superheat  (at  from  50  to 
100  degrees). 

o.i  to  0.2  per  cent  per  pound  of  initial  pressure. 

I  per  cent  per  I  per  cent  of  moisture. 

The  only  true  comparison  is  on  the  basis  of  B.t.u.  per  h.p. 
per  unit  of  time  (minute)  or  on  the  basis  of  thermal  efficiency 
*  Moyer's  Steam  Turbines,  page  288:  —  Wiley  &  Sons. 


PERFORMANCE  OF  STEAM  ENGINES 


355 


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356 


HEAT-POWER  ENGINEERING- 


on  the  d.h.p.  The  engine  having  the  lowest  water  rate  and  the 
highest  cylinder  efficiency  does  not  always  use  the  least  heat  per 
unit  of  power,  nor  have  the  highest  thermal  efficiency. 

178.  Steam-Engine  Performance:  Data.  —  (a)  The  perfor- 
mance of  engines  is  dependent  on  many  things,  of  which  the 
more  important  ones  are:  (i)  initial  pressure,  (2)  back  pres- 
sure (condensing,  noncondensing) ,  (3)  cut-off,  or  expansion  ratio, 
(4)  number  of  expansion  cylinders,  (5)  quality,  or  superheat, 
(6)  use  of  jackets,  (7)  use  of  reheating  receivers,  (8)  speed,  and 
(9)  the  proportions,  size,  and  arrangement  of  cylinders,  clear- 
ance spaces,  and  passages.  These  items  must  be  considered  in 
comparing  economies. 


Gauge  Pressures  (Lbs./Sq.  In.) 

I 
1 

1 

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B.t.u.  per  I.H.P.  per  Min. 
Fig.  230. 

Table  VII  is  a  brief  summary  of  Gebhardt's  more  extensive 
tables,*  with  a  few  additions  and  omissions.     It  will  serve  as  a 

*  See  Gebhardt's  "Steam  Power  Plant  Engineering,"  pages  296,  306,  and  314. 
Wiley  &  Son,  publishers. 

Also  Heck's  "The  Steam  Engine,"  Vol.  II,  pages  600-652. 


PERFORMANCE  OF  STEAM  ENGINES 


357 


rough  comparison  of  some  of  the  best  performances  that  have 
been  obtained  with  the  principal  types  of  engines.  The  condens- 
ing, multiple-expansion  engines  are  in  most  cases  steam- jacketed 
unless  the  steam  is  superheated. 

Although  the  tabulation  as  here  given  does  not  bring  out  this 
point,  it  should  be  remembered  that  while  the  lowest  B.t.u. 
per  i.h.p.-min.  corresponds  to  the  highest  thermal  efficiency,  it 


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Thermal  Eff.  on  the  I.H.P 
Fig.  231. 

does  not  follow  that  it  is  accompanied  by  low  water  rate  and 
high  cylinder  efficiency. 

(b)  Figs.  230.  and  231  show  respectively  the  variations  of 
B.t.u.  per  i.h.p.-min.  and  the  thermal  efficiency  on  the  i.h.p., 
with  initial  and  exhaust  pressure,  with  superheat,  with  type  of 
engine,  etc.  Reference  to  these  figures  shows  that,  as  compared 
with  the  Clausius  cycle  with  28-inch  vacuum,  the  losses  of 
various  types  of  real  engines  are  about  as  follows  in  the  best 
condensing  practice: 


358  HEAT-POWER  ENGINEERING  ,- 

Quadruple 20% 

Triple 25% 

Compound 33% 

Simple 50% 

(c)  Table  VIII  gives  a  brief  summary  of  steam-engine  efficien- 
cies, including  some  of  the  best.  Table  IX  gives  the  pounds  of 
steam  consumed  per  i.h.p.-hour  by  ordinary  engines  which  op- 
erate under  the  usual  commercial  conditions  and  in  which  no 
special  provision  is  made  for  improving  economy  —  such  as  super- 
heating, jacketing,  etc.  Larger  engines,  of  course,  give  better 
results  than  smaller  ones. 

TABLE  VIII.  —  SUMMARY  OF  EFFICIENCIES  OF   STEAM  ENGINES. 

Carnot  cycle  efficiency  * 10      to  32% 

Clausius  cycle  efficiency  * 8      to  28% 

Indicated  efficiency 40      to  88 . 2% 

Thermal  efficiency  on  i.h.p 5      to  25 . 05% 

Mechanical  efficiency 85      to  97% 

Thermal  efficiency  on  d.h.p 4      to  23 . 9% 

Over-all  efficiency 35      to  84% 

Heat  used  per  i.h.p.-min 169 -3  to  700  B.t.u. 

TABLE  IX.  — STEAM   CONSUMPTION. 

Type  of  Engine.  Lbs.  i.h.p.-hour 

Simple  "  high-speed  "  engines  (noncondensing) 28  to  36 

Simple  Corliss  engines  (noncondensing) 25  to  28 

Compound  slide-valve  engine  (noncondensing) 24  to  26 

Compound  slide-valve  engine  (condensing) 15  to  21 

Compound  Corliss  engine  (condensing) 14  to  16 

Triple-expansion  (condensing) 1 2\  to  13 

*  Obtained  from  Figs.  73  and  75  respectively  with  the  following  assumptions: 
The  lower  limit  of  pi  is  assumed  at  50  pounds  pressure  and /2  =  21 2°  F,  The 
upper  limit  of  p\  is  assumed  at  150  pounds  pressure  and  k  =  100°  F. 


CHAPTER    XXII. 

STEAM  TURBINES. 


179.  Introductory,  (a)  The  earliest  steam-driven  prime  mover 
recorded  in  history  is  Hero's  steam  turbine  (about  200  B.C.),  which 
is  shown  in  Fig.  232.  It  was  a  "reaction  turbine,"  driven  by  the 
repulsive  force  produced  by  a  jet  of  steam  issuing  rearwards  as 
regards  the  direction  of  rotation.  Branca's  "impulse  turbine" 


Nozzle 


Fig.  232.  Fig.  233. 

(1629),  shown  in  principle  in  Fig.  233,  is  the  next  historical  refer- 
ence to  the  use  of  steam  in  a  turbine.  The  first  patents  in 
foreign  countries  appeared  about  1820  and  the  primary  patent 
in  the  United  States  was  issued  m  1831.  Although  many  steam 
turbines  were  invented  in  the  succeeding  years,  it  was  not  until 
the  latter  8o's  of  the  last  century  that  the  modern  commercially 
successful  types  began  to  be  developed. 

(b)  A  steam  turbine  may  be  defined  as  a  device  in  which  one 
or  more  jets  of  the  working  substance  moving  at  high  velocity 
(and  therefore  possessing  kinetic  energy)  act  or  react  on  vanes 
or  buckets  on  one  or  more  wheels,  or  drums,  in  such  manner  as 
to  cause  them  to  rotate  and  transmit  power  by  means  of  the 
shaft  on  which  they  are  mounted. 

The  shaft,  the  wheels  or  drums,  and  their  attachments  con- 
stitute the  "rotor."  The  working  substance  is  steam,  which 
may  have  moisture  entrained  in  it.  The  velocity  of  the  jet  is 
acquired  by  the  expansion  of  the  steam  through  a  nozzle,  or  its 
equivalent,  during  which  process  some  of  the  heat  energy  of 
the  steam  is  converted  into  the  kinetic  energy  of  the  issuing  jey 

359 


360  HEAT-POWER  ENGINEERING    ,- 

In  "  impulse  turbines  "  the  nozzles  are  stationary  and  the  jets 
act  on  the  turbine  vanes;  in  the  "reaction"  type,  the  nozzles, 
or  their  equivalents,  are  mounted  on  the  rotor,  which  is  driven 
by  the  reaction  of  the  jet.  In  some  turbines  the  rotors  are 
driven  by  both  impulse  and  reaction. 

(c)  The  velocity  diagrams  used  in  designing  the  buckets  of 
the  steam  turbine  are  similar  in  many  respects  to  those  used 
for  water  turbines.     But,  despite  this  resemblance,  the  problems 
of  design  and  construction  in  the  former  differ  greatly  from  those 
in  the  latter.     This  is  principally  because,  in  the  steam  turbine, 

(1)  the  jet  velocities  are  enormously  greater  (in  some  cases  this 
velocity  exceeds  3600  feet  per  second,  or  41  miles  per  minute), 

(2)  the  bucket  velocities  are  very  much  higher,  (3)  the  working 
substance  is  elastic  and  tends  to  expand  as  fully  as  the  surround- 
ing media  will  allow,  and  (4)  because  the  kinetic  energy  of  the 
jet  is  obtained  from  heat   conveyed  by  the  working  substance 
and  not  from  "hydraulic"  head. 

(d)  The  steam  turbine  differs  as  much  from  the  steam  engine 
as  to  its  mechanism  and  method  of  operation  as  does  the  water 
turbine.     Although  both  of  these  steam-actuated  prime  movers 
use  the  available  heat  of  the  steam,  the  turbine  utilizes  it  in 
increasing  the  velocity  (kinetic  energy)  of  the  jet  of  working  sub- 
stance, whereas  this  heat  in  the  steam  engine  produces  certain 
pressure- volume  changes  within  a  cylinder. 

(e)  The  thermodynamic  problems  encountered  in  the  steam  tur- 
bine are  centered  in  the  nozzle,  where  (theoretically)  all  the  heat- 
energy  transformations  occur.     After  the  jet  has  issued  from  the 
nozzle  end  the  problem  becomes  a  dynamic  one,  namely,  to  con- 
vert the  jet's  kinetic  energy  into  power  which  can  be  delivered 
by  the  shaft. 

The  problem  of  nozzle  design  and  the  thermodynamic  theory 
involved  will  be  considered  in  detail  in  a  later  chapter.  For 
present  purposes  it  is  only  necessary  to  know  that  high  veloc- 
ity can  be  attained  at  the  expense  of  associated  heat  and  that 
this  transformation  occurs  entirely  within  the  nozzles  or  their 
equivalent. 

(f)  In  turbines,  there  is  a  certain  definite  ratio  of  bucket  velocity 
to  jet  velocity  that  will  theoretically  give  the  best  economy.     In 
practice,  however,  if  the  full  expansion  from  initial  to  final  pres- 
sure takes  place  in  a  single  set  of  nozzles,  the  bucket  velocity  for 


STEAM   TURBINES 


361 


best  economy  is  usually  greater  than  the  structure  of  the  rotor 
will  stand,  because  of  the  enormous  centrifugal  force  produced. 
Also,  the  high  rotative  speed  involved  with  high  bucket  speeds 
usually  prohibits  the  direct  connection  of  the  driven  machinery 
to  the  turbine  shaft.  Hence,  if  the  expansion  occurs  in  a  single 
set  of  nozzles,  it  is  usually  necessary  to  use  lower  bucket  veloci- 
ties than  those  which  would  give  the  highest  economy,  and  also 
to  use  gearing  of  some  kind  between  the  turbine  and  the  machine 
it  drives. 

In  order  to  obtain  lower  jet  and  bucket  velocities,  most 
turbines  are  of  the  "  multi-stage  "  type.  Fig.  234  shows  dia- 
grammatically  an  impulse  turbine  of  this  type.  In  such  tur- 
bines each  stage  by  itself  constitutes  a  simple  turbine,  in  the 
nozzle  of  which  the  steam  expands  through  a  small  range  and 
therefore  acquires  relatively  low  velocity.  The  stages  are  usu- 
ally arranged  in  series  with  diaphragms  between  and  with  all 
rotors  mounted  on  the  same  shaft. 

In  Fig.  234,  the  sections  of  the  turbine  casing  and  the  dia- 
phragms are  shown  by  crosshatching,  and  the  nozzle  and  tur- 
bine wheel  sections  are  black. 
Steam  enters  at  the  left,  ex- 
pands through  the  first  nozzle 
(or  ring  of  nozzles)  Ni,  in 
which  it  acquires  a  relatively 
low  velocity,  and  discharges  1 
against  the  buckets  on  the 
wheel  in  the  first-stage  casing, 
in  which  the  pressure  is  but  Fig.  234. 

little   lower   than  the  initial. 

The  steam  then  expands  through  the  nozzle  (or  ring  of  nozzles) 
7V2,  in  the  diaphragm  between  the  first  and  second  stages,  and 
acts  on  the  buckets  of  the  wheel  in  the  second  chamber,  where 
the  steam  pressure  is  somewhat  lower  than  it  is  in  the  first  stage. 
In  similar  manner  the  process  is  continued  in  a  third  stage,  and 
in  many  instances  in  from  twenty  to  forty  stages,  until  the 
exhaust  pressure  is  reached  in  the  last  stage. 

The  nozzles  in  all  the  stages  must  all  deliver  the  same  weight 
of  working  substance  per  second.  They  may  be  designed  to  do 
this  with  equal  velocities,  in  which  case  the  bucket  velocities  in 
all  stages  would  be  the  same  and  the  mean  diameters  of  the 


362 


HEAT-POWER  ENGINEERING 


wheels  would  be  equal ;  or  the  jet  velocities  may  be  varied  and  the 
bucket  velocities  and  wheel  diameters  be  made  to  correspond. 

As  the  steam  traverses  the  turbine  it  expands  by  increments 
in  the  successive  nozzles,  and  increases  in  volume,  hence  the 
nozzle  areas  must  increase  in  like  manner  through  the  series, 
as  is  illustrated  in  Fig.  234. 

By  properly  proportioning  the  cross-sectional  areas  of  the 
inlet  and  outlet  nozzles  of  any  stage,  the  designer  can  fix  at 
any  desired  value  the  pressure  that  will  be  maintained  in  that 
•stage. 

1 80.  Thermodynamics  of  the  Ideal  Steam  Turbine,  (a)  In 
all  types  of  steam  turbine  the  steam  is  expanded  through  noz- 
zles, or  their  equivalent,  and  the  velocity  of  the  working  sub- 
stance itself  is  increased  by  the  conversion  of  some  of  its  own 
associated  heat  into  avaifable  mechanical  energy,  which  appears 
as  the  kinetic  (velocity)  energy  of  the  issuing  jet.  As  the 
nozzles,  or  their  equivalent,  are  relatively  small,  and  as  the 
velocity  of  the  steam  through  them  is  enormous,  there  is  little 

opportunity  for  loss  of  heat,  as 
such,  to  the  surrounding  media, 
or  for  the  reception  of  heat,  as 
such;  hence,  the  conversion  of 
heat  energy  into  kinetic  energy 
must  in  practice  be  almost 
strictly  adiabatic,  and  it  will  be 
shown  in  a  later  chapter  that 
the  expansion  may  be  considered 
equivalent  to  an  isentropic  pro- 
cess in  the  ideal  case. 

(b)  Assuming  that  the  steam 
is  initially  wet,  and  that  its  state 
is  represented  by  point  1  on  the 
T0-diagram  in  Fig.  235,  the  heat 
(A<2i)  supplied  per  pound  of 
steam  delivered  to  the  turbine  is 
represented  by  the  area  bounded 


Fig.  235. 


by  the  bold  line.  Let  point  2  represent  the  state  of  the  working 
substance  after  isentropic  expansion  to  the  exhaust  pressure  and 
temperature.  Then  the  hatched  area  represents  the  heat  (Aft) 


STEAM   TURBINES  363 

remaining  in  the  steam  at  the  end  of  the  process.  Thus  the  heat 
theoretically  available  for  the  turbine  to  deliver  as  useful  work  is 

AE  =  Aft  -  A()2, 

and  this  is  shown  by  the  stippled  area,  abl2,  which  is  seen  to  have 
the  same  boundary  lines  as  those  of  a  Clausius  cycler  with  the 
same  conditions  of  expansion.  The  isentropic  process  from  1  to 
2  may  occur  in  one  nozzle,  converting  AE  into  kinetic  energy,  "or 
it  may  occur  in  any  number  (n)  of  nozzles  in  series,  each  con- 
verting part  of  AE,  but  with  cumulative  effect  equal  to  that 
produced  by  AE  in  the  single  nozzle.  Thus,  regardless  of  the 
number  of  stages,  it  may  be  said  that  the  heat  energy  available 
for  doing  work  in  the  steam  turbine  is  equivalent  to  the  AE  avail- 
able with  the  Clausius  cycle  having  the  same  expansion  line  and 
same  weight  of  steam.  The  value  of  AE  per  pound  may  be 
computed  by  the  method  given  on  page  173;  or  it  can  be  ob- 
tained from  the  area  on  the  T</>-diagram  ;  or  it  can  be  more 
conveniently  found  from  the  Mollier  chart  (Appendix). 

(c)  Having  determined  the  number  of  B.t.u.  represented  by 
AE,  the  steam  consumption  per  h.  p.  -hour,  or  water  rate,  in  the 
ideal  turbine  is 


and  if  the  turbine  drives  an  electric  generator  the  theoretical 
water  rate  per  kilowatt-hour  is 

TF7___L..?545  =  34!I  (      } 

'**     0746     AE         AE  ' 

(d)  The  actual  turbine  of  course  has  a  poorer  (larger)  water 
rate  than  the  ideal.  If  Wd  is  the  actual  water  rate  per  h.p.- 
hour  delivered  by  the  turbine  shaft,  and  WdK  is  that  per  kilo- 
watt-hour delivered  by  the  generator,  then  the  over-all  efficiency 
of  the  turbine  (alone)  is 

,.    ......    (316) 


and  the  over-all  efficiency  of  turbine  and  generator  is 


The  OEfd  corresponds  to  the  OEf  of  the  steam  engine  (p.  190) 


HEAT-POWER  ENGINEERING  - 


If  il  is  desired  to  estimate  the  probable  performance  of  a 
turbine,  and  the  OEf  is  known  for  similar  turbines  under  similar 
conditions  of  operation,  the  probable  water  rate  per  d.h.p.-hour 
is,  from  Eqs.  (314)  to  (317), 

Wd  =  2545  4-  (AE  X  OEfd),  ....     (318) 
and  per  kilowatt  hour  it  is 

WdK  =  34ii  -5-  (A£  X  OE/K).  .     .    V  -.     (319) 

In  very  large  turbo-generator  outfits  the  value  of  OE/K  should 
be  0.65  or  more.  In  general  the  smaller  the  turbine  the  poorer 
the  efficiency,  as  is  shown  in  a  very  general  way  in  Fig.  236. 


10  000   15  000    20  000 
Kw.  Full  Load 


25  000   30  000 


Fig.  236. 

(e)  The  ultimate  comparison  of  the  performances  of  turbines 
with  each  other  and  with  steam  engines  is  either  on  the  basis  of 
B.t.u.'s  supplied  per  minute  per  unit  of  output,  or  on  the  basis 
of  thermal  efficiencies.  In  the  ideal  turbine  the  B.t.u.  supplied 
per  h.p.  per  minute  are 

Bi  =  Wi  (ffl  +  xiri  +  CpDi  -  g2)  ^  60, 

in  which  q2  is  the  heat  remaining  in  the  condensate,  which  heat 
is  considered  as  being  returnable  to  the  boiler  with  the  feed 
water  (as  in  Sect.  115  (d)).  In  the  actual  case  the  B.t.u.  sup- 
plied per  d.h.p.  per  minute  are 

Bd  =  Bj/OEfd  =  Wd(qi  +  *in  +  CPD,  -  q2)  +  60.     (320) 
The  B.t.u.  supplied  per  kilowatt  per  minute  in  the  ideal  case  are 
BIK  =  WIK  (qi  +  x^  +  CPD1  -  q2)  -i-  60, .     .     (321) 
and  in  the  actual  case 

BdK  =  BiK/OE/K  =  WdK(qi  +  xlrl  +  CPD^  -  q2)  -^  60.  (322) 
The  values  of  BdR  vary  from  250  to  800  B.t.u.  per  minute. 


STEAM   TURBINES  365 

(f)  The  ratio  of  the  heat  delivered  as  useful  energy  to  that 
supplied  in  the  steam  is  the  thermal  efficiency.  The  thermal 
efficiency  on  the  d.h.p.,  as  in  the  case  of  the  steam  engine 
(page  210),  is 

2545      =  2545 

o  *  Bd      T  -'- 


TDFf  = 

" 


arid  based  on  the  kilowatt  output  it  is 

TDEfK  =      3411       =  -  -Ml1  ___  _. 

60  X  BdK       WdK  (qi  +  Xiri  +  CpDl  -  q2) 

(g)  Fig.  237  shows  typical  curves  for  a  large  turbine-gener- 
ator outfit.      It  is  seen  that  the  curve  of  total  steam  consump- 


1000  2000  3000  4000 

Kilowatts  at  Switchboard 


Fig.  237. 

tion  (T.C.  curve)  is  practically  a  straight  line;  and  tfcis  is  a  char- 
acteristic of  such  curves  for  nearly  all  types  of  turbines.  If,  in 
the  figure,  the  T.C.  curve  is  extended  to  intersect  the  Y-axis,  the 
intersept  (F0)  represents  the  steam  required  to  operate  the 
turbine  when  delivering  no  power.  It  is  the  amount  needed  to 
overcome  the  friction  of  the  turbine  and  the  "  windage  "  (or 
friction  between  the  turbine  disks  and  the  vapor  in  which  they 
rotate),  that  required  for  driving  the  governor,  oil  pumps,  etc., 
and  that  for  meeting  the  losses  due  to  leakage  and  radiation. 

The  water-rate  curve  (W.R.),  or  curve  of  steam  used  per  kilo- 
watt hour,  is  also  shown  in  Fig.  237.  The  water  rates  at  the 
different  loads  are  obtained  by  dividing  each  total  consumption 
by  the  corresponding  kilowatts  as  found  by  test,  i.e.,  by  dividing 


366  HEAT-POWER  ENGINEERING, 

the  ordinates  of  the  T.C.  curve  by,  the  corresponding  abscissas. 
If  the  T.C.  curve  passed  through  the  origin,  as  it  would  in  the 
ideal  case,  the  W.R.  curve  would  be  a  horizontal  straight  line, 
and  the  economy  of  the  turbine  would  be  the  same  at  all  loads. 
The  greater  the  Y  intercept  of  the  T.C.  curve  the  more  curva- 
ture does  the  W.R.  curve  have,  and  the  greater  are  the  consump- 
tions of  steam  under  light  loads  [as  compared  with  those  under 
heavy  loads.  It  will  therefore  be  noticed  that  the  best  economy 
is  obtained  when  the  turbine  is  operated  atjts  maximum  power. 
As  a  turbine  when  operating  under  its  usual  load  should  have 
some  reserve  power  (or  "  overload  capacity  "),  it  must  normally 
operate  at  a  load  and  an  efficiency  less  than  the  maximum.  On 
this  account,  and  because  wide  fluctuations  of  load  may  occur, 
a  flat  water-rate  curve  is  desirable. 

Many  turbines  have  an  auxiliary  "  overload  valve  "  which 
admits  live  steam  to  the  low-pressure  stages  of  the  turbine  when 
it  is  considerably  overloaded.  At  such  load  the  T.C.  curve  and 
W.R.  curve  change  character,  as  in  Fig.  237  at  O  and  O '. 

In  Fig.  237  is  also  shown  the  curve  of  over-all  efficiency  of 
turbine  and  generator  (OE/K).  In  this  case  AE  has  been  taken 
as  the  available  heat  in  the  steam  just  before  it  reaches  the 
throttle  valve.  Thus  OEfK  includes  the  losses  entailed  by  the 
governor  valve  throttling  the  steam,  which  is  the  principal 
reason  for  the  decrease  of  this  efficiency  when  the  turbine  output 
is  diminished.  Why  this  loss  occurs  is  explained  in  (k)  of  this 
section. 

(h)  Fig.  238  shows  on  a  Mollier  chart  an  expansion  line 
starting  with  dry  saturated  steam  at  p  pounds  pressure  and 

S 


extending  to  various  lines  of  terminal  pressure.  It  is  seen  that  ex- 
pansion to  15  pounds  pressure  theoretically  makes  available  heat 
represented  by  a,  and  that  further  expansion  to  one-half  pound 
absolute  back  pressure  would  add  to  this  an  amount  of  heat 
represented  by  g.  Thus,  if  steam  from  an  ideal  noncondensing 
engine  or  turbine  is  expanded  in  a  second  ideal  turbine  to  one- 


STEAM    TURBINES  367 

half  pound  absolute  pressure,  the  total  power  obtainable  would 
evidently  be  nearly  twice  (in  this  instance)  that  derived  from  the 
noncondensing  unit.  Many  "low-pressure "  or  "exhaust-steam  " 
turbines  are  operated  with  steam  received  from  an  engine  at 
about  atmospheric  pressure,  and  these  in  many  instances  give 
as  much  power  as  do  the  engines  which  furnish  the  stearm. 

Again  referring  to  the  expansion  line  in  Fig.  238,  and  starting 
with  terminal  pressure  2j  Ibs.,  it  is  seen  that  the  succeeding  half- 
pound  drops  are  accompanied  by  the  heat  increments  lettered 
c,  d,  e,  and  /,  the  amounts  of  which,  in  this  particular  case,  in- 
crease the  available  energy  respectively  in  the  percentages  4.7, 
5.6,  6.3,  and  10.  It  is  apparent  that  these  heat  increments  rapidly 
become  larger  as  the  back  pressure  is  lowered,  hence  a  one-inch 
change  in  vacuum  from  28  to  29  ins.  is  much  more  effective  than 
one  from  26  to  27  ins.  The  actual  case  would,  of  course,  differ 
somewhat  from  the  ideal,  but  the  real  gains  from  improving  the 
vacuum  are  about  proportional  to  the  theoretical;  hence,  with 
steam  turbines,  it  is  desirable  to  use  as  low  back  pressures  as  the 
other  considerations  will  permit. 

(i)  In  the  T0-diagram  in  Fig.  239  the  Clausius  cycle  is  super- 
imposed on  the  Rankine,  ge  being  the  constant  volume  line  at 
release  in  the  latter.  Now,  by  de- 
creasing the  back  pressure,  with  tem- 
perature reduction  from  T2  to  jTs,  the 
increased  amount  of  heat  made  avail- 
able in  the  ideal  turbine  is  shown  by 
area  abed,  whereas  in  the  engine  it  is 
only  aefd.  Actually  there  is  still 
greater  difference  between  the  gains, 
for  in  the  engine  the  increased  range 


of  temperature  augments  the  loss  due  Fi    2^ 

to  cylinder  condensation,  whereas  in 

the  turbine  there  is  no  equivalent  to  such  condensation  since 
the  steam  flows  continuously  in  the  same  direction,  and  there- 
fore constantly  comes  in  contact  with  parts  which  have  pre- 
viously become  heated  to  its  own  temperature.  Evidently, 
then,  the  turbine  can  use  very  low  back  pressures  to  better 
advantage  than  the  engine,  other  things  being  equal. 

(j)   The  gain  due  to  using  superheated  steam  is  illustrated  on 
the  Mollier  chart  in  Fig.  240.     In  expanding  from   dry  satu- 


368 


HEAT-POWER  ENGINEERING'- 


1277    1195 


Fig.  240. 


rated  steam  at  p  pounds  pressure  to  1  pound  pressure,  B.t.u. 
represented  by  AE  are  seen  to  become  theoretically  available, 

whereas  in  expanding  through  the 
same  pressure  range  but  starting 
with  steam  superheated  150  de- 
grees,  B.t.u.  represented  by  AEf  are 
made  available.  If  p  is  165  pounds 
absolute,  a  gain  of  nearly  1 1  per  cent 
is  effected  per  pound  of  steam,  and 
only  about  0.9  as  much  steam  would 
be  used  as  with  saturated  mate- 
rial. The  gain  in  fuel  economy  is  not  in  this  proportion,  how- 
ever, as  additional  heat  was  supplied  per  pound  of  steam  in 
superheating  it.  The  heat  (above  32  degrees)  of  1  pound  of  the 
superheated  steam  is  seen  to  be  1277  B.t.u.,  and  in  the  case 
of  the  saturated  steam  it  is  1195.  If  the  feed  water  is  at  72°  F., 
it  contains  about  40  B.t.u.  above  32  degrees.  The  fuel  used  per 
pound  in  the  two  cases  will  then  be  in  the  ratio  (1277  —  40)  -f- 
(1195  —  40)  =  1.07.  Thus  the  heat  supplied  by  the  fuel  per  unit 
of  work  when  superheated  steam  is  used  is  0.9  X  1.07  =  0.96 
times  that  needed  with  saturated  steam,  and  the  theoretical  saving 
in  fuel  is  4  per  cent  in  this  instance.  The  actual  saving  may  be 
greater  than  this,  for  superheating  results  in  the  steam  having 
less  moisture  after  the  adiabatic  expansion,  and  the  presence  of 
moisture  somewhat  increases  the  friction  that  the  steam  en- 
counters in  passing  over  nozzle  and  blade  surfaces. 

In  the  steam  engine,  superheating  may  effect  greater  improve- 
ment in  economy  than  occurs  in  the  turbine,  because  of  its  influ- 
ence in  preventing  cylinder  condensation. 

(k)  It  is  quite  common  practice  to  decrease  the  power  output 
of  a  turbine  by  throttling  the  steam  supply.  This  process  not 
only  reduces  the  amount  of  steam,  but 
lowers  its  pressure  and  changes  its 
entropy  in  such  manner  that  the  heat  p 
available  per  pound  with  any  fixed 
terminal  pressure  is  reduced  despite 
the  fact  that  the  total  heat  of  the  steam 


Fig.  241. 


remains  the  same.  This  is  illustrated  in  Fig.  241,  in  which  AE  is 
the  heat  available  per  pound  of  steam  before  throttling,  and 
AE'  is  that  after  throttling,  the  total  heat  AO]  of  the  steam  being 


STEAM   TURBINES 


369 


initially  the  same  in  both  cases.  It  is  therefore  evident  that  the 
throttling  process  must  theoretically  decrease  the  economy  of  the 
turbine. 


181.  Thermodynamics  of  Actual  Turbines.  In  the  energy 
stream  of  Fig.  242,  AE  is  the  heat  that  would  be  made  available 
for  doing  work  when  there  is  complete  expansion  of  I  pound  of 


Available  Energy 


Energy  delivered 
by  Shaft 


Fig.  242. 

steam  through  the  nozzle,  or  nozzles,  of  a  single  stage  of  an 
ideal  turbine,  and  Aft  is  the  unavailable,  or  waste,  heat. 

(a)  In  the  actual  case,  some  of  the  steam  may  not  pass  through 
the  nozzle,  for  there  may  be  leakage  to  the  exhaust.     For  ex- 
ample, in  Fig.  234  some  of  the  steam  may  leak  from  chamber  2 
to  chamber  j  through  the  clearance  space  a  between  the  third 
diaphragm  and  the  shaft.     This  leakage  loss  (which  may  repre- 
sent from  zero  to  5  per  cent,  or  more,  of  the  total  energy)  is  shown 
by  stream  line  a  in  Fig.  242,  and  the  energy  still  available  for 
doing  work  is  represented  by  A . 

(b)  Because  of  the  frictional  resistance  offered  by  the  nozzle 
walls,  and  because  of  eddy  currents,  etc.,  all  of  the  heat  theo- 
retically made  available  by  the  steam  expanded  through  the 
nozzles  is  not  converted  into  kinetic  energy  of  the  jet.     The 
portion  of  AE  not  utilized  remains  in  the  steam  as  heat;  hence 
in  the  figure  the  nozzle  loss  b  is  shown  as  subtracted  from  the 
available  energy  and  added  to  that  wasted.     This  loss  may  be 


370  HEAT-POWER  ENGINEERING 

from  3  to  15  per  cent  of  the  total  available  energy.     The  energy 
still  available  is  shown  in  the  figure  by  B. 

(c)  Similarly,  not  all  of  the  kinetic  energy  of  the  jet  is  ab- 
stracted by  the  turbine  buckets.  The  remainder,  or  bucket 
loss,  which  may  be  from  10  to  30  per  cent,  is  reconverted  into 
heat  by  eddy  currents  and  by  the  reduction  of  velocity  in  the 
turbine  chamber,  and  this  heat  is  added  to  that  already  in  the 
steam  before  it  reaches  that  point.  This  loss  is  represented  by 
c  in  the  figure,  and  the  energy  still  available,  by  C. 
>  (d)  Further,  because  of  the  "  windage,"  or  friction  between  the 
rotor  and  the  enveloping  vapor,  not  all  of  the  energy  absorbed 
by  the  buckets  is  transmitted  to  the  turbine  shaft.  This  loss 
may  be  from  2  to  8  per  cent  with  the  high  velocities  of  rotation 
prevailing.  This  frictional  energy  is  converted  into  heat  by 
the  eddy  currents  set  up  in  the  vapor,  and  this  heat  is  added 
to  that  already  stored  in  the  vapor,  as  shown  at  d  in  the  figure. 
The  energy  still  available  for  doing  work  is  shown  by  D. 

(e)  The  heat  not  utilized  remains  in  the  steam  and  is  shown 
by  H  in  the  figure.     If  the  steam  from  this  casing  is  used  in 
another  turbine,  or  as  another  stage  of   the  same   turbine,  the 
diagram  of  energy  flow  for  this  second  element  would  also  resem- 
ble Fig.  242,  but  the  initial  width  of  the  steam  line  would  be  H. 

(f)  In  addition  to  the  foregoing,  there  are  the  radiation  loss 
and  the  mechanical  losses  from  bearing  friction  and  (possibly) 
from  the  driving  of  oil  pumps,  governor,  etc.     These  are  shown 
at  e,  /,  and  g.     G  represents  the  energy  finally  delivered  by  the 
shaft.     The  ratio  of  G  to  AE  is  the  over-all  efficiency  of  the 
turbine*  (not  including  the  generator). 

(g)  Losses  a,  b,  c,  d,  and  e  constitute  the  equivalent  of  the 
cylinder  losses  in  the  steam  engine;  hence,  the  ratio  of  the  heat 
shown  at  E  to  AE  may  be  called  the  cylinder  efficiency  (lEf). 

(h)  Fig.  242  will  also  apply  qualitatively  to  multistage  tur- 
bines considered  as  a  whole,  in  which  case  a,  b,  c,  d,  and  e  show 
the  combined  losses  of  all  stages. 

(i)  On  the  Mollier  chart  in  Fig.  243,  let  the  initial  state  of 
the  steam  be  shown  by  point  1,  with  pressure  plt  entropy  </>i, 
quality  *lf  and  associated  heat  Aft  per  pound.  In  the  ideal 
case,  after  expansion  through  the  nozzle  to  a  pressure  of  p2 
pounds  per  square  inch,  the  state  point  would  be  at  2,  with 
*  This  is  sometimes  called  the  "shaft  efficiency." 


STEAM  TURBINES 


37* 


entropy  <fr,  quality  x2,  and  associated  heat  Aft.  The  heat  theo- 
retically made  available  is  shown  by  AE.  In  the  real  case, 
as  has  been  seen,  only  a  part  of  AE  is  actually  delivered  to 


AQi 


Fig.  243. 


the  shaft  by  the  wheels  or  drums.  This  amount  is  shown  by 
AE'  =  (lEf  X  AE)  in  the  figure.  Evidently  the  heat  remaining 
in  the  exhaust  steam  is  shown  by  Aft'  =  (Aft  —  AE'). 

With  this  amount  of  heat  in  the  exhaust  steam  and  with  the 
terminal  pressure  P2  as  before,  the  state  point  showing  the  con- 
dition of  steam  in  the  actual  case  must  be  at  2',  the  point  on 
the  pressure  line  having  heat  value  equal  to  Aft'.  Thus  tho 
actual  condition  of  the  exhaust  steam  is  such 
that  the  quality  is  x<l ,  the  entropy  is  02,  and 
the  heat  above  32  degrees  is  Aft'.  This  is 
the  condition  of  the  steam  exhausted  to  the 
condenser  or  to  the  atmosphere,  or  to  the 
next  stage,  as  the  case  may  be. 

(j)  Fig.  244  is  a  T<£-diagram  correspond- 
ing to  the  Mollier  chart  in  Fig.  243  and  is 
similarly  lettered.  Aft  is  shown  by  the  area 
bounded  by  heavy  lines,  Aft  by  area  0o620i,  Fig  244 

and  Aft'  by  the  hatched  area.     AE'  is  the 

difference  between  the  areas  Aft  and  Aft'  and  is  not  shown 
directly  by  any  area  on  the  diagram. 

182.  The  Dynamics  of  Impulse  Steam  Turbines,  (a)  In  dis- 
cussing the  dynamics  of  turbines,  it  is  necessary  to  distinguish 
between  the  "  absolute  "  velocity  and  the  "  relative  "  velocity 
of  the  jet  of  steam.  Absolute  velocity  is  the  linear  speed  (v)  of 
the  jet  with  respect  to  things  that  are  stationary;  the  relative 
velocity  (R)  is  the  speed  of  jet  relative  to  the  buckets,  which 
themselves  are  moving  with  a  velocity  u. 


HEAT-POWER  ENGINEERING 

(b)  The  available  energy  of  w  pounds  of  steam  flowing  through 
the  nozzle  per  second  is  w  X  778  X  AE,  and  the  kinetic  energy 
which  it  imparts  to  the  jet  is 

=  ^- ........     (325) 


in  which  v  is  the  absolute  velocity  of  the  jet  in  feet  per  second. 
Hence,  if  the  nozzle  efficiency  is  Efnj 


X 
from  which  the  velocity  of  the  jet  is  found  to  be  (feet  per  second) 


v  =  223.8  VAE  X  Efn.     .     .     .     .     .     (326) 

(c)  To  completely  utilize  the  kinetic  energy  of  the  jet  in  an 
impulse  turbine,  the  absolute  velocity  of  the  jet  must  of  course 
be  reduced  to  zero  (regardless  of  the  final  direction  of  motion), 
and  it  is  the  function  of  the  blades  on  the  rotor  to  perform  this 
reduction  and  receive  the  energy.     If,   after  passing  over  the 
blades,  the  jet  still  has  velocity  (%),  it  is  evident  that  there  is 
loss  of  energy  due  to  the  residual  velocity  equal  in  amount  to 

^-^        wv22  ,       , 

KE2=  — .     .     .  .t     .     .     .     (327) 

(d)  If  in  Fig.  245  the  jet  has  an  absolute  velocity  v\  and  the 
bucket  has  an  absolute  velocity  u  =  v\/2  in  the  same  direction, 

the  relative  velocity  of  jet  to  bucket  is 
R  =  Vi/2  as    it    enters.      Then    if    the 
bucket  directs  this  jet  rearwards  (op- 
posite and  parallel  tovi),  the  absolute 
[Bucket      velocity  v2  of  the  working  substance  is 
zero,  and  the  entire  energy  has  been 
p.  absorbed. 

Could  the  friction  between  the  jet 

and  the  surface  of  the  bucket,  the  eddying,  and  spilling  of  the 
working  substance,  be  eliminated,  the  efficiency  of  conversion  in 
such  a  case  would  be  100  per  cent. 

(e)  If  in  Figure  246  the  line  7  represents  the  absolute  velocity 
»i  of  the  jet  and  its  direction  of  motion  compared  with  that  of 
the  bucket,  the  direction  and  velocity  of  which  are  shown  by  u, 
the  relative  velocity  of  jet  to  bucket  is  shown  in  amount  and 
direction  by   Rit  which  is  found  by  constructing  the  triangle 


STEAM   TURBINES 


373 


abc  with  side  be  =  u.     If  R*  is  the  relative  velocity  and  direction 

in  which  the  jet  is  discharged  with  re- 

spect  to  the  moving  bucket,  then  v2  is 

the  absolute  velocity  and  direction  of  the 

jet,  and    its  vector   is   found  by  con- 

structing  the    triangle    def  with   side 

ef  =  u.     Evidently  the  presence  of  this 

residual  velocity   v2   represents   a   loss 

of  energy  which  is  equal  to  wv^/2g. 

Hence  the  bucket  efficiency,  neglecting 

other  losses,  is  Fig.  246. 


(       . 
(328) 


It  will  be  apparent  from  Fig.  246  that  vz  can  never  be  made 
zero  if  Vi  and  v2  are  not  both  parallel  to  u,  and  that  unless  this  is 
the  case  the  bucket  efficiency  must  be  less  than  unity.  It  will 
also  be  evident  that  vz  is  a  minimum,  and  the  efficiency  is  maxi- 
mum, when  u  is  of  such  value  as  to  cause  v2  to  be  at  right  angles 
to  u.  This  value  of  v  can  be  determined  either  graphically  or 
mathematically  by  methods  which  need  not  be  considered  here. 
If  angle  abc  =  20°,  which  is  about  as  small  an  angle  as  can  be 
used  when  the  nozzle  is  placed  at  the  side  of  the  buckets,  and  if 
RI  and  R2  form  equal  and  opposite  angles  with  the  direction  of 
the  bucket's  motion,  u  will  be  about  47  per  cent  of  Vi. 

Further  discussion  of  the  dynamics  of  turbines  will  be  given 
in  connection  with  the  descriptions  of  the  various  types. 

183.  De  Laval  Type  of  Single-Stage  Turbines.  —  This  type  of 
turbine  (developed  about  1888)  is  shown  diagrammatically  at  A 
in  the  chart  given  on  page  374;  and  the  details  of  its  mechanism 
are  shown  in  Fig.  247.  The  velocity  diagram  resembles  Fig.  246, 
but  as  the  velocity  (vi)  of  jet  issuing  from  the  nozzle  may  be 
from  3000  to  4000  feet  per  second,  it  is  not  usually  possible  to  use 
bucket  velocities  (u)  which  correspond  to  maximum  efficiency, 
for  no  available  materials  or  possible  constructions  will  withstand 
such  speeds.  The  bucket  velocities  are  therefore  made  as  high 
as  is  safe.  The  wheels  of  the  3OO-horse-power  De  Laval  turbine 
are  about  30  inches  in  diameter  and  rotate  at  about  10,600  r.p.m., 
with  peripheral  speed  of  about  1380  feet  per  second.  The 


274  HEAT-POWER  ENGINEERING 

CHART.  —  PRINCIPAL  COMMERCIAL  TYPES  OF  STEAM  TURBINES. 


ft.  Sec. 


Nozzle      Blades 

A.   De  Laval  Type. 


4  5 


Stages  t= 


Stages  =1        2345 
B.   Rateau-Zoelly  Type. 


NOTES. 

General.  In  each  of  the  above  diagrams  the  upper  portion  shows  a  longi- 
tudinal section  of  the  turbine,  the  middle  of  the  figure  represents  a  transverse 
section  through  the  buckets  and  nozzles,  and  below  this  are  curves  which 
show  how  the  pressure  and  velocity  of  the  steam  vary  during  the  passage 
of  the  vapor  through  the  turbine.  The  pressures  and  velocities  are  shown 
'  respectively  by  the  ordinates  of  the  heavy  and  of  the  light  curves. 

A.  De  Laval  Type  (see  Sect.  183).     In  this  type  of  turbine  it  is  to  be  par- 
ticularly noted  that  the  full  drop  in  pressure  and  the  entire  increase  in  velocity 
of  the  vapor  are  completed  before  the  jet  issues  from  the  end  of  the  nozzle, 
as  shown  by  the  curves;  thus  there  is  no  expansion  of  the  steam  after  it 
reaches  the  wheel  casing.     The  velocity  curve  also  shows  the  jet's  velocity- 
decrease  resulting  from  the  absorption  of  the  kinetic  energy  by  the  buckets, 
and  further  shows  the  residual  (lost)  velocity  associated  with  the  kinetic  energy 
not  utilized. 

B.  Rateau-Zoelly  Type  (see  Sect.  185).     Each  pressure    stage    is   seen    to 
resemble  a  single-stage  turbine  of  the  De  Laval  type. 


STEAM  TURBINES  375 

CHART  (Continued).  —  PRINCIPAL  COMMERCIAL  TYPES  OF  STEAM  TURBINES. 


1st  Stag 


C.    Curtis  Type. 


Initial 
Pressure 


Steam 


vpg 
St  t}oi 


label 


D.   Parsons  Type. 


NOTES    (Continued). 

C.  Curtis  Type  (see  Sect.  186).     The  diagram  shows  a  turbine  having  two 
pressure  stages,  each  of  which  has  two  velocity  stages.     It  is  seen  by  the  curves 
that  the  pressure-drops  and  velocity-increases  occur  entirely  within  the  noz- 
zles N\  and  N2  (i.e.,  there  is  no  expansion  of  the  vapor  in  the  wheel  casings). 
In  each  pressure  stage  the  jet  first  passes  over  the  moving  blades  Mi  to  which 
it  surrenders  part  of  its  kinetic  energy  (thereby  losing  some  of  its  velocity), 
and  is  then  guided  by  the  stationary  blades  S  to  act  on  the  second  set  of  mov- 
ing blades  M2,  which  absorb  still  more  of  the  energy  by  further  decreasing  the 
velocity  of  the  jet.     Thus  the  (kinetic)  velocity  energy  is  absorbed  in  two 
steps,  or  stages,  in  each  pressure  stage. 

D.  Parsons  Type  (see  Sect.  188).    Expansion  takes  place  in  both  the  station- 
ary and  the  moving  blades,  as  is  shown  by  the  steam-pressure  line  in  the  dia- 
gram.    The  steam  is  accelerated  in  passing  through  the  first  row  of  stationary 
buckets;  the  issuing  jets  are  then  retarded  by  coming  in  contact  with  the  first 
moving  buckets,  to  which  they  surrender  part  of  their  kinetic  energy;  and 
while  passing  between  these  latter  buckets  the  stream  is  further  expanded  and 
issues  from  them  with  a  reaction.     Thus  the  moving  blades  receive  energy 
by  both  impulse  and  reaction.     This  process  is  continued  in  each  of  the  suc- 
ceeding pairs  of  stationary  and  moving  sets  of  blades. 


376  HEAT-POWER  ENGINEERING 

5-horse-power  turbine  has  a  wheel  about  4  inches  in  diameter, 
the  r.p.m.  are  30,000,  and  the  rim  speed  is  515  feet  per  second. 

To  provide  the  maximum  theoretical  strength,  the  smaller 
wheels  have  sections  resembling  that  in  Fig.  247  at  (a);  while 
the  larger  wheels  are  without  central  hole,  the  shaft  being  made 
in  two  parts,  each  fastened  to  the  side  of  the  wheel  by  flanges. 
The  buckets  and  the  method  of  attaching  them  to  the  wheel 
are  shown  at  (b)  in  the  figure.  The  flanges  on  the  bucket  tips 
form  a  continuous  "  shroud  ring,"  and  this  prevents  the  jets 
from  flattening  and  "  spilling  "  over  the  ends  of  the  blades. 

Although  the  wheels  are  balanced  with  the  greatest  care,  the 
gravity  axis  never  exactly  coincides  with  the  geometrical  axis 
of  the  shaft.  To  prevent  difficulty  which  might  arise  with  such 
high  speeds  from  this  lack  of  balance,  the  shaft  is  made  slender 
and  flexible  so  that  the  wheel  can  "  gyrate  "  about  its  gravity 
axis.  Owing  to  the  high  speed  the  "  torque  "  on  the  shaft  is 
small  and  a  small  diameter  is  therefore  permissible. 

In  most  instances  the  rotative  speeds  are  too  great  to  permit 
of  "  direct  connection  "  to  the  generator,  pump,  or  other  machine 
which  is  to  be  driven,  hence  reducing  gears  of  ratio  about  10  :  i 
are  used. 

To  obtain  continuity  of  action  and  noiselessness,  the  gears  are 
of  the  opposed  "herring-bone"  type,  with  very  narrow  teeth, 
which  are  cut  and  adjusted  with  extreme  accuracy.  The  pinion 
may  drive  either  one  or  two  pairs  of  large  gears,  each  of  the 
pairs  delivering  power  independently.  The  power  is  delivered 
from  the  gear  shaft  through  a  flexible  coupling,  the  bushings 
shown  black  in  the  figure  being  made  of  rubber. 

The  governor  shown  at  e  is  of  the  centrifugal  fly-ball  type. 
As  the  weights  W,  W,  (pivoting  on  knife-edges  at  P)  fly  out  due 
to  centrifugal  force,  the  rod  R  is  moved  longitudinally,  thus 
moving  the  bell  crank  L  (in  view  (c))  and  regulating  the  amount 
of  opening  of  the  governor  valve  5  (which  is  vertical  on  actual  tur- 
bines). Thus  the  turbine  is  throttle-governed.  There  generally 
are  several  nozzles  like  d  around  the  periphery  of  the  wheel,  and 
these  are  provided  with  hand-shut-off  valves.  If  the  load  on  the 
turbine  is  very  small,  it  is  better  to  close  some  of  these  valves, 
so  that  the  nozzles  remaining  in  action  may  operate  at  or  near 
their  maximum  capacity  (the  most  efficient  condition)  rather 
than  have  all  the  valves  in  operation  with  steam  greatly  throt- 


STEAM   TURBINES 


377 


378      . 


HEAT-POWER   ENGINEERING 


(b) 


•r-^      Live  Steam 

Fig.  248A.     Pelton  Type. 


Fig.  2486.     Multistage  Impulse  Turbine  (Kerr). 


STEAM   TURBINES 

tied  (with  the  'accompanying  loss).  Sometimes  there  are  two 
sets  of  nozzles,  one  to  be  used  when  operating  condensing,  and 
the  other  when  noncondensing. 

184.  Pelton   Type   of   Steam  Turbine.     Single-stage  impulse 
steam  turbines,  with  buckets  like  those  used  on  Pelton  water 
wheels,  may  be  built;  but  the  same  difficulties  are  encountered 
in  them  that  appear  in  the  De  Laval  type  of  single-stage  turbine. 

By  making  the  turbine  multistage,  and  using  a  sufficient 
number  of  stages,  these  difficulties  may  be  avoided,  the  jet 
velocities  may  be  reduced  to  twice  the  bucket  speeds  that  can 
be  used  safely,  —  thereby  obtaining  the  highest  bucket  efficiency 
(see  Section  182  (d)),  — and  the  rotative  speeds  may  be  made  such 
as  to  permit  the  direct  driving  of  electric  generators,  centrifugal 
pumps,  blowers,  etc., -without  the  use  of  gearing. 

Fig.  248A  shows  the  principal  elements  of  a  turbine  which  is 
of  this  type.  In  this  figure  (a)  shows  one  wheel,  the  nozzles 
(one  in  section),  the  section  of  the  casing  of  the  adjacent  stage 
of  higher  pressure,  and  the  bucket.  The  longitudinal  section 
of  the  turbine  is  shown  in  (b).  The  steam  passes  from  A  to 
the  chamber  5,  thence  through  nozzles  N  to  the  first  stage,  I, 
where  the  jet  impinges  on  the  buckets  on  the  wheel,  the  section 
of  which  is  shown  black.  From  the  first  stage  the  steam  passes 
in  like  manner  through  the  nozzles  N  in  the  diaphragm,  to  act 
on  the  buckets  of  the  second  wheel;  and  so  on  through  the 
turbine  until  the  steam  is  exhausted  at  E.  To  prevent  the 
possibility  of  any  leakage  of  air  through  the  stuffing  boxes  at  B 
(which  would  affect  the  vacuum),  a  chamber  is  provided  which 
can  be  filled  with  water  (forming  a  "  water  seal  ")  or  with  steam 
at  pressure  slightly  above  atmospheric.  The  governor  and  gov- 
ernor valve  are  somewhat  similar  to  those  of  the  De  Laval 
turbine.  These  turbines,  formerly  known  as  the  "  Kerr,"  have 
been  replaced  by  the  type  shown  in  Fig.  2486. 

185.  Rateau  Type  of  Steam  Turbine.     Turbines  having  from 
20  to  40  stages  arranged  somewhat  as  in  Fig.  234  were  developed 
by  Professor  Rateau  of  Paris  in  1897.     The  nozzles,  instead  of 
being  of  circular  cross-section,  are  rectangular,  and  are  grouped 
closely  together  so  that  the  intervening  walls  are  thin  plates  of 
uniform  thickness.     The  buckets  on  all  wheels,  except  the  last 


HEAT-POWER  ENGINEERING 


few,  are  of  the  same  length.  The  group  of  nozzles  in  the  first 
diaphragm  extends  over  a  short  arc,  that  in  the  next  diaphragm 
is  a  little  longer,  and  so  on;  thus  as  the  steam  passes  through  the 
turbine  the  circular  arc  covered  by  the  nozzles  and  the  passage 
areas  increase  in  size.  (See  B  in  chart  on  page  374.) 

The  Zoelly  turbine  is  similar  to  the  Rateau,  except  that  (i) 
about  half  as  many  stages,  and  higher  nozzle  and  bucket  speeds, 
are  used;  (2)  in  all  the  diaphragms  the  nozzle  bands  extend 
farther  around  the  peripheries;  and  (3)  the  radial  widths  of  the 
nozzle  groups,  and  the  lengths  of  blades  on  the  wheels,  increase 
from  one  end  of  the  turbine  to  the  other.  Fig.  2486  shows  a 
modern  turbine  of  the  Rateau-Zoelly  type. 

186.  Curtis  Type  of  Steam  Turbine.  —  Referring  to  Fig.  246, 
it  is  seen  that  the  energy  loss  from  the  residual  velocity,  v2,  is 
quite  large.  Curtis  (in  1896)  patented  the  arrangement  whereby 
the  jet,  with  this  residual  energy,  is  directed  to  act  on  other  sets 
of  rotating  blades,  from  which  it  departs  with  residual  velocity 
much  less  than  in  the  previous  case.  This  process  is  termed 
"velocity  compounding." 

Theoretically,  this  process  may  be  continued  indefinitely,  and 
the  final  residual  velocity  may  be  reduced  to  any  desired  value. 


Steam  Client 


Nozzles 

Moving  Blades 

Stationary  Blades 

Moving  Blades 


Fig.  249. 

In  practice,  however,  the  bucket  fric- 
tion and  other  losses  make  it  inexpedi- 
ent to  use  more  than  two  or  three  rows 
of  rotating  blades  per  stage.  Fig.  249 
shows  the  arrangement  of  a  single 
stage  having  two  rows  of  moving 
blades  (M),  with  one  set  of  stationary 
ones  (S)  between,  all  receiving  steam 
from  a  set  of  nozzles  (N),  each  nozzle  being  controlled  by  a  sepa- 
rate valve.  Fig.  250  is  the  corresponding  ideal  velocity  diagram. 
The  velocities  RI,  R2,  and  v2  are  found  in  the  same  manner  as  in 


STEAM   TURBINES 


Fig.  246.  The  stationary  blade  6"  turns  the  discharge  jet  K  to  the 
direction  J'  so  as  to  cause  it  to  act  on  the  bucket  Mz  with  ve- 
locity z>3  =  v2  (neglecting  losses).  The  velocity  diagram  v^R^R^* 
is  constructed  in  the  same  manner  as  in  Fig.  246,  and  i?4  is  the  final 
velocity,  the  corresponding  residual  energy  (loss)  being  wv^/2  g. 
As  the  steam  expands  fully  in  passing  through  the  nozzle,  the 
pressure  throughout  the  casing  of  the  stage  is  uniform.  This 
and  the  velocity  variation  are  shown  in  diagram  C  on  p.  375. 
The  smaller  turbines  of  this  type  usually  have  but  one  stage, 
while  the  larger  ones  have  from  two  to  five  "  pressure  stages  " 

separated  by  diaphragms, 
each  diaphragm  containing 
the  nozzles  for  the  following 
stage.  These  turbines  have 
either  horizontal  or  vertical 
shafts.  In  the  latter  arrange- 
ment, which  is  shown  in  Figs. 
251  and  252,  the  shaft  is 


Stuffing  Box  with 
Carbon  Packing  Rings 


Fig.  251. 


Fig.  252. 


supported  by  a  "  step  bearing,"  to  the  center  of  which  oil  is  sup- 
plied at  sufficient  pressure  to  support  or  float  the  shaft  and  all 
parts  fastened  to  it. 

Fig.  251  shows  diagrafnmatically  a  four-stage  turbine  in  which 
the  steam  enters  at  the  top  and  exhausts  at  the  bottom.  Such 
turbines  rest  on  a  subbase,  which  is  either  connected  to  the  con- 
denser or  itself  forms  the  walls  of  a  surface  condenser,  as  in  Fig. 


382 


HEAT-POWER  ENGINEERING 


252;  the  generator  is  placed  above  the  turbine  and  the  governor 
is  mounted  on  the  upper  end  of  the  shaft.  Fig.  253  shows  one 
arrangement  of  step  bearing,  and  a  portion  of  the  rotating 


Shroud  Riu;: 


Spacing 
Block 


STEP  BEARING 


Fig.  253. 


Oil  Drain 
Oil  Supply 
( Under  High  Pressure) 


11  bucket  segment,"  with  buckets  held  in  place  by  "  dovetails:' 
The  buckets  are  separated  by  "  spacing  blocks  "  and  their  tips 
are  riveted  to  shroud  rings. 

On  large  turbines  the  governor  usually  moves  a  small  "  pilot 
valve  "  which  controls  the  position  of  a  hydraulically  operated 
piston,  the  rod  of  which  moves  a  shaft  having  cams  which  open 
or  close  the  nozzles  of  the  first  stage.  Thus  the  power  output 
of  the  turbine  depends  on  the  number  of  first-stage  nozzles  in 
action.  The  governing  is  by  the  method  of  "  cutting  out  noz- 
zles "  or  cutting  them  in. 

187.  Velocity  Compounding  with  a  Single  Row  of  Rotating 
Buckets.  Instead  of  using  a  second  set  of  rotating  blades  in 
an  impulse  turbine  to  abstract  some  of  the  energy  remaining  in 
the  jet  when  it  leaves  the  first  set,  as  is  done  in  the  Curtis  type 
of  turbine,  this  energy  can  be  used  (in  part)  by  causing  the 
same  jet  to  impinge  repeatedly  on  a  single  set  of  blades. 

Fig.  254  shows  diagrammatically  the  elements  of  the  "  Elec- 
tra  "  turbine  (European),  which  is  of  this  type,  and  has  blades 
perpendicular  to  the  plane  of  the  wheel  disk.  The  full  expansion 
of  the  steam  occurs  entirely  within  the  nozzle  A7,  and  the  guide 
passages  G  merely  redirect  the  steam  so  as  to  cause  it  to  im- 
pinge properly  on  the  buckets.  As  the  volume  of  the  steam 
remains  constant  while  passing  through  the  guide  passages,  the 


STEAM  TURBINES 


383 


cross-sectional  area  of  these  passages  must  increase  as  the  veloc- 
ity (residual)  of  the  steam  decreases. 

The  path  of  the  jet,  instead  of  being  serpentine  as  in  Fig.  254, 
may  be  helicoidal  as  shown  at  a  in  Fig.  255.     It  may  be  con- 


Fig.  254. 

sidered  that  the  lower  part  of  this  path  is  in  the  semicircular 
buckets  of  the  turbine  wheel  shown  at  b  and  c  in  the  figure,  and 
that  the  upper  part  is  in  the  stationary  guides  of  similar  form. 
With  this  construction  it  is  possible  to  obtain  good  steam  econ- 


Wheel 


Fig-  255- 


omy  with  low  rotative  speeds,  even  though  a  single  wheel  be 
used.  The  same  scheme  is  applicable  to  turbines  having  two 
or  more  pressure  stages.  The  power  that  is  obtainable  with  any 
wheel  is  limited  by  the  number  of  nozzles  and  guide  "  blocks  " 
that  can  be  placed  around  the  periphery. 

The  forerunner  of  this  type  of  turbine  was  the  "  Riedler- 
Stumpf  "  turbine  (European),  with  double  semicircular  buckets 
like  the  Pelton. 

In  Fig.  256  is  shown  a  Terry  turbine  with  casing  opened. 
The  method  of  operation  is  as  shown  in  Fig.  255.  Flange  B 
couples  to  the  facing  B'  when  the  turbine  is  closed,  and  valve 


384 


HEAT-POWER  ENGINEERING' 


Governor 

Valve 


Fig.  256. 

X  can  be  used  to  shut  off  some  of  the  nozzles  when  the  load  is 
small.     The  casing  is  subjected  to  the  exhaust  steam  only. 

The  Sturtevant  turbine,  Fig.  257,  operates  in  a  similar  man- 
ner, but  is  of  somewhat  different  construction.  The  helical  and 
serpentine  paths  are  used  in  several  other  turbines. 

1 88.  Reaction  Turbines,  (a)  A  simple  reaction  wheel  (sim- 
ilar to  Hero's)  is  shown  in  Fig.  258.  The  pioneer  developers 
(De  Laval  and  Parsons)  of  the  modern  steam  turbine  and  many 
other  inventors  have  tried  to  produce  a  commercial  form  of 
turbine  based  on  this  principle,  but  without  success.  Experi- 
enced designers  now  recognize  the  fact  that  other  forms  are 
better  for  most  purposes.  The  sectioned  part  a  in  the  figure 


STEAM  TURBINES 


385 


Nozzle 
.Exhaust  Ports 


Fig.  257. 

constitutes  a  rotating  nozzle  of  the  converging  type,  correspond- 
ing to  a  small  pressure  drop  from  PI  to  P2. 

(b)  Another  simple  reaction  turbine  is  shown  in  Fig.  259,  with 
blades  mounted  on  the  periphery  of  a  disk,  or  drum,  which  is 
arranged  to  rotate  about  axis  XX.  It  is  seen  that  the  space  be- 


Fig.  258. 


Fig.  259. 


tween  the  blades,  as  shown  at  b,  has  the  same  form  as  the  nozzle 
a  in  Fig.  258 ;  hence  there  are  as  many  rotating  nozzles  as  there 
are  spaces  between  blades. 

In  this  arrangement  there  is  a  "  full  peripheral  discharge  "  of 
the  steam  around  the  entire  circumference,  and  it  is  important 
to  note  that  there  is  a  difference  between  the  pressures  PI  and 


386 


HE  A  T-POWER  ENGINEERING' 


P2   on  the  two  sides  of  the  disk,  a  condition  contrary  to  that 
present  in  the  impulse  type  of  turbine. 

(c)  Fig.  260  may  be  used  to  show  certain  features  of  the 
modern  type  of  reaction  turbine,  Between  the  tips  of  the 
blades,  on  the  drum,  and  the  casing  there  is  necessarily  a  radial 
clearance  space,  and  because  of  the  inequality  between  the  pres- 
sures Pi  and  P2  leakage  occurs  through  this  space.  This  clear- 
ance is  of  course  always  made  the  minimum  practicable.  The 
relative  amount  of  leakage  is  evidently  dependent  on  the  ratio 
of  this  annular  space  to  the  passage  area  between  blades;  thus, 
the  longer  the  blades  are,  the  less  the  leakage,  with  the  same 


.Clearance 


Fig.  260. 

clearance.  If  the  peripheral  diameter  is  decreased,  not  only  is 
the  annular  space  reduced,  but  the  blades  must  be  lengthened  to 
maintain  the  same  passage  area  between  them;  hence  there  is  a 
twofold  reduction  in  the  leakage  accompanying  such  change. 

(d)  It  is  apparent  that  the  difference  between  pressures  PI 
and  P2  in  Fig.  259  causes  an  end  thrust  on  the  shaft.     The  same 
is  true  of  the  arrangement  in  Fig.  260.     This  thrust  may  be 
resisted  (i)  by  the  thrust  bearing  T  in  this  figure;  or  (2)  by  the 
balance  piston  B,  which  presents  to  the  pressures  PI  and  Pz 
areas  equal  to  those  exposed  by  the  blades  and  drum  end;  or 
(3)  by  using  a  "  double-flow  "  arrangement  of  drum  wherein 
there  are  two  similar  rows  of  blades  having  discharges  which 
are  equal  but  opposite  in  direction  and  hence  give  opposite  end 
thrusts.     In  any  case  there  must  be  a  thrust  bearing  to  main- 
tain the  rotor  in  its  proper  position. 

(e)  The  leakage  between  the  piston  B  and  the  shell  is  usually 
reduced  by  employing  mating  collars,  as  in  Fig.   260,  which 


STEAM   TURBINES 


387 


Fig.  261. 


form  a  "labyrinth  passage"  which  becomes  more  or  less  sealed 
by  the  moisture  present  in  the  vapor. 

(f)  In  Fig.  261,  R2  represents  the  velocity  of  the  jet  relative 
to  the  rotating  blades,  u  is  the  blade  velocity,  and  v2  is  the  abso- 
lute residual  velocity  of   the  jet.     In  practice 

the  velocity  u  is  rather  low  (usually  from  150 
to  300  foot-seconds),  hence  the  heat  drop  per 
stage  is  relatively  very  small. 

(g)  The    so-called  Parsons'    "  reaction  tur- 
bine,"   besides    having  the    rotating   reaction 
blades  similar  to  those  in  Fig.  260,  has  station- 
ary guide  blades  which  act  as  nozzles,  the  jets 
from  which  impinge   on   the   rotating   blades. 

Hence  such  turbines  combine  the  impulse  and  the  reaction 
principles. 

Fig.  262  shows  such  an  arrangement,  S  and  M  being  respec- 
tively stationary  and  moving  blades.     It  is  seen  that  not  only  is 

there  leakage  at  the  tips  LI  of 
the  moving  blades,  but  also  at 
the  ends  L2  of  the  stationary 
ones.  These  turbines  are  made 
multistage,  with  stationary  and 
rotating  blades  alternating.  The 
action  of  the  steam  on  the  mov- 
ing blades  is  twofold:  (i)  The 
direction  of  the  jet  is  changed, 
and  if  no  other  action  took  place 
it  would  leave  with  low  velocity— 
thus  there  is  an  impulse  action; 
and  (2)  the  steam  expands  while 
passing  through  the  moving 
blades  and  acquires  velocity  by 
virtue  of  that  expansion,  so  that 
when  discharged  rearwards  there 
is  a  reaction  effect.  The  residual 
velocity  of  the  jet  leaving  the 
rotating  blade  is  redirected  and 

increased  by  the  next  stationary  blades  and  discharged  against  the 
next  row  of  moving  blades,  and  so  on  from  one  end  of  the  turbine 
to  the  other.  (See  D  in  the  chart  on  page  3/5.) 


388 


SEAT-POWER  ENGINEERING 


STEAM   TURBINES 


389 


As  the  bucket  velocities  are  small,  it  is  necessary  to  use  small 
heat  drops  per  stage,  hence  a  great  many  stages  are  used.  As 
the  volume  of  steam  under  high  pressure  is  small,  the  passages 
between  blades  must  be  small,  and  the  blades  themselves  are 
consequently  short.  To  reduce  the  leakage  the  high-pressure 
stages  are  hence  made  small  in  diameter  compared  with- low- pres- 
sure stages,  where  the  volume  of  the  steam  is  large  and  the 
blades  are  long.  The  heat  drops  in  each  of  the  first  stages  are 
about  2  or  3  B.t.u.,  whereas  in  the  last  stages  drops  of  about 
10  B.t.u.  may  be  used. 

(h)  One  arrangement  of  the  Westinghouse-Parsons  turbine  is 
shown  in  section  in  Fig.  263.  After  passing  the  governor  valve 
the  steam  enters  at  A  and  flows  between  the  blades  on  three  cyl- 
inders, RI,  R2,  and  Rs,  which  progress  in  diameter,  until  it  reaches 
the  exhaust  opening  X.  The  three  balance  pistons,  PI,  P2,  and  P3, 
with  equalizing  pipes  EI,  E2j  and  £3,  balance  the  thrust,  and  the 
thrust  bearing  T  constrains  the  rotor  to  its  proper  position. 
The  governor  moves  the  pilot  valve,  which  in  turn  controls  the 
governor  valve.  The  operation  is  such  as  to  cause  the  latter 
valve  to  constantly  move  up  and  down,  admitting  the  steam 
"  by  puffs,"  which  vary  in  duration  with  the  load.  If  the 
demand  on  the  turbine  becomes  more  than  can  be  met  by  all 
the  steam  that  can  flow  between  the  first  blades,  the  turbine's 
speed  will  decrease  slightly  and  the  governor  will  then  open  the 
overload  valve,  thus  admitting  steam  to  a  point  (C)  where  the 
passage  area  between  blades  is  greater,  so  more  steam  can  be  used 
to  meet  the  emergency,  although  less  efficiently  than  before. 


Fig.  264. 


(i)  Fig.    264   shows   the   general    arrangement   of   the   Ailis- 
Chalmers-Parsons  turbine,  which  is  of  the  same  general  type  as 


3QO  HEAT-POWER  ENGINEERING 

the  Westinghouse,  but  differs  somewhat  in  its  arrangement, 
construction,  and  method  of  governing.  The  largest  balance 
piston  P3  is  placed  at  the  exhaust  end  of  the  rotor  and  the  gov- 
erning is  by  the  throttling  method. 

(j)  In  multistage  turbines  the  elements  in  the  different  stages 
need  not  all  be  of  the  same  type.  It  is  sometimes  desirable  to 
use  in  the  first  stages  that  type  which  operates  best  with  steam 
at  high  pressures,  and  in  the  remaining  stages  the  type  best 
suited  for  low-pressure  conditions.  See  Chart  on  page  394a. 

189.  Applications  of  the  Steam  Turbine.  Owing  to  the  high 
rotative  speeds  and  to  the  inability  to  vary  these  speeds  sud- 
denly or  to  reverse  the  direction  of  rotation,  there  are  many 
fields  of  "  direct  driving "  which  the  steam  turbine  cannot 
enter. 

(a)  Driving   electric    generators,    which    furnish    current    for 
almost  an  unlimited  number  of  purposes,  is  the  largest  field  of 
application. 

(b)  Turbines  are  used  with  direct-driven  centrifugal   pumps 
which  discharge  against  low  or  high  heads  (circulating  pumps, 
boiler-feed  pumps,  etc.). 

(c)  They   are   used   for   driving   centrifugal   air   compressors 
(which  are  usually  multistage),  fans,  blowers,  etc. 

(d)  In  some  instances  small  low-speed    turbines  have   been 
used  for  belt  driving.     Ordinarily  it  is  not  feasible  to  reduce  the 
rotative  speeds  by  use  of  gearing  unless  specially  designed  and 
constructed  for  the  purpose. 

(e)  The  torque  on  a  turbine  shaft  is  relatively  very  small, 
hence  turbines  are  not  applicable  where  a  large  starting  effort  is 
involved. 

(f)  In  many  instances  steam  is  available  at  pressures  which 
are  too  low  to   use  in  an  engine,  but  can    be  used  advanta- 
geously in   "  low-pressure  "  or  "  exhaust-steam  "  turbines,  pro- 
vided a  high  vacuum  can  be  maintained  in  the  condenser. 

In  plants  in  which  engines  are  operated  noncondensing,  there 
can  be  added  turbines  of  this  type  to  receive  exhaust  steam  at 
about  atmospheric  pressure  and  to  exhaust  into  a  condenser 
having  good  vacuum.  In  such  cases  it  is  desirable  to  maintain 
a  pressure  slightly  above  atmospheric  in  the  pipes  between  the 
engine  and  the  turbine  to  avoid  leakage  of  air  into  the  steam 


STEAM   TURBINES  391 

with  resultant  decrease  of  vacuum.  When  the  steam  is  received 
at  about  atmospheric  pressure,  the  exhaust  turbine  will  develop 
a  horse  power  with  about  30  pounds  of  steam  per  hour,  provided 
the  vacuum  is  good.  The  probable  water  rate  in  any  case  can 
be  computed  by  using  Eq.  (318).  With  this  and  the  available 
amount  of  steam  known,  the  power  that  can  be  developed  by 
the  exhaust  turbine  can  be  readily  computed. 

Condensing  engines  can  be  operated  noncondensing  with  late 
cut-off,  thus  giving  about  their  normal  power,  and  the  exhaust 
steam  can  be  used  in  a  low-pressure  turbine,  the  combined 
outfit  thus  giving  power  greatly  in  excess  of  (sometimes  double) 
the  normal  power  of  the  engine  alone.  Such  arrangements 
usually  are  more  economical  than  either  the  engine  under  the 
original  conditions  or  a  turbine  which  receives  steam  direct 
from  the  boiler.  The  less  economical  the  engine,  the  more 
heat  remains  in  its  exhaust  steam  for  use  in  the  turbine. 

(g)  If  the  supply  of  steam  furnished  a  low-pressure  turbine  is 
intermittent,  as  in  a  rolling  mill,  a  regenerator  or  accumulator 
can  be  used  to  make  up  any  temporary  deficiency  which  may 
occur.  This  device  consists  of  a  closed  vessel  which  contains 
water  over  or  through  which  the  steam  passes  on  its  way  to  the 
turbine.  Thus  this  water  becomes  heated  to  the  temperature 
of  the  steam.  Should  the  supply  of  steam  cease,  the  steam 
pressure  would  decrease  and  as  a  result  some  of  the  water  would 
vaporize  and  supply  the  turbine  with  working  substance  at 
continually  decreasing  pressure  for  a  short  interval  of  time. 
Usually  there  is  also  provision  for  supplying  steam  direct  from 
the  boilers,  through  a  reducing  valve,  in  case  the  normal  supply 
fails  for  a  considerable  length  of  time;  and  sometimes  the  tur- 
bine has  a  high-pressure  stage  which  is  normally  inoperative, 
but  which  is  brought  into  action  in  such  an  emergency. 

(h)  Marine  propulsion  is  another  large  field  for  the  appli- 
cation of  the  steam  turbine.  A  saving  in  the  weight  of  the 
turbine  and  of  space  occupied  can  be  effected  by  using  high  ro- 
tative speeds,  and  the  economy  can  be  improved  by  using  high 
bucket  velocities.  On  the  other  hand,  the  propeller  on  a  slow- 
moving  vessel  is  inefficient  if  operated  at  rotative  speeds  which 
are  high.  Hence  in  applying  the  turbine  to  the  direct  driving  of  a 
propeller,  a  compromise  must  be  effected ;  evidently  the  best  results 
should  be  obtained  on  high-speed  vessels,  and  such  is  the  case. 


392  HEAT-POWER  ENGINEERING  '' 

There  have  been  invented  numerous  speed-reducing  devices 
(mechanical,  hydraulic,  and  electric)  to  be  placed  between  the 
turbine  and  propeller  shaft,  but  there  is  still  doubt  as  to  their 
feasibility,  and  until  such  devices  are  used  the  application  of  the 
turbine  will  probably  be  limited  principally  to  vessels  of  high  speed. 

Special  provision  must  be  made  for  backing;  usually  a  small 
"  backing  element  "  is  placed  at  the  end  of  the  turbine.  As 
turbines  are  very  uneconomical  when  operating  below  their 
normal  speeds,  they  should  not  be  used  for  low-speed  cruising. 
Sometimes  smaller  "  cruising  turbines  "  are  added  for  such  ser- 
vice. Turbines  are  not  satisfactory  when  much  maneuvering 
must  be  done,  and  in  some  instances  a  combination  of  engines 
and  turbines  has  been  used  for  such  service. 

190.  Advantages  and  Disadvantages  of  the  Steam  Turbine. 
(a)  When  operating  under  normal  load  (i.e.,  with  the  usual  allow- 
ance for  overloading),  a  comparison  of  the  best  performances 
does  not  show  that  the  turbine  has  any  advantage  over  the 
engine  even  when  unusually  good  vacuums  are  used  with  the 
former.  It  is  probable,  however,  that  the  average  large  con- 
densing turbine  with  high  vacuum  gives  better  performance 
than  the  average  large  condensing  engine.  In  general,  non- 
condensing  and  small  turbines  do  not  compare  so  favorably. 
In  many  cases  it  is  found  that  from  the  standpoint  of  fuel 
economy  there  is  little  choice  between  the  turbine  and  the 
engine,  in  which  cases  the  selection  must  be  based  on  other 
considerations. 

Comparison  should  be  made  at  normal  load  and  should  be  either 
on  the  basis  of  B.t.u.  actually  supplied  per  d.h.p.-minute,  or  of 
the  thermal  efficiencies,  rather  than  on  the  basis  of  the  steam 
used,  unless  the  conditions  of  operation  are  identical. 

(b)  The  water-rate  curve  for  the  turbine  is  usually  flatter  than 
that  of  the  engine,  and  hence  with  widely  fluctuating  load  the 
average  economy   is   nearer  the  best  for  that  machine;  espe- 
cially is  this  the  case  if  the  unit  is  overloaded. 

(c)  The  space  occupied  by  the  turbine  is  much  less  than  by 
the  ordinary  engine,  especially  if  the  latter  is  horizontal.     In 
some  cases,  however,  this  is  partly  offset  by  the  greater  space 
that  may  be  occupied  by  the  larger  size  of  auxiliary  apparatus 
frequently  used  with  turbines. 


STEAM   TURBINES 


393 


(d)  The  turbines  use  no  oil  internally,  hence  the  condensate 
is  suitable  for  direct  return  to  the  boilers,  and  the  heat-trans- 
mitting surfaces  of  the  boilers,  condensers,  feed-water  heaters, 
etc.,  being  free  from  oily  coating,  operate  under  best  conditions. 

(e)  Turbines   have   the   advantage  of  greater   uniformity  of 
rotation,  and  can  give  close  speed  regulation.     If  properly  "  bal- 
anced," they  are  practically  free  from  vibration,  hence  do  not 
require  massive  foundations  or  flywheels. 

(f)  Other  considerations  are  the  first  cost  of  turbine  and  gen- 
erator (which  is  generally  less  than  that  of  the  engine-generator 
outfit),  and  the  cost  of  auxiliary  apparatus  (which  is  often  greater 
with  high  vacuums).     The  cost  of  ground  occupied,  the  build- 
ing  and    foundations,    the   reliability,    the   cost   of   condensing 
water,  supplies,  attendance  and  repairs,  the  allowance  for  de- 
preciation, etc.,  must  also  be  considered.     Such  matters,  how- 
ever, relate  to  the  Economics  of  Power-Plant  Engineering,  which 

•will  not  be  discussed  here. 

(g)  There  are  many  fields  in  which  it  is  necessary  to  operate 
at  low  angular  velocity,  at  variable  speed,  with  reversal  of  motion, 
or  with  large  starting  torque,  which  the  steam  turbine  cannot 
enter.     There  are  other  fields  in  which  high  angular  velocity 
is  desirable,  or   not  disad- 
vantageous,   and   in  many 

of  these  the  turbine  is  as 
satisfactory  as,  or  more  so 
than,  the  engine. 


20 


18 


IQI.   Steam-Turbine     &  _ 

Performance,     (a)  Fig.  237     J  ° 
shows  the  general  character      § 14 

O 

of   the  steam-consumption.     ^13 
curves  for  steam  turbines,        12 
the    curve    for    total    con-        u 
sumption    being     substan-        10 
tially  straight.     The  water- 
rate  curve  is  usually  flatter 
than    that    of   the    steam 


V 


STEAM  CONSUMPTION  VvriEN 
INITIAL  PRESSURE  =165  LBS.ABS 
SUPERHEAT  =0°  F. 
VACUUM  =28  INCHES 


Thousand  K.W. Hated  Power 
Fig.  265. 


engine,  which  indicates  less  variation  in  economy  with  fluctua- 
tions of  load.  Inspection  of  this  curve  shows  that  the  best  econ- 
omy is  obtained  at  the  maximum  load  (not  at  the  normal),— 


394 


HEAT-POWER  ENGINEERING 
overload  valve  "  which  reduces  the  efficiency 


NITIAL  PRESS.=  165  LBS.AB8. 
SUPERHEAT  =  0°  F. 
VACUUM=    8  INCHES 

\ 

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TL~ 

j 

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B.t. 

i.  pei 

D.hJ 

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Thousand  K.W. Rated  Power 
Fig.  266. 


unless  there  is  an 
when  open. 

(b)  The  curves  in  Fig.  265  show  the  economies  of  the  larger 

sizes  of  standard  American 
turbines  when  operating 
under  rated  loads  which  are 
used  as  abscissas. 

These  curves  are  based 
on  Prof.  J.  A.  Moyer's 
tables,*  in  which  the  steam 
consumptions  as  obtained 
by  test  are  reduced  to  the 
equivalent  values  which  the 
same  turbines  would  prob- 
ably give  if  operated  under 
pressure  of  165  pounds  ab- 
solute, zero  superheat,  and- 
28-inch  vacuum.  The  cor- 
rections were  made  by  using  the  following  reduction  factors : 

For  all  types  of  turbine: 

Per  pound  of  initial  pressure,  TV  per  cent. 

Generator  efficiency,  91  per  cent  (300  to  400  kilowatts),  95 
per  cent  (500  kilowatts),  96.5  per  cent  (1000  to  3000  kilo- 
watts), and  98  per  cent  (5000  to  10,000  kilowatts). 

For  Parsons  type: 

Per  degree  of  superheat,  TV  per  cent  (300  to  1000  kilowatts) 

and  \  per  cent  (1200  to  7500  kilowatts). 
Per  inch  of  vacuum,  4  per  cent  (300  to  1000  kilowatts)  and 

3  per  cent  (1200  to  7500  kilowatts). 

For  Curtis  type  (may  also  be  used  for  Rateau  and  Zoelly  turbines) : 
Per  degree  of  superheat,  J  per  cent. 

Per  inch  of  vacuum,  7  per  cent  (26  to  28  inches)  and  9  per 
cent  (28  to  29.5  inches). 

These  correction  factors  should  be  used  only  when  the  changes 
involved  are  slight,  otherwise  the  results  may  not  be  reliable. 

(c)  In  Fig.  265,  the  curve  for  "  steam  per  d.h.p.-hr."  is  based 
on  the  brake  horse  power,  or  power  delivered  by  the  turbine 


*  Page  287,  Moyer's  "The  Steam  Turbine."    Wiley  &  Sons. 


STEAM   TURBINES 

CHART 

TURBINES  HAVING  COMBINATIONS  OF  STAGES  OF  DIFFERENT 

TYPES 


Fig.  A.     "  Return  Flow  "  (Terry). 


Fig.  B.  Comparison  of  Lengths  of 
Rotor  (Reaction  vs.  Combination  of  Veloc- 
ity Stage  and  Reaction). 

Impulse  Wheel 

Reaction  Elements 

0) 


Fig.  C.     Double  flow  — 10,000  to  20,000  kw.  (Westinghouse) . 


tL. 


Fig.  D.    Seven-stage  Impulse  Turbine  (General  Electric), 


394^ 


HEAT-POWER  ENGINEERING  '' 


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(Interbo 


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STEAM   TURBINES 


395 


SMALL  TURBINES 
STEAM  PRESS.    150  LBS.  GAUGE 
DRY  STEAM 
ATMOS.    EXHAUST 


shaft,   and  does  not  include  the  generator  losses.     The  other 
curve  includes  the  losses  of  both  the  turbine  and  the  generator. 

(d)  Fig.  266  shows  the  B.t.u.  consumptions  and  the  thermal 
efficiencies  corresponding  to  the  water-rate  curves  of  Fig.  265. 
Values  better  than  here  shown  can  be  obtained  by  using  higher 
superheats,  higher  pressures,  and  lower  vacuums  —  especially  by 
using  the  latter. 

Some  of  the  best  results  so  far  obtained  with  large  turbines 
are  given  in  Table  X.* 

(e)  Small  turbines  are  generally  much  less  economical  in  the 
consumption  of  steam  than  large  ones.     In  most  instances  this 
is  largely  due  to  the  use  of 

bucket  velocities  which  are 
much  less  than  those  cor- 
responding to  the  best  per- 
formance, and  which  result 
from  using  small  wheel  di- 
ameters and  low  rotative 
speeds  which  permit  of  di- 
rect connection  to  genera- 
tors, pumps,  etc.  The 
economy  of  such  turbines 
is  greatly  influenced  by  a 
change  in  bucket  speed. 

Fig.  267  shows  curves  of 
steam  consumption  per  brake  horse-power  for  several  types  of 
small  turbines,  f  It  shows  that  in  general  the  smaller  sizes  have 
poorer  economy. 

(f)  The  results  of  some  tests  of  the  59th  Street  Power  Plant 
of   the  Interborough  Rapid  Transit  Co.,  New  York  City,t  can 
be  used  to  compare  the  performances  of  the  same  power  plant 
operating  first  without  and  then  with  exhaust  steam  turbines. 
This   plant   was   originally   equipped   with   condensing   engine- 
generator  units  each  developing  5000  kw.  at  normal  (economical) 
load,  and  having  a  maximum  rating  of  7500  kw.     Subsequently, 
exhaust  steam  turbines  of  7500  kw.  maximum  capacity  were 

*  Also  see  Christie,  "Present  State  of  Development  of  Large  Steam  Turbines," 
Trans.  A.  S.  M.  E.,  1912. 

t  See  Orrok,  "Small  Steam  Turbines,"  Trans.  A.  S.  M.  E.,  1909. 
i  Trans.  A.  S.  M.  E.,  1910,  page  78. 


396  HEAT-POWER  ENGINEERING 

added,  and  these  were  arranged  to  operate  with  high  vacuums 
on  steam  received  at  about  atmospheric  pressure  from  the 
engines,  which  latter  were  changed  to  have  later  cut-offs  than 
before.  The  addition  of  the  turbine  to  one  of  the  engine  units 
gave  the  following  results:  — 

(1)  The  maximum  capacity  was  doubled. 

(2)  The  load   giving  the  best  steam  performance   (or  load 
under  which  the  unit  should  normally  operate)  was  increased  to 
about  2\  times  its  former  value. 

(3)  The  average  steam  economy  (between  7000  and  15,000 
kw.)  was  25  per  cent  better  than  that  of  the  old  engine  unit. 

(4)  It  was  estimated  that  the  average  steam  economy  was 
13  per  cent  better  than  would  have  resulted  by  using  a  high- 
pressure  turbine  of  the  best  design  in  place  of  the  combined  unit. 

(5)  The  average  thermal  efficiency  of  the  combined  unit  was 
20.6  per  cent  (between  6500  and  15,500  kw.). 


CHAPTER   XXIII. 

EXTERNAL-COMBUSTION   GAS  ENGINES. 

192.  Definition,     (a)    The   name  gas  engine   is  applied   to 
prime  movers  in  which  the  working  substance  is  material  in 
gaseous  form  comparatively  far  removed  from  the  conditions  of 
liquefaction.     Hence  the  working  substances  may  be  assumed  to 
obey  the  laws  of  ideal  gases,  and  each  gas  engine  follows  approxi- 
mately one  of  the  gas  cycles  discussed  in  Chapter  VIII. 

(b)  At  present  gaseous  working  substances  consist  of  air  mixed 
with   other   materials  such   as   carbon   monoxide,   hydrocarbon 
vapors  and  gases,  water  vapor,  and  carbon  dioxide. 

(c)  The  "  hot  body  "  is  approximated  in  real  engines  by  the 
burning  of  fuel  in  some  chamber  at  a  rate  which  maintains  the 
required  high  temperature.     In  some  types  of  gas  engines  the 
fuel,  and  resulting  hot  "products  of  combustion,"  are  separated 
from  the  working  substance  by  metallic  walls  through  which 
the  heat  received  by  the  working  substance  must  pass.      Such 
engines  are  known  as  external-combustion  gas  engines. 

In  other  gas  engines  the  fuel  and  the  air  for  its  combustion 
are  burned  inside  the  cylinder  of  the  engine,  and  the  hot  products 
of  combustion  form  the  expanding  working  substance.  Such 
engines  are  called  internal-combustion  gas  engines,  or  simply 
internal-combustion  engines. 

193.  The  Hot- Air  Engine,     (a)  Many  attempts  have  been 
made  to  utilize  air  as  a  working  medium  in  external-combustion 
engines,  but  only  two  such  engines  survive  to-day  in  this  country, 
and  they  are  built  only  in  small  sizes  and  for  special  service. 
Inventors  have  long  tried  to  produce  an  actual  gas  engine  to 
work  with  close  approximation  to  the  Carnot  cycle.     Even  if 
this  were  possible,  it  would  be  unwise  commercially  because  of 
the  excessive  cylinder  volume  necessary  for  a  given  output  of 
power. 

This  may  be  made  clear  by  drawing,  as  in  Fig.  268,  a  Carnot 
cycle,  an  Ericsson  cycle,  and  a  Stirling  cycle  for  comparable 


398  HEAT-POWER  ENGINEERING 

conditions  so  as  to  show  the  greatest  volume  occupied  by  the 
gas  in  each  case.  This  is  best  done  by  imagining  one  pound  of 
gas  (air  in  the  figure)  to  receive  the  same  amount  of  heat  and  to 
work  between  the  same  temperature  limits  in  each  case.  The 
efficiency  and  work  done  will  then  be  the  same  in  each  case,  and 
will  be 

Ef=  (Ti-  r2)/rlf 

and 

AE  =  Aft  X  Ef  =  Aft  (Ti  -  r2)/7\. 

The  figure  shows  that  the  maximum  volume  occupied  by  the 
working  substance,  and  hence  the  necessary  cylinder  volume,  is 

much  greater  in  the  case  of  the 
Carnot  engine  than  for  either  of 
the  others. 

(b)  The  cylinder  volume,  how- 
ever, determines  to  a  consider- 
able extent  the  size  and  cost  of  the 
engine.      As  will  be  brought  out 
later,  the  real  external-combus- 
tion gas  engines  operating  on  the 
Stirling  and  Ericsson  cycles  are 
almost    prohibitively  large,  and 
it  is  therefore  obvious  that  the 
Carnot  gas  engine  with  external 
combustion   must    be    commer- 
cially impossible. 

(c)  The  two  external-combus- 
tion gas  engines  now  in  use  in 
this  country  are  the  Rider  hot- 
air    engine    and    the    Ericsson 
hot-air    engine.       The    former 
approximates  the  Stirling  cycle 
and  the  latter  the  Ericsson  cycle. 

Both  of  these  engines  are  direct-connected  to  small  water  pumps 
which  utilize  the  net  work  of  the  engine.  They  are  simple  and  sat- 
isfactory pumping  engines,particularly  for  farm  and  suburban  use. 
(d)  The  capacity,  that  is,  the  power  made  available,  is  limited 
by  the  slow  rate  of  heat  transfer  between  the  metallic  walls  and 
the  more  or  less  quiescent  gas;  by  the  slow  rate  of  heat  conduction 
in  the  gas  itself;  by  the  low  specific  heat  and  density  of  the  gas; 


10  5>0 

Volume,  Cu.Ft. 

Fig.  268. 


EXTERNAL-COMBUSTION  GAS  ENGINES 


399 


Ideal  Engine 


and  by  the  comparatively  low  maximum  temperature  at  which 
it  is  advisable  to  maintain  metal. 

In  order  that  gas  may  absorb  or  give  up  heat  rapidly,  it  must 
pass  over  the  metallic  surfaces  in  a  thin  stream  and  at  high 
velocity.  This  necessitates  a  large  engine.  The  time  neces- 
sary for  heat  exchanges  is  so  great  that  the  engine  must  run  at 
very  slow  speeds  with  few  cycles  per  minute.  Obviously,  the 
smaller  the  number  of  cycles  the  greater  must  be  the  energy 
made  available  per  cycle,  and  hence  the  greater  the  size  of  the 
engine  to  deliver  a  given  amount  of  power. 

The  effect  of  low  specific  heat  is  to  increase  the  weight  of  gas 
necessary  for  a  given  heat  change,  and  the  low  density  results 
in  a  large  volume  for  a  given  weight.  Both  effects  increase  the 
size  and  cost  of  engine  for  a  given  power. 

194.  Rider  Hot-Air  Engine,  (a)  This  engine,  which  approxi- 
mates the  Stirling  cycle  (Section  54),  is  shown  in  Fig.  269,  and  by 
comparing  it  with  Fig.  23,  re- 
produced at  (b)  in  the  upper 
right-hand  corner  of  Fig.  269, 
it  is  seen  to  have  all  the  parts 
of  the  ideal  engine  following 
this  cycle.  In  the  two  figures 
similar  parts  are  designated 
by  the  same  letter.  The  ideal 
hot  body  is  replaced  by  a  fur- 
nace, the  gases  of  which  at 
temperature  T\  jacket  the  hot 
cylinder  Y.  The  regenerator 
R  is  approximated  by  a  pass- 
age filled  with  closely  spaced 
plates  HH.  The  cold  cylin- 
der Fi  is  jacketed  by  water  X 
from  pump  P  and  is  main- 
tained at  a  practically  con- 
stant temperature  T2.  The 
water  replaces  the  cold  body. 
By  means  of  connecting  rods 
J  and  /'  the  pistons  D  and  C  are  connected  to  cranks  I  and  /' 
which  are  fastened  to  the  shaft,  with  the  crank  for  the  hot  cylinder 


REAL  ENGINE 

Fig.  269. 


40o  HEAT-POWER  ENGINEERING. 

leading  the  other*  by  about  90  degrees.  The  crank  shaft  carries 
a  flywheel  W  which  maintains  uniformity  of  rotation,  even 
though  the  power,  developed  and  delivered,  varies  widely. 

(b)  In  the  ideal  cycle,   Fig.   22,   and    (a)  in  Fig.   269,  it   is 
assumed  that  during  the  isothermal  reception  of  heat  by  the  gas, 
the  left  piston  remains  stationary  at  the  bottom  of  its  stroke, 
while  the  right  piston  rises;  that  during  the  isothermal  rejection 
of  heat  the  reverse  action  occurs;  and  that  during  the  isovolumic 
changes  the  two  pistons  move  at  such  rates  as  to  keep  the  total 
inclosed   volume   constant   while   the   gas   passes   through    the 
regenerator. 

In  the  actual  case  these  actions  are  roughly  approximated  by 
connecting  the  pistons  to  cranks  which  are  nearly  at  right  angles. 
When  either  piston  is  at  or  near  its  lowest  position,  most  of  the 
working  substance  is  in  the  other  cylinder,  where  the  piston  is 
at  about  half-stroke  (since  the  cranks  are  at  about  right  angles). 
The  material  meanwhile  is  undergoing  an  isothermal  change, 
which  is  expansion  if  the  gas  is  in  cylinder  F,  or  compression  if 
in  FI.  In  two  intermediate  positions  of  the  cranks  the  pistons 
are  moving  with  equal  and  opposite  velocities,  while  the  gas 
is  undergoing  isovolumic  transfer  from  one  cylinder  to  the  other. 
Thus  in  the  Rider  engine  the  Stirling  cycle  is  roughly  approxi- 
mated, with  considerable  blending  between  the  various  processes. 

(c)  The  actual  diagram  obtained  from  this  engine  cannot  readily 
be  directly  compared  with  the  theoretical,  and  a  reproduction 
is  therefore  omitted.     The  maximum  and  minimum  temperatures 
are  respectively  lower  and  higher  than  the  theoreljj 

corners  of  the  diagram  are  very  much  rounc 

(d)  If  the  furnace  temperature  be  assume5OO°  F.,  a  low 
value,  and  the  jacket  temperature  at  60°,  a  rather  high  value, 
the  Stirling  cycle  efficiency  is 


The  actual  thermal  efficiency  on  the  i.h.p.  (TIEf)  is  seldom 
as  much  as  2  per  cent,  so  that  the  best  indicated  efficiency  is 
about 

lEf  =  2/73.5  =  0-027  =  2.7  per  cent. 

*  That  is,  preceding  it  in  the  direction  of  rotation* 


EXTERNAL-COMBUSTION  GAS  ENGINES 


401 


The  corresponding  efficiency  for  internal  combustion  gas-en- 
gines and  steam  engines  is  generally  50  per  cent  or  more.  The 
poor  economy  of  this  engine  is  thus  very  striking. 

195.  Ericsson  Hot-Air  Engine,  (a)  This  engine,  which  ap- 
proximates roughly  the  Ericsson  cycle  (Section  55),  is  shown  in 
Fig.  270,  in  which  the  parts  are  lettered  to  correspond  with  the 


XIdealU 
Engine 

REAL  ENGINE 

Fig.  270. 

shown  in  Fig.  23.  The  furnace  U  replaces 
the  "  displacer  "  piston  j  is  the  hot  cylinder 
Y,  jacketed  S>^^^ furnace  gases,  and  above  it  is  the  cold  cylin- 
der YI  with  jacket  X  supplied  with  water  from  pump  P.  The 
upper  or  working  piston  2  transmits  the  power.  When  the 
displacer  piston  j  is  up,  most  of  the  gas  is  below  it  in  the  hot 
cylinder.  Upon  descending,  this  piston  transfers  the  gas  to  the 
cold  cylinder  Y\  above,  and  when  ascending,  returns  it  to  the 
hot  cylinder  Y.  The  function  of  the  regenerator  R  is  performed 
by  the  walls  of  the  cylinder  and  of  the  loose-fitting  displacer 
piston,  between  which  the  gas  passes  in  transferring  from  one 
cylinder  to  the  other. 

The   engine   has  an  ingeniously  arranged   mechanism  which 
gives  such  kinematic  motion  to  the  displacer  and  working  pistons 


402  HEAT-POWER  ENGINEERING 

as  to  produce  approximately  the  PV-changes  of  the  theoretical 
Ericsson  cycle. 

(b)  The  conditions  of  heat  transfer  are  even  poorer  in  this 
engine  than  they  are  in  the  Rider,  and  as  a  result  the  power 
developed  for  the  same  heat  supply,  and  for  same  size  of  cylinder, 
is  only  about  one-third  of  that  obtained  with  the  other  engine. 

(c)  It  is  worthy  of  note  that  a  very  large  hot-air  engine  of  a 
different  type,  which  was  constructed  by  Ericsson,  gave  a  thermal 
efficiency  of  about  10  per  cent.     It  was,  however,  enormously 
bulky  and  mechanically  unsatisfactory. 


CHAPTER    XXIV. 

INTERNAL-COMBUSTION  ENGINES. 

METHODS  OF  OPERATION. 

196.  Advantages  and  Types,  (a)  Although  external-combus- 
tion engines  with  gaseous  working  substance  are  not  generally 
commercially  successful,  the  w/eraa/-combustion  engine,  on  the 
other  hand,  is  widely  used,  and  is  capable  of  giving  the  highest 
economies  now  attained  by  any  type  of  heat  engine. 

The  success  of  the  internal-combustion  engine  is  chiefly  due 
to  the  fact  that,  since  the  products  of  combustion  constitute  the 
working  substance,  the  maximum  temperature  is  that  due  to 
combustion;  whereas  in  the  external-combustion  engine  the 
maximum  temperature  of  the  working  substance  is  limited  by 
the  capacity  of  metallic  walls  to  withstand  high  temperature,  and 
to  transmit  heat. 

In  internal-combustion  engines  with  proper  design  the  highest 
temperature  attainable  may  be  used  without  danger  to  metallic 
walls,  and  it  is  thus  possible  to  approach  theoretical  efficiencies 
corresponding  to  temperatures  of  from  2500°  to  3000°  F.  Be- 
cause of  the  high  pressures  that  accompany  high  temperatures,  the 
engines  are  also  small  for  a  given  capacity. 

(b)  During  the   past   twenty  years  the  use  of  internal-com- 
bustion engines  has  rapidly  increased,  until   now   many  large 
power   plants   depend   entirely   upon   them   for   power.     These 
engines   operate   on  either  the  Otto  cycle  or  the  Diesel  cycle. 
Engines  following  the  latter  cycle  were  until  recently  a  more  or 
less  special  type  adapted  only  to  certain  limited  conditions,  but 
this  limitation  is  rapidly  disappearing. 

(c)  There   are   two   distinct   types   of   engine   following   the 
Otto  cycle;  one  requires  two  piston  strokes,  and  the  other  four, 
to  complete  a  cycle.      They  are  known  as  two-stroke   cycle 
and  four-stroke  cycle  engines,  or  improperly  as  "  two-cycle  " 
and  "  four-cycle  "  engines.     The  four-stroke  cycle  is  in  more 

403 


To  Atmosphere 


Fig.  271. 


HEAT-POWER  ENGINEERING-' 

common  use,  though  it  has  several  theoretical  and  practical  disad- 
vantages as  compared  with  the  other  type. 

197.   Cylinder  Operations  of  Four-Stroke   Otto   Cycle,     (a) 
The  heat  is  evolved  within  the  cylinder  by  the  burning  of  a 

mixture  of  fuel  gas,  or  vapor, 
with  air,  which  supplies  oxygen 
for  combustion.  The  gaseous 
products  of  combustion  form 
the  working  substance,  which, 
after  expansion,  must  be  ex- 
pelled from  the  cylinder  to 
give  place  to  a  fresh  combusti- 
ble charge  for  the  next  cycle. 
The  engine  is  shown  diagram- 
matically  in  Fig.  271. 
(b)  Imagine  a  cylinder  as  shown  in  the  figure,  with  an  inlet 
valve  /  and  an  exhaust  valve  E  located  in  the  head  and  arranged 
to  open  inwardly;  and  assume  that  the  piston  is  in  its  extreme 
left  position,  that  its  motion  can  be  controlled  as  desired,  that  a 
cycle  has  just  been  completed, 
and  that  the  "  clearance  space  " 
or  "  combustion  space  "  between 
the  face  of  the  piston  and  the 
cylinder  head  is  filled  with  burnt 
gases  at  atmospheric  pressure. 

Now  with  the  valve  E  closed, 
and  with  I  open  to  a  supply  of 
combustible  mixture  at  atmos- 
pheric pressure,  the  first  stroke 
of  the  piston  (to  the  right)  will 
cause  some  of  this  mixture  to  pass 
into  the  cylinder,  where  it  will  mix  with  the  burnt  gases,  and  thus 
diluted  will  fill  the  available  space  at  approximately  atmospheric 
pressure.  The  line  ed  in  Fig.  272,  at  a  height  of  14.7  pounds 
per  square  inch  above  the  horizontal  axis,  represents  this  process. 
Now  imagine  the  inlet  valve  /  closed  and  the  piston  moved  to 
the  left  performing  the  second  stroke.  During  this  stroke  the 
mixture  will  be  compressed  until,  finally,  its  volume  is  reduced 
to  that  of  the  clearance  space.  This  compression  may  be 


euu 

600 

p 

'400 

200 
0 

b 

\ 

\ 

s^^ 

a 

^ 

^ 

">*>• 

—tc 

Jd 

.02            .04             .00            .08              .1 
V 

Fig.  272. 

INTERNAL-COMBUSTION  ENGINES 


405 


assumed  to  be  adiabatic,  although  this  would  not  be  absolutely 
true  in  any  real  case  on  account  of  the  thermal  properties  of  the 
metallic  walls.  The  ideal  process  is  represented  by  the  adiabatic 
compression  line  da,  corresponding  to  the  similar  line  in  Fig.  26, 
page  94. 

At  this  point  a  the  charge  is  ignited  by  an  electric- spark,  or 
other  means,  and  it  may  be  assumed  to  burn  completely  with 
the  piston  stationary.  This  would  cause  an  increase  in  tem- 
perature and  pressure  corresponding  to  the  ideal  isovolumic 
addition  of  heat,  as  shown  by  the  line  ab,  Fig.  272. 

The  piston  will  then  make  a  third  stroke,  being  driven  out 
by  the  high-pressure  gas  expanding  according  to  the  curve  be, 
which  may  be  considered  an  adiabatic. 

In  the  ideal  case  heat  would  be  given  to  the  cold  body  accord- 
ing to  process  cd,  while  the  volume  remained  constant,  but  in 
the  actual  case  the  exhaust  valve  E,  in  Fig.  271,  is  opened, 
allowing  the  high-pressure  gas  to  expand  into  the  atmosphere 
until  the  pressure  in  the  cylinder  falls  to  d. 

During  the  fourth  stroke  the  returning  piston  expells  the  remain- 
ing gas  according  to  the  line  de,  and  at  e  the  starting  conditions 
are  restored,  with  the  clearance  space  filled  with  burnt  gases  at 
atmospheric  pressure. 

(c)  Although  four  strokes  are  required  to  complete  the  prac- 
tical cycle,  the  work  area  under  the  line  ed  cancels  that  under  de; 
thus  the  ultimate  result  is  the  development  of  a  cycle  inclosing 
the  work  area  abcda,  exactly  as  in  the  ideal  Otto  engine  discussed 
in  Section  56,  page  94. 

The  two  strokes  corresponding  to  ed  and  de  are  really  pumping 
strokes,  used  to  draw  in  the  new  charge  of  combustible  and  to 
expel  the  burnt  gases.  They  are,  therefore,  necessitated  by  prac- 
tical considerations,  though  not  essential  to  the  ideal  cycle. 

(d)  A  real  engine  of  this  type  is  shown  semi-diagrammatically 
in  Fig.  273.     The  cylinder  head  has  been  broken  away  to  show 
the  valves,  which  correspond  exactly  to  valves  /  and  E  of  Fig.  271. 
Instead  of  using  a  mixture  reservoir,  assumed  in  the  ideal  case, 
the  real  engine  forms  its  own  mixture  during  the  suction  stroke, 
drawing  the  constituents  through  the  pipes  in  the  figure. 

The  cylinder  and  cylinder  head  of  the  real  engine  are  water- 
jacketed  to  prevent  overheating  of  the  metal. 

The  valves  in  this  case  are  positively  operated  by  linkage 


406 


HEAT-POWER  ENGINEERING 


(not  shown)  moved  by  cams  on  the  "  half-time  shaft,"  or  "  cam 
shaft,"  shown  along  the  side  of  the  engine.  This  shaft  is  driven 
by  gears  from  the  crank  shaft,  the  gears  being  so  proportioned 
as  to  give  the  cam  shaft  one  revolution  for  every  two  revolutions 
of  the  crank  shaft. 


Fig.  273. 

198.  The  Air  Card,  (a)  The  series  of  operations  j  ust  described 
cannot  be  carried  out  perfectly  in  any  real  engine;  thus  the 
picture  of  what  actually  occurs  in  the  working  cylinder  is  quite 
different  from  Fig.  272. 

(b)  The  losses  in  the  cylinder  are  commonly  determined  by 
comparing  the  actual  diagram  with  the  diagram  of  an  ideal  Otto 
cycle  with  air  as  the  working  substance.     This  ideal  diagram  is 
also  called  the  "  air  card,11  or  "  air  diagram,11  and  it  is  constructed 
for  an  engine  like  that  shown  in  Fig.  271,  operating  as  described 
in  the  last  section,  but  with  air  only  in  the  cylinder. 

Referring  to  Fig.  272,  it  is  assumed  that  at  the  point  d  the 
clearance  and  displacement  volumes  are  filled  with  air  at  atmos- 
pheric pressure  and  temperature;  that  the  compression  da  is 
adiabatic;  that  at  a  heat  is  added  equal  to  that  which  would  be 
liberated  by  complete  burning  of  the  combustible  mixture  used 
per  cycle  in  the  real  engine;  that  from  b  the  expansion  is  adia- 
batic to  c\  and  that  the  heat  is  then  removed,  as  in  the  ideal 
case,  until  the  air  returns  to  starting  conditions  at  d. 

(c)  The  pressure  at  a  can  be  found  from  Eq.  (45  b)  and  the 
temperature  can  then  be  computed  from  Eqs.  (51)  and  (52). 


INTERNAL-COMBUSTION  ENGINES 


407 


The  height  of  the  point  b  is  obtained  thus:  First  find  the  theo- 
retical temperature  to  which  this  quantity  of  heat  would  raise  the 
charge  of  air,  with  heating  taking  place  at  constant  volume,  and 
with  specific  heat  of  air  constant;  then  determine  the  corre- 

PaVa          PbVh 

spending  pressure  Pb  from  the  relation     "      =  •   - 

J-  a  lb 

199.   Real  Indicator   Card  for  Four- Stroke   Cycle,      (a)  In 

Fig.  273  is  shown  a  real  engine  with  the  cylinder  surrounded 
by  a  water  jacket  to  prevent  overheating  of 
the  metallic  walls.  Fig.  274  shows  another 
engine  in  which  the  cylinder  is  covered  by 
ribs  presenting  large  radiating  surface  so 
that  air  may  be  the  cooling  medium  instead 
of  water.  The  actual  cards  obtained  from 
such  engines  differ  in  many  respects  from 
the  ideal  air  card  just  discussed,  because 
of  (i)  chemical  and  physical  properties  of 
the  real  working  substances;  (2)  thermal 
properties  of  the  metallic  parts  of  the  en- 
gine; and  (3)  mechanical  faults,  such  as 
leaking  piston  and  valves.  The  variations 
are  shown  in  Fig.  275,  in  which  the  real 

card  (full  lines)  has  been  superimposed  on  the  ideal  diagram 
(dotted).  Parts  of  the  real  card  have  here  been  overdrawn  to 
accentuate  the  variations. 

(b)  Starting  at  the  end  c  of  the  expansion  line,  in  the  ideal 
case  with  the  mechanism  of  Fig.  271,  the  exhaust  valve  would 
be  opened  to  allow  the  charge  of  the  preceding  cycle  to  escape 
into  the  exhaust  pipe.  In  the  real  case,  however,  this  valve  must 
start  to  open  before  the  end  of  the  stroke,  say  at  c',  which  is 
usually  at  from  85  to  90  per  cent  of  the  out-stroke.  This  is  neces- 
sary so  that  the  valve,  which  cannot  be  opened  instantly  to  its 
full  extent,  may  have  time  to  open  fully  before  the  end  of  the 
stroke  is  reached;  and  because  the  gas  in  the  cylinder,  due  to 
its  inertia,  takes  an  appreciable  time  to  pass  through  the  exhaust 
valve  despite  the  fact  that  the  gas  pressure  of  from  15  to  35  pounds 
or  more  above  the  atmosphere  is  available  to  accelerate  it. 

From  c'  the  expansion  line  drops  rapidly  to  the  end  of  the 
stroke,  both  because  additional  space  is  vacated  by  the  piston 


Fig.  274. 


4o8 


HEAT-POWER  ENGINEERING 


as  it  continues  outward,  and  because  of  the  exit  of  gas  from  the 
cylinder. 

(c)  The  line  d'e'  is  higher  than  the  ideal  exhaust  line  de. 
This  is  due  to  the  pressure  difference  necessary  to  cause  the  flow 
of  gas  through  the  exhaust  valve  and  pipe  to  the  atmosphere. 
As  the  area  opened  by  the  valve  is  limited  by  practical  consider- 
ations, a  high  average  velocity  of  gas  flow  through  this  valve  is 


P400 


Fig.  275. 

necessary  in  order  to  empty  the  cylinder  in  the  available  time. 
This  velocity  varies  from  80  to  125  feet  or  more  per  second,  and 
to  produce  it  the  exhaust  pressure  line  d'e'  must  be  from  one  to 
three  pounds  above  atmospheric.  Instead  of  being  straight, 
this  line  is  generally  more  or  less  wavy  because  of  the  inertia  of 
the  gases. 

(d)  At  e',  with  the  piston  at  the  end  of  the  stroke,  the  clear- 
ance is  filled  with  products  of  combustion  at  a  pressure  slightly 
above  atmospheric  and  at  a  temperature  probably  700°  to  900° 
Fahr.  As  the  piston  starts  on  the  "  suction  stroke,"  these 
gases  expand  to  some  pressure  /,  from  one  to  six  pounds  below 
that  of  the  mixture  supply  (which  is  usually  at  atmospheric 
pressure),  before  the  new  charge  begins  to  flow  through  the  open 
inlet  valve  into  the  cylinder.  This  flow  continues  as  the  piston 
moves  out  until  the  end  of  the  stroke  is  reached  at  g,  when  the 
cylinder  is  filled  with  a  mixture  of  the  new  charge  and  the 


INTERNAL-COMBUSTION  ENGINES  409 

burnt  gas  previously  left  in  the  clearance.     This  "  suction  line,1" 
fg,  is  only  approximately  straight  and  horizontal. 

Evidently  during  both  the  exhaust  and  the  suction  strokes  the 
piston  must  do  work  on  the  gas,  and  this  decreases  the  power  that 
the  engine  can  deliver. 

(e)  The  compression  line  gaf  is  generally  below  da  (i)  because 
compression  begins  at  g  with  pressure  below  atmospheric;   (2) 
because  the  physical  properties  (7,  etc,)  of  the  real  mixture  are 
different  from  those  assumed  for  air  (3)  because  the  process  is 
not  adiabatic,  for  there  is  heat  interchange  between  the  gas  and 
the  walls  of  the  piston,  cylinder,  and  head;  and  (4)  because  of 
leakage  past  piston  and  valves.     This  process  is  generally  inter- 
mediate between  an  adiabatic  and  an  isothermal. 

(f)  At  or  near  a'  ignition  occurs,  and  as  it  actually  takes  an 
appreciable  time  for  the  flame  to  spread  throughout  the  mixture, 
and  as  the  piston  does  not  remain  stationary  at  the  end  of  the 
stroke  during  the  complete  process  of  combustion,  the  sloping 
ignition  line  a'b'  results,  instead  of  the  vertical  line  ab  of  the 
ideal  process.     Combustion  is  seldom  complete,  even  when  the 
highest  pressure  is  reached,  hence  heat  is  still  being  added  when 
expansion  starts. 

(g)  The  pressure  does  not  rise  as  high  as  the  ideal  value  b, 
presumably  because  (i)  the  initial  pressure  a!  is  less  than  the 
ideal  at  a;  (2)  the  movement  of  the  piston  increases  the  volume 
during  combustion;  (3)  the  average  specific  heat  of  the  mixture 
is  different  from  that  assumed  for  air  and  increases  as  the  tem- 
perature rises;  (4)  the  surrounding  metallic  walls  absorb  some 
of  the  heat  generated;  (5)  the  chemical  reactions  accompanying 
combustion  may  result  in  products  occupying  less  volume  than 
the  original  mixture;  (6)  there  may  be  a  certain  amount  of  dis- 
sociation at  the   higher   temperatures;   and   (7)   there  may  be 
leakage  past  the  piston  and  through  the  valves. 

(h)  The  expansion  line  is  at  first  generally  above  an  ideal 
adiabatic  curve  b'l  because  of  "  after  burning,'"  or  the  continu- 
ation of  combustion,  which  usually  adds  heat  in  excess  of  that 
absorbed  by  the  metal  walls  and  that  converted  into  external 
work.  Later,  as  the  motion  of  the  piston  continues,  the  relatively 
cooler  cylinder  walls  are  uncovered  and  they  rapidly  absorb  heat 
from  the  gas,  causing  the  expansion  line  to  drop  below  the  adia- 
batic. 


4io-  HEAT-POWER  ENGINEERING,. 

(i)  During  part  of  the  compression,  and  all  of  the  combustion 
and  expansion,  heat  is  absorbed  by  the  inclosing  metallic  walls, 
from  which  part  of  it  is  carried  away  by  the  water  or  air  jacket. 
This  is  a  direct  loss,  but  it  is  necessary  in  order  to  prevent  over- 
heating the  metal. 

(j)  During  the  suction  stroke  the  incoming  gas  receives  heat 
from  the  confining  walls  and  from  the  exhaust  gas  still  remain- 
ing in  the  clearance  space,  until  at  the  end  of  the  stroke  the  gas 
and  inner  surface  of  the  walls  are  probably  at  nearly  the  same 
temperature.  Because  of  the  expansion  of  the  gas  due  to  this 
temperature  (which  is  often  from  700°  to  900°  Fahr.),  and  because 
of  the  reduction  of  pressure  below  atmospheric  during  the  suc- 
tion stroke,  the  weight  of  fresh  mixture  drawn  in  is  reduced,  and 
hence  less  than  the  theoretical  work  per  cycle  is  done  in  a  given 
cylinder. 

200.  Losses  in  the  Four-Stroke-Cycle  Engine,  (a)  A  com- 
plete analysis  of  all  the  losses  in  the  cylinder  of  an  internal-com- 
bustion engine  would  be  very  complicated,  and  is  as  yet  unsat- 
isfactory because  of  the  lack  of  experimental  data.  For  the 
purposes  of  this  book,  it  will  serve  to  indicate  the  principal 
sources  of  loss  and  to  treat  them  qualitatively  rather  than  quanti- 
tatively. 

(b)  The  Otto  cycle  efficiency  is  from  Eq.  (81) 


It  is  seen  to  be  dependent  only  on  the  compression  ratio  ( Va'/  Vg), 
which  the  designer  can  control,  subject  to  practical  considera- 
tions, by  the  selection  of  proper  clearance  volume,  Va'.  Thus 
theoretically,  nothing  is  lost  by  the  low  pressure  or  high  tem- 
perature at  g. 

(c)  Section  199  (j),  however,  showed  that  the  actual  weight 
of  fresh  charge  drawn  into  the  cylinder  during  the  suction  stroke 
is  always  less  than  the  theoretical,  and  this  of  course  reduces  the 
power  developed. 

Let  7.'  be  the  volume  corresponding  to  the  actual  weight  of 
gas  drawn  in,  and  V.  be  that  equivalent  to  the  piston  displace- 
ment per  stroke,  both  volumes  being  measured  at  atmospheric 

pressure  and  temperature.    Then  the  ratio  (~\  is  called  the 


INTERNAL-COMBUSTION  ENGINES  411 

volumetric  efficiency.  In  practice  its  value  may  reach  90  per 
cent  in  well-designed  slow-speed  engines,  or  it  may  be  reduced 
by  high  speed  or  incorrect  design  to  50  per  cent  or  less.  Evi- 
dently, in  a  given  engine  the  amount  of  heat  liberated  per 
cycle  depends  on  the  volumetric  efficiency,  and  hence  for  definite 
power  output  a  lower  volumetric  efficiency  makes  necessary  larger 
cylinder  and  greater  cost  of  engine  unless  operated  so  as  to  give 
more  cycles  per  minute. 

(d)  The  effect  of  the  falling  of  the  real  compression  line 
below  the  adiabatic,  upon  the  performance  and  efficiency  of  the 
engine,  is  difficult  to  state  in  any  general  way.     Since  the  line 
lies  between  the  isothermal  and  adiabatic,   the  work  done  is 
slightly  less  than  that  which  corresponds  to  an  adiabatic  process, 
and  this  compensates  more  or  less  fully  for  the  loss  of  heat  which 
makes  this  line  fall  below  the  adiabatic,  and  for  the  correspond- 
ing lowering  of  the  efficiency. 

(e)  The  combustion  line  a'bf  represents  the  most  complicated 
process  in  the  cycle  and  is  the  most  difficult  to  investigate,  as 
the  phenomena  take  place  with  comparative  rapidity  and  vary 
with  the  character  of  the  mixture,  the  method  of  ignition,  the 
surface  form  of  the  combustion  space,  etc.     The  real  loss  during 
this  process  cannot  be  accurately  measured  by  comparison  with 
the  ideal  air  diagram,  but  could  be  determined  by  comparison 
with  a  card  drawn  for  the  working  substance  actually  used  in 
the  real  engine,  considering  specific  heats  variable  and  accounting 
for  any  other  theoretical  modifying  conditions.     As  this  would 
mean  a  different  standard  for  every  fuel,  and  for  every  different 
mixture   of  fuel   and  air,   the   "  air  standard  "   is  retained  for 
simplicity. 

In  considering  the  sloping  combustion  line  a'b',  it  is  again  a 
case  of  balancing  gains  and  losses.  The  piston  movement 
reduces  the  maximum  pressure  and  temperature,  thus  decreasing 
the  heat  lost  to  the  cylinder  walls,  but  this  is  offset  more  or  less 
completely  by  the  larger  surfaces  exposed  while  the  temperature 
is  high.  The  slope  which  will  give  the  highest  efficiency  cannot 
be  predicted,  but  usually  an  inclination  which  will  bring  the  top 
of  the  combustion  line  at  about  2  per  cent  of  the  stroke  seems  to 
give  the  best  results.  The  loss  of  area  between  the  real  and 
theoretical  combustion  lines  is  partly  compensated  by  the  broad- 
ening of  the  top  of  the  diagram.  This  change  in  form  of  the 


HEAT-POWER  ENGINEERING,- 


diagram  improves  the  mechanical  operation  of  the  engine  be- 
cause the  pressure  changes  are  less  sudden  and  less  intense. 

(f)  The  expansion  line  b'c'  generally  incloses  slightly  more 
area  than  the  adiabatic  b'l  (Fig.  275),  unless  the  engine  is  of 
such  proportions  as  to  expose  excessive  wall  area. 

By  opening  the  exhaust  valve  at  c',  as  in  Fig.  276  (a),  less  area 
of  diagram  is  usually  lost  than  if  the  opening  is  at  the  end  of 


Fig.  276. 

the  stroke,  as  in  Fig.  276  (b) ;  and  as  less  hot  gas  remains  in  the 
cylinder  the  tendency  to  overheat  the  metal  walls  is  reduced. 

The  actual  heat  interchanges  during  exhaust  are  problem- 
atical. The  enormous  rush  of  gas  through  the  exhaust  valve 
consumes  heat  which  is  lost  to  the  atmosphere,  but  there  is  a 
corresponding  gain  due  to  increased  volumetric  efficiency  result- 
ing from  contact  of  the  new  charge  with  cooler  walls. 

Quite  remarkable  success  has  been  achieved  by  engines  in 
which  cold  air  is  blown  through  the  cylinder  during  part  of  the 
exhaust  period.  This  operation  cools  the  walls  and  tends  to 
remove  the  burnt  gases  from  the  clearance  space,  and  hence  the 
charge  drawn  in  is  cooler  and  purer  than  in  the  ordinary  type  of 
engine.  Such  engines  are  known  as  "scavenging"  or  "positive 
scavenging  "  engines. 

201.   Requirements    for    High    Efficiency    of    Combustion. 

(a)  There  are  two  antagonistic  requirements  for  high  efficiency 
of  combustion:  (i)  The  final  compression  pressure  and  temper- 
ature (at  a',  Fig.  275)  must  be  high,  since  this  not  only  gives  high 
efficiency  theoretically  (see  Eq.  (80)),  but  also  because  experience 
shows  that  the  charge  is  often  more  readily  ignited  and  burned 
from  high  pressure.  The  limit  is  reached  when  the  pressure  is 
so  high  as  to  cause  "  preignition"  that  is,  spontaneous  ignition 
of  the  mixture  during  compression.  With  other  things  equal, 
the  greater  the  pressure  and  temperature  at  the  end  of  compres- 
sion, the  higher  will  be  the  final  temperature  at  V .  (2)  The 
maximum  temperature  attained  (at  the  point  bf)  should  be  as  low 
as  possible,  because  the  specific  heats  and  loss  of  heat  to  metallic 
walls  increase  rapidly  at  high  temperatures. 


INTERNAL-COMBUSTION  ENGINES  413 

(b)  These  two  requirements  for  high  actual  efficiency  can  be 
harmonized  in  practice  by  using  a  mixture  with  large  excess  of 
air.  This  may  be  highly  compressed  without  danger  of  preigni- 
tion;  it  burns  rapidly  enough  at  high  pressures  for  satisfactory 
combustion;  and,  because  of  the  excess  of  air  present,  the  final 
temperature  attained  is  comparatively  low. 

Unfortunately,  however,  the  mixture  which  gives  highest 
actual  efficiency  "  on  the  brake "  does  not  give  maximum 
possible  power  from  a  cylinder  of  given  size  operating  at  given 
speed ;  thus  there  is  a  tendency  to  operate  engines  with  mixtures 
"  richer  "  in  combustible  than  those  giving  the  highest  efficiency. 

202.  Indicated  Work  and  Power  of  the  Four-Stroke-Cycle 
Engine,  (a)  In  the  diagram  shown  in  Fig.  277,  with  the  "  lower 
loop  "  fghef  considerably  exaggerated, 
the  arrows  indicate  the  directions  in 
which  the  various  lines  are  traced. 

(b)  If  areas  on  a  PV-diagram  sur- 
rounded by  lines  generated  in  one  di- 
rection (here  clockwise)  represent  work 

done  upon  the  piston,  or  positive  work,  "~ ~ 

then  areas  inclosed  by  lines  of  reverse 

direction   (here  counter-clockwise)   indicate  work  done  by  the 

piston  upon  the  working  substance,  or  negative  work. 

Thus  the  work  represented  by  the  upper  area  or  "  loop," 
abcdea,  is  positive;  the  work  corresponding  to  the  "  lower  loop," 
fghef j  is  negative;  and  the  net  useful  work  on  the  piston  would 
be  represented  by  the  difference  between  these  areas. 

(c)  The  exact  interpretation  of  "indicated  power"  in  the 
case  of  a  four-stroke-cycle  gas  engine  is  still   unsettled.      All 
things  considered,  it  seems  best  to  calculate  i.h.p.  from  the  upper 
loop  alone.     Then  the  difference  between  the  i.h.p.  and  the  d.h.p. 
is  the  work  lost  in  overcoming  both  the  fluid  friction  and  the 
friction  of  the  mechanism. 

The  fluid-friction  loss  is  measured  by  the  area  of  the  lower 
loop;  it  would  equal  zero  with  frictionless  flow.  The  engine-friction 
loss  is  the  difference  between  the  total  friction  loss  and  that  due 
to  fluid  friction ;  it  would  equal  zero  with  a  frictionless  mechanism. 

(d)  The  mechanical  efficiency  is  the  ratio  .  h'P-     As  applied 
to  gas  engines,  it  includes  both  kinds  of  friction  loss  when  the 


4i4 


HEAT-POWER  ENGINEERING"' 


i.h.p.  is  computed  according  to  the  method  just  given.  It  is 
advisable  to  adhere  to  this  method  because  of  the  difficulty  of 
obtaining  the  correct  area  of  the  lower  loop. 

203.  The  Two-Stroke-Cycle  Otto  Engine,  (a)  Comparison 
of  single-cylinder  single-acting  Otto  engines  of  the  four-stroke- 
cycle  and  the  two-stroke-cycle  types  shows  that  in  the  former 
there  is  one  power  stroke  out  of  four,  while  in  the  latter  there  is 
one  power  stroke  out  of  two.  Hence  with  the  same  rotative 
speed  and  cylinder  dimensions  the  two-stroke-cycle  engine  theo- 
retically  should  give  twice  the  power  of  the  four- stroke-cycle 
engine,  and  should  require  much  less  flywheel  weight  to  main- 
tain the  same  degree  of  uniformity  in  rotative  speed. 

Moreover,  in  the  four-stroke-cycle  engine  the  mechanism,  which 
is  designed  for  very  high  pressures,  is  used  half  the  time  for  pump- 
ing gas  at  low  pressure  (while  forming  the  lower  loop  of  the 
diagram).  And  to  make  matters  still  worse,  the  density  of  the 
mixture,  and  therefore  the  weight  of  gas  drawn  in  per  cycle,  is 
reduced  by  heat  received  from  the  hot  cylinder  walls,  and  this 
increases  the  cylinder  size  for  a  given  power  output.  In  the 
two-stroke-cycle  engine,  on  the  other  hand,  a  separate,  specially 
designed  pump,  with  cool  walls,  may  be  used  more  effectively 
for  this  service. 

(b)  The  two-stroke-cycle  engine  is  represented  diagrammatic- 
ally  in  Fig.  278.  The  pump  cylinder  has  an  inlet  valve  A,  and 


To  Atmosphere 


Fig.  278. 

a  discharge  valve  7,  which  latter  also  serves  as  an  inlet  valve 
to  the  power  cylinder.  This  cylinder  has  a  nrig  of  portt,  E,  cut 
through  the  walls  at  such  a  point  that  the  piston,  by  uncovering 
them  near  the  end  of  its  stroke,  acts  as  an  exhaust  valve. 


INTERN  A  L-COMB  USTION  ENGINES 


415 


(a) 


(6) 

14.7  Lbs'.  sq.  in. 


(c)  Now  imagine  the  ideal  cycle  performed  without  mechani- 
cal or  thermal  loss  as  follows:  Consider  the  power  cylinder 
filled  with  mixture  at  atmospheric  pressure,  the  power  piston 
just  covering  the  exhaust  ports  E.  The  first  stroke  is  to  the  left, 
causing  compression  of  the  charge  according  to  the  line  d'a  in 
Fig.  279  (a).  Combustion  produces  the 
line  ab.  Expansion  during  the  second 
stroke  occurs  according  to  the  line  bc\ 
and  when  the  piston  passes  the  ports,  J3, 
exhaust  occurs  according  to  the  line  cd, 
thus  nearly  completing  the  cycle  in  the 
power  cylinder.  Meanwhile  the  pump 
piston  has  moved  down  and  drawn  in 
from  the  reservoir  a  charge  of  mixture 

sufficient  to  fill  the  power  cylinder,  the  theoretical  process  being 
represented  by  ef  in  Fig.  279  (b).  The  valve  A  is  then  closed, 
and  after  the  pressure  in  the  power  cylinder  has  dropped  to 
atmospheric  at  d  in  Fig.  279  (a),  the  valve  /  is  opened  and  the 
pump  piston  is  quickly  raised,  driving  the  mixture  into  the  power 
cylinder,  according  to  the  theoretical  line  fe.  While  this  is  occur- 
ring the  power  piston  moves  from  d  to  d' '. 

In  the  ideal  case  the  charge  entering  the  power  cylinder  will 
drive  the  remaining  exhaust  gases  out  through  the  ports  as  it 
moves  down  the  length  of  the  cylinder  in  a  solid  column,  and 
arrive  at  the  exhaust  ports  just  as  the  returning  power  piston, 
covers  them.  The  power  cylinder  is  thus  charged  with  a  com- 
bustible mixture,  with  volume  as  shown  at  d' ,  at  atmospheric 
pressure,  and  with  the  conditions  assumed  at  starting. 

The  theoretical  pumping  work,  represented  by  the  area  under 
ef  minus  the  area  under  fe,  is  zero,  as  in  the  case  of  the  ideal 
four-stroke  cycle.  In  the  power  •  cylinder  the  Otto  cycle  is 
followed  except  at  the  end  cdd',  which  is  modified  for  practical 
reasons. 

(d)  The  differences  between  the  actual- work  diagram  and 
the  ideal  Otto  cycle  are  quite  similar  to  those  occurring  in  the 
four-stroke-cycle  engine,  and  arise  largely  from  the  same  causes. 

The  pump  does  not  actually  operate  in  the  ideal  manner.  It 
is  usually  driven  from  a  crank  on  the  engine  shaft,  and  in  con- 
sequence the  gas  must  be  pumped  to  some  intermediate  reservoir, 
where  it  must  be  maintained  at  a  pressure  of  from  0.5  to  7  pounds 


416 


HEAT-POWER  ENGINEERING  .- 


above  atmospheric  in  order  to  fill  the  power  cylinder  in  the 
short  time  available  after  the  inlet  valve  opens.  Energy  is  not 
only  lost  in  overcoming  the  pump  friction  and  resistance  to  flow, 
but  is  also  expended  in  compressing  the  mixture  in  the  pump 
cylinder.  The  work  done  on  the  gas  is  shown  by  the  area  of 
the  actual  pump  card. 

Because  of  its  great  velocity,  the  entering  charge  generally 
mixes  more  or  less  with  the  burnt  gases,  and  some  portion  usu- 
ally escapes  through  the  exhaust  ports  before  they  are  covered. 

Although  theoretically  the  two-stroke-cycle  engine  would 
develop  twice  the  power  given  by  a  four-stroke-cycle  engine  of 
the  same  size  and  r.p.m.,  the  actual  ratio  is  usually  from  1.4  to 
1.6,  owing  to  the  losses  due  to  the  method  of  operation. 


Fig.  280. 

(e)  In  some  two-stroke-cycle  engines  the  power  cylinder  is 
first  scavenged  by  admitting  air  under  pressure  ahead  of  the 
mixture  so  that  none  of  the  fresh  charge  escapes  with  the  ex- 
haust. The  saving  thus  effected  is,  however,  offset  more  or  less 
completely  by  the  necessity  of  using  two  pumps  instead  of  one, 
with  increased  complexity  and  greater  expenditure  of  energy 
in  pumping.  One  engine  of  this  type  is  shown  semi-diagram- 
matically  in  Fig.  280  and  is  known  as  the  Koerting  design. 

In  some  single-acting  engines  operating  on  the  two-stroke 
cycle,  the  mixture  is  first  admitted  to  the  crank  case,  as  in 


INTERNAL-COMBUSTION  ENGINES 


417 


Fig.  281  (a),  where  it  is  compressed  by  the  under  side  of  the  piston 

acting  as  a  pump  during  the  down  stroke.     The  opening  of 

separate  inlet  and  exhaust  valves 

is  replaced  by  the  uncovering  of 

the  inlet  and  exhaust  ports  by  the 

piston  when  near  the  end  of  its 

stroke,  as  shown  in  Fig.  281  (6). 

The  fresh  chargeenteringthrough 

the  inlet  port  is  so  baffled  as  to 

assist  in  driving  the  burnt  gases 

toward  the  exhaust  port. 

204.     The     Diesel      Engine.  Fig.  28l. 

(a)  Engines  commercially  known 

by  this  name  operate  approximately  on  the  cycle  discussed  in 
Section  58,  and  shown  in  Fig.  29.  The  real  cycle  may  be  .com- 
pleted in  either  two  or  in  four  strokes. 

(b)  The  mechanical  operations  within  the  power  cylinder  of 
the  real  engines  are  very  similar  to  those  of  the  Otto  engine. 
With  four-stroke  operation  the  suction  stroke  charges  the  cylinder 
with  air,  which  on  the  return  stroke  is  compressed  into  a  clear- 
ance volume  so  small  that  the  terminal 
pressure  is  very  high,  equal  to  400  to 
500,  or  more,  pounds  per  square  inch, 
with  correspondingly  high  temperature. 
Just  before,  or  when,  the  piston  reaches 
the  end  of  the  compression  stroke,  a 
small  quantity  of  finely  atomized  liquid 
fuel  is  blown  into  the  clearance  space 
by  means  of  air  at  very  high  pressure. 
The  fuel  immediately  ignites,  due  to 


Fig.  282. 


the  high  temperature  of  the  air  that  was  compressed  in  the 
clearance  space  by  the  engine  piston.  The  combustion  which 
ensues  continues  a  little  longer  than  the  period  of  injection.  As 
the  moving  piston  increases  the  volume  a  little  faster  than  the 
gas  tends  to  expand  under  the  action  of  the  heat  developed,  and 
as  heat  is  lost  in  the  cylinder  walls,  the  upper  line  of  the 
card  slopes  slightly,  as  in  Fig.  282.  In  this  figure  the  ideal  and 
real  diagrams  are  shown  superimposed,  with  the  lower  loop 
exaggerated. 


4 1 8  HEA  T-POWER  ENGINEERING  '' 

(c)  Within  the  past  few  years  several  designs  of  two-stroke- 
cycle  engines  operating  on  this  cycle  have  been  made,  and  some 
of  these  give  considerable  promise  of  success. 

205.  Modifications   to  Suit   Different   Fuels.     Theoretically, 
the  internal  combustion  engines  just  discussed  can  use  any  fuel 
that  can  be  introduced  as  gas  or  vapor  (or  even  as  finely  divided 
solid)  in  a  combustible  mixture.     In  practice  the  fuels  used  are 
the  combustible  commercial  gases,  petroleum  products,  the  by- 
product tars  from  gas  works  and  such,  and  alcohol.     It  is  gen- 
erally necessary  to  make  the  design  of  some  parts  of  the  engines 
and  auxiliaries  special  for  each  different  fuel,  and  as  a  result 
commercial  engines  are  often  named  after  the  fuel  used;  thus 
there  are  "  producer-gas  engines,"  "  gasoline  engines,"  "  kerosene 
engines,"  etc.     The  chief  differences  between  types  are  given  in 
the  following  sections. 

206.  Compression  and  Maximum  Pressures,     (a)  In   prac- 
tice one  of  the  most  important  considerations  is  the  final  com- 
pression pressure.     In  theory  the  thermal  efficiency  will  increase 
with  the  final  compression  pressure,  and  within  limits  this  is 
true  in  the  real  engines  (see  Section  219). 

It  is  found,  however,  that  compression  above  certain  limiting 
pressures  causes  spontaneous  ignition,  or  preignition,  which  tends 
to  stop  the  engine. 

With  some  fuels  the  spontaneous-ignition  temperature  and 
pressure  are  so  high  that  the  compression  limit  is  not  set  by 
preignition,  but  by  commercial  considerations.  Thus,  with  very 
high  compression  the  "  up-keep  "  may  exceed  the  gain  due  to 
increased  thermal  efficiency.  For  example,  engines  using  blast- 
furnace gas  usually  compress  only  to  about  175  pounds  gauge, 
or  even  less,  although  the  preignition  pressure  is  much  higher, 
and  the  thermal  efficiency  of  engines  compressing  to  200  pounds 
has  been  shown  to  be  better. 

(b)  The  usual  compression  pressures  (terminal)  in  the  differ- 
ent types  of  engines  as  now  designed  are  given  in  Table  XL 
This  shows  that  the  lowest  compression  pressures  are  used  with 
the  fuels  high  in  hydrocarbons,  while  high  pressures  are  used 
with  fuels  low  in  these  constituents. 

High   compression   increases   the  thermal  efficiency,  not  only 


INTERNAL-COMBUSTION  ENGINES 


419 


because  it  improves  the  theoretical  cycle,  but  also  because  it  aids 
ignition  and  makes  combustion  more  rapid.  This  is  particularly 
true  with  the  weaker  fuels,  like  blast-furnace  gas. 

TABLE  XL  —  COMMON   COMPRESSION   PRESSURES. 


Fuel. 

Comp.  Press. 
Lbs.  above 
Atmos. 

Fuel. 

Comp.  Press. 
Lbs.  above 
Atmos. 

Kerosene  

50  to     75 

Producer  gas  

I2O  to   150 

Gasoline  

60  to     75 

Blast-furnace  gas  

140  to  175 

Illuminating  gas 

70  to     QO 

Alcohol 

140  to  180 

Natural  gas  

100  to  125 

(c)  In  theory,  with  other  things  equal,  the  greater  the  calorific 
value  of  a  charge  and  the  higher  the  temperature  before  igni- 
tion, the  higher  will  be  the  maximum  temperature  and  pressure 
attained  by  the  combustion.  In  practice  this  is  modified  by 
the  considerations  brought  out  in  preceding  sections  of  this 
chapter. 

In  general,  engines  in  which  the  maximum  pressure  is  high 
because  of  rich  mixtures  and  high  compression  must  be  stronger 
and  heavier  than  those  using  "weak"  mixtures  and  low  com- 
pressions. 


CHAPTER   XXV. 

INTERNAL-COMBUSTION  ENGINES  (cont.). 

MECHANICAL  FEATURES. 

207.  Cylinder  Arrangement,  (a)  In  the  theoretical  discus- 
sion of  preceding  chapters,  only  single-cylinder,  single-acting 
engines  were  considered.  In  practice  there  are  three  principal 
reasons  for  making  "  multi-cylinder  units  "  and  for  making 
"  double-acting  engines."  These  are: 

(1)  The  turning  effort  at  the  shaft  of  an  internal-combustion 
engine  with  one  single-acting  cylinder  is  very  uneven.      This 
can  be  partly  counteracted  by  the  use  of  a  very  heavy  flywheel, 
but  this  is  objectionable  for  several  reasons.     As  a  result,  both 
multi-cylinder  and  double-acting  constructions  are  used  to  give 
overlapping  cycles  and  therefore  more  even  turning  efforts. 

(2)  The  power  which  can  be  obtained  from  a  given  cylinder 
depends  upon  the  quantity  of  heat  which  can  be  liberated  in 
that  cylinder  by  combustion.     This,  in  turn,  depends  upon  the 
volume  of  mixture  which  can  be  contained  in  the  cylinder,  and 
hence   upon   the   cylinder   dimensions.     Experience   has   shown 
that  a  cylinder  diameter  of  from  42  to  45  inches  is  about  as  large 
as  is  commercially  advisable  with  present  methods  of  construc- 
tion and  with  the  materials  now  in  use.     As  the  length  of  the 
cylinder  cannot  be  increased  without  limit,  it  results  that  the 
maximum  power  that  can  be  obtained  per  cylinder  is  limited. 

A  single-acting  cylinder  can  be  constructed  to  develop  from 
500  to  700  horse  power,  and  when  larger  powers  are  required  per 
unit,  double-acting  or  multi-cylinder  constructions  must  be  used. 

(3)  Because   of    the    high   pressure   generated   in   gas-engine 
cylinders,  the  forces  transmitted  by  the  moving  parts  of  the 
engine  are  very  large,  and  these  parts  must  be  made  correspond- 
ingly large.     With  the  single-cylinder  construction,  the  unbal- 
anced forces  are  of  great  magnitude.      These  can  be  decreased 
by  a  proper  arrangement  of  several  cylinders. 

420 


INTERNAL-COMBUSTION  ENGINES  421 

(b)  The  attainment  of  a  more  even  turning  effort  than  is 
possible  with  a  single  cylinder  is  of  such  great  importance  that 
very  few  single-cylinder  engines  are  now  built  in  sizes  above 
50  horse  power,  and  they  are  seldom  used  in  sizes  above  about 
25  to  30  horse  power  excepting  for  work  where  close  regulation 
is  not  very  important. 

An  idea  of  the  handicap  under  which  internal  combustion 
labors  in  this  respect  can  best  be  obtained  by  a  comparison  with 
a  single-cylinder  double-acting  steam  engine.  To  produce  as 
many  impulses  in  a  given  time  as  an  engine  of  this  type,  a  single- 
acting  four-stroke-cycle  engine,  running  at  the  same  speed,  would 
require  four  cylinders;  if  double-acting,  two  cylinders  would  be 
needed.  The  two-stroke  cycle  construction  gives  the  same  num- 
ber of  impulses  as  does  a  steam  engine  of  the  same  type,  i.e., 
single-  or  double-acting. 

The  double-acting,  internal-combustion  engine,  however,  offers 
more  difficulties  in  construction  and  operation  than  does  a 
similar  steam  engine.  The  piston  and  piston  rod  must  be  water- 
cooled  in  order  to  prevent  overheating,  and  the  maintenance 
of  a  tight  piston-rod  packing  is  more  difficult  with  hot  gases  than 
with  steam. 

208.  Classification,  (a)  Like  steam  engines,  the  internal- 
combustion  engines  are  classified  in  a  number  of  ways.  The 
principal  designations,  and  a  brief  discussion  of  each,  are  given 
in  the  following  paragraphs.  Such  things  as  center-crank  and 
side-crank  construction,  and  right-  and  left-hand  arrangement  are 
common  to  all  kinds  of  engines  and  need  not  be  further  considered. 

(b)  Internal-combustion  engines  are  made  both  vertical  and 
horizontal.  For  sizes  up  to  about  500  to  700  horse  power  either 
construction  is  used,  each  having  certain  advantages  and  certain 
disadvantages.  Above  700  horse-power  commercial  economy 
generally  dictates  double-acting  cylinders.  Very  few  vertical 
engines  have  been  built  double-acting,  as  there  is  considerable 
difficulty  in  accommodating  the  valves  for  the  lower  cylinder  end 
in  this  construction,  hence  the  larger  powers  are  nearly  always 
supplied  by  horizontal  engines.  The  vertical  engine  has  the 
advantage  of  occupying  much  less  floor  space  than  the  hori- 
zontal and  can  be  mounted  on  a  less  massive  foundation.  It 
is  generally  operated  at  a  higher  speed,  particularly  in  the  larger 


422 


HEAT-POWER  ENGINEERING 


sizes,  and  is  usually  built  with  an  inclosed  crank  case  so  that 

lubrication  can  be  somewhat  simplified. 

(c)  The  cylinders  of  multi-cylin- 
der vertical  engines  are  practically 
always  arranged  side  by  side  and 
as  close  to  one  another  as  possible. 
These  engines  are  designated  as 
two-cylinder  vertical,  three-cylinder 
vertical,  etc.  A  three-cylinder 
vertical  engine  is  shown  in  Figs. 
283  and  284.  With  horizontal 
engines,  however,  the  cylinders 
are  often  widely  separated,  giving 


Fig.  283. 


Exhaust 


what   is   called   a   twin   engine. 

It  is  also  very  common  practice  to  place  two  horizontal  cylin- 
ders with  their  axes  coinciding. 
When  so  arranged,  the  engine 
is  called  a  tandem.  A  com- 
bination known  as  a  twin- 
tandem  double-acting  is  shown 

in   Fig.   285.  MValve 

(d)  Internal-combustion  en-   Mixing vaive1 
gines  are  sometimes   classified 
according  to  the  use  to  which 

they  are  put.  Thus  there  are 
stationary  engines,  stationary 
electric  lighting  engines,  marine 
engines,  automobile  engines, 
etc.  From  this  classification 
has  sprung  another,  an  engine 
of  one  type  being  designated 
by  its  type  name,  even  when 
used  for  a  different  purpose. 
There  are  thus  "  auto-type 
marine  engines  "  and  "  marine- 
type  stationary  engines." 

(e)  Since    certain    modifica- 
tions, or  different  fittings,  are 


Fig.  284. 


necessary  with  different  fuels,  internal-combustion  engines  are 
sometimes  classified  according  to  the  fuel  which  they  are  intended 


INTERNAL-COMBUSTION  ENGINES 


423 


to  use.     Thus  there  are  kerosene  engines,  gasoline  engines,  illumi- 
nating-gas engines,  producer-gas  engines,  etc. 

(f)  These  engines  are  also  occasionally  classified  on  the  basis 
of  the  type  of  governing  used  (see  sec.  212).  Thus  there  are  hit- 
and-miss  engines,  throttling  engines,  etc. 


Fig.  285. 

209.  Methods  of  Producing  Combustible  Mixtures,     (a)  With 
fuels  initially  gaseous,  a  "  mixing  valve  "  is  generally  used  to 
control  the  proportions  of  fuel  and  air,  the  two  gases  being  made 
to  mix  intimately  either  before  or  during  entrance  to  the  cylinder. 
This  mixing  valve  may  be  incorporated  with  the  inlet  valve  or 
it  may  be  separate  and  at  some  distance  from  it.     Examples  of 
both  types  are  given  later. 

(b)  Fuels  initially  liquid  must  either  be  atomized  or  vaporized 
and  mixed  with  air  to  support  combustion.  With  the  more 
volatile  liquid  fuels,  such  as  gasoline  and  alcohol,  the  process 
generally  takes  place  outside  of  the  engine  cylinder  in  a  "  carbu- 
retor"; the  mixture  then  passes  to  the  cylinder  as  in  the  case  of 
fuel  initially  gaseous.  With  the  less  volatile  liquid  fuels,  like 
kerosene  or  crude  oil,  vaporization  and  mixing  are  more  difficult, 
and  generally  take  place  within  the  engine  cylinder,  the  fuel 
being  sprayed  in  either  by  pump  or  air  pressure  and  being 
vaporized  by  heat  from  hot  walls  or  gas.  Examples  of  such 
devices  are  given  later. 

210.  Carburetors,     (a)  When  an  engine  uses  a  volatile  liquid 
fuel,  like  gasoline  or  alcohol,  it  is  customary  to  mix  the  fuel  vapor 
and  air  outside  of  the  cylinder  in  a  carburetor,  in  which  air, 
which  may  or  may  not  be  previously  heated,  is  brought  into 


424 


HEAT-POWER  ENGINEERING 


intimate  contact  with  the  liquid  and  becomes  charged  with  the 
vapor. 

(b)  A  great  variety  of  types  of  carburetors   has   been   per- 
fected and  used.     Thus  there  are  bubbling  carburetors,  in  whkh 
some  or  all  of  the  air  is  made  to  pass  or  bubble  through  the 
volatile  liquid,   on  its  way   to   the  engine.     There  are  surface 
carburetors,  in  which  the  volatile  liquid  is  spread  over  screens, 
marbles,  or  anything  else  which  will  give  a  large  wetted  surface 
over  which  the  air  may  be  drawn.     Wick  carburetors  have  also 
been  used.     In  these  the  liquid  is  drawn  up  into  wicks  by  capil- 
lary action,  and  the  air  passing  over  the  surface  of  the  wicks 
vaporizes  part  of  the  exposed  liquid. 

(c)  Practically  the  only  type  now  used  in  this  country  is  the 
jet  carburetor.     This  apparatus  is  made  in  many  forms,  but  the 
fundamental  principle  of  all  is  the  same.     A  fine  jet  of  gasoline 
is  injected  into  the  air  pipe  and  generally  only  during  the  suction 
stroke.     The  impelling  force  is  usually  either  the  pressure  due  to 
a  slight  head  of  gasoline  or  the  difference  between  suction  pres- 
sure and  atmospheric  pressure,  or  this  difference  augmented  by 
the  suction  effect  of  rapidly  moving  air  upon  a  nozzle  immersed 
in  it. 

(d)  One  of  the  most  common  types  of  jet  carburetor,  known  as 
a  carbureting  valve,  is  shown  in  Fig.  286.     The  valve  is  some- 
times  the   inlet   valve  of   the 
cylinder,  but  more  often  it  is  a 
separate  valve  through  which 
air  is  admitted  to  the  mixture 
pipe  leading  to  the  main  inlet 
valve.     A  small  hole  is  drilled 
in  the  seat  of  the  carbureting 
valve  in  such  a  position  that  it 
is    closed   when    the    latter   is 
seated.      When  the  valve  rises 

(automatically)  to  admit  air  to  the  engine,  the  liquid  under  slight 
pressure  issues  from  the  hole  in  a  very  small  stream,  which  mixes 
with  the  air  and  is  partly  or  wholly  vaporized  before  the  mixture 
enters  the  cylinder. 

(e)  Another  form  of  jet  carburetor  is  shown  in  Fig.  287.     The 
liquid  is  maintained  at  such  a  height  that  its  surface  almost 
reaches  the  tip  of  the  spray  or  injection  nozzle  when  quiescent. 


Fig.  286. 


INTERN  A  L-COMB  USTION  ENGINES 


425 


The  air  passing  around  this  nozzle  on  its  way  to  the  engine  creates 
a  partial  vacuum  at  the  nozzle,  which  vacuum  augments  the 
lowering  of  the  pressure  caused  by  suction  in  the  engine.  The 
air  pressure  on  the  surface  of  the  liquid  in  the  small  tank  then 
forces  a  fine  jet  out  of  the  nozzle,  and  this  is  picked  up  by  the 
surrounding  air.  The  throat,  or  Venturi  tube,  increases  the 
velocity  of  the  air  flowing  through  it,  which  materially  assists  in 
picking  up  and  carrying'  the  liquid  during  vaporization.  This 
type  is  commonly  used  on  stationary  engines,  the  liquid  level 
being  maintained  by  a  direct-connected  pump  and  overflow  as 
shown. 


Fig.  287. 


Fig.  288. 


(f)  In  Fig.  288  is  shown  a  type  of  float-feed  carburetor.     This 
is  similar  in  action  to  that  last  described,  the  principal  difference 
being  the  float  for  maintaining  the  proper  liquid  level.     This 
operates  by  opening  and  closing  the  small  valve  shown  as  the 
liquid   level  sinks  and   rises,  the  liquid  being  supplied  to  this 
valve  under  pressure. 

This  type  of  carburetor  is  most  common  on  automobile  and 
marine  engines,  the  central  float,  which  maintains  approximately 
the  correct  level  despite  tipping  of  the  carburetor,  and  the 
compact  structure  both  recommending  it  for  such  purposes. 

(g)  When  an  engine  is  run  at  widely  varying  speeds,  it  is  a  very 
difficult  matter  to  adjust  a  carburetor  of  the  type  last  shown  to 
give  a  suitable  mixture  under  all  conditions.     If  the  mixture  is 
correct  at  low  speeds,  it  is  apt  to  be  too  rich  at  high  speeds. 
This  is  overcome  by  introducing  an  auxiliary  air  valve  between 
the  spray  nozzle  and  the  engine     This  valve,  operating  auto- 
matically or  under  hand  control,  admits  air,  which,  combining 
with  the  over-rich  mixture,  forms  one  of  correct  proportions. 


426 


HEAT-POWER  ENGINEERING  , 


Similar  devices  are  sometimes  necessary  with  the  carburetor 
used  on  engines  which  run  at  a  constant  speed,  being  used  to 
make  the  adjustment  of  the  carburetor  easier  or  more  certain. 

211.  Treatment  of  Heavy  Oils,  (a)  The  use  of  fuels  like 
kerosene,  distillate,  crude  oil,  and  such,  presents  greater  difficulty 
than  the  utilization  of  gasoline  or  alcohol.  Kerosene  can  be 
handled  more  or  less  satisfactorily  with  carburetors  similar  to 
those  described,  but,  being  less  volatile  than  gasoline,  the  action 


Fig.  289. 

is  not  so  perfect.  It  is  generally  necessary  to  preheat  the  air 
and  to  jacket  the  mixture  pipe  with  hot  jacket  water,  or  with 
exhaust  gases.  Even  with  these  additions,  it  is  often  found 
difficult  to  operate  satisfactorily,  and  most  carbureting  kerosene 
engines  are  arranged  to  spray  water  into  the  cylinder  or  to  satu- 
rate the  mixture  with  water  vapor  on  its  way  to  the  cylinder, 
particularly  when  running  under  heavy  loads.  Just  what  the 
action  of  the  water  vapor  may  be  is  still  undetermined,  but  it 
seems  to  give  more  certain,  quieter,  and  cleaner  combustion. 

(b)  Many  kerosene  and  other  oil  engines  operate  on  what 
is  known  as  the  hot-bulb  or  hot-head  principle.  An  engine  of  this 
type  is  shown  in  Fig.  289. 

The  oil  is  injected  into  the  hot  bulb  during  the  suction  or  com- 
pression strokes  and  is  there  vaporized  by  the  hot  walls.  Air 


INTERNAL-COMBUSTION  ENGINES  427 

is  compressed  into  the  bulb  during  the  compression  stroke  of  the 
engine,  and,  when  the  mixture  acquires  the  proper  proportions, 
spontaneous  ignition  takes  place.  The  bulb  is  heated  to  redness 
by  a  blow-torch  before  starting  the  engine,  and  thereafter  is  main- 
tained at  the  proper  temperature  by  the  heat  generated  during 
combustion. 

There  is  always  a  certain  amount  of  carbon  or  lampblack 
deposited  within  the  hot  bulb  by  the  "  cracking  "  of  the  oil 
molecules  during  vaporization,  and  it  is  therefore  necessary  to 
clean  the  bulb  periodically. 

(c)  Practically  the  only  other  distinct  method  of  using  the 
heavier  oil  fuels  in  internal-combustion  engines  is  that  exemplified 
in  the  Diesel  oil  engine  described  in  Section  204.     This  gives  by 
far  the  most  perfect  combustion  with  the  heavier  fuels,  but  is  open 
to  criticism  because  of  the  high  pressures  involved. 

(d)  To  overcome  this  difficulty,  engines  are  now  being  built 
which  may  be  considered  a  compromise  between  the  hot-bulb 
and  the  Diesel  types.     The  pressures  are  lower,  but  the  hot  bulb 
insures  successful  ignition  and  combustion.     These  engines  are 
proving  highly  economical  in  the  use  of  fuel,  and  can  be  kept  in 
good  mechanical  condition  with  greater  ease  than  can  the  high- 
pressure  Diesel  engine. 

212.   Methods   of   Governing   Internal-Combustion   Engines. 

(a)  Stationary  engines  are  generally  mechanically  regulated  to 
maintain  approximately  constant  speed  of  rotation.  Automobile 
and  marine  engines  are  commonly  hand-governed,  although  they 
are  sometimes  fitted  with  a  limit  governor  to  prevent  over- 
speeding,  or  "racing." 

(b)  In  order  to  govern  or  regulate  an  engine,  the  i.h.p.  must 
be  varied  to  suit  the  demand,  as  shown  in  Section  134.     There 
are  three  available  methods  of  doing  this:   (i)  The  amount  of 
energy  made  available  per  cycle  may  remain  constant,  but  the 
number  of  cycles  per  unit  of  time  may  be  changed ;  (2)  the  num- 
ber of  cycles  may  remain  constant  and  the  amount  of  energy 
made  available  per  cycle  may  be  varied;  and  (3)  a  combination 
of  the  two  preceding  may  be  used. 

(c)  In  general,  there  are  four  different  ways  of  applying  these 
methods.     They  are  called :  (i)  hit-and-miss  governing,  (2)  quan- 
tity governing,  (3)  quality  governing,  and  (4)  combination  sys- 


428  HEAT-POWER  ENGINEERING 

terns.  These  are  each  considered  in  detail  in  the  following 
paragraphs. 

(d)  In  hit-and-miss  governing,  the  number  of  working  cycles 
per  unit  of  time  is  varied  so  as  to  adjust  the  average  Lh.p.  to 
the  demand  for  power.  With  this  system,  some  part  of  the 
mechanism  for  opening  the  inlet  valve  is  under  the  control  of 
the  governor,  so  that  when  a  "  working  cycle  "  is  to  occur  it  hits 
another  part  and  opens  the  valve,  but  when  the  cycle  is  to  be 
omitted  it  misses  engagement  and  the  valve  remains  closed. 
When  a  miss  occurs,  not  only  does  the  inlet  valve  remain  closed, 
but  the  exhaust  valve  is  usually  held  open,  so  that,  during  the 
strokes  corresponding  to  the  ordinary  cycle,  the  piston  pumps 
exhaust  gas  into  and  out  of  the  exhaust  pipe  without  waste  of 
energy,  except  for  the  slight  friction  and  heat  loss. 

In  some  engines,  when  the  working  cycle  is  to  be  omitted,  a 
fuel  valve,  which  is  separate,  is  held  closed  while  the  inlet  and 
exhaust  valves  act  as  usual;  thus  the  piston  draws  in  a  charge 
of  pure  air,  which  it  compresses,  expands,  and  exhausts.  This 
method  is  generally  considered  less  satisfactory  than  the  former, 
because  of  the  cooling  effect  on  the  cylinder  walls. 

With  hit-and-miss  governing  all  working  cycles  are  theoreti- 
cally exactly  alike,  and  are  equal  to  the  maximum  for  the 
particular  engine.  As  all  types  of  internal-combustion  engines 
show  greatest  thermal  efficiency  when  developing  normal  cycles 
of  about  maximum  power,  this  method  of  governing  has  the  theo- 
retical advantage  of  giving  high  thermal  efficiencies  at  all  loads. 
The  cycles  actually  produced,  however,  are  not  all  alike,  because 
of  irregular  cooling  and  heating  effects,  the  varying  mixtures 
resulting  from  intermittent  operation,  etc.  The  variations 
become  more  marked  with  increase  of  the  number  of  misses,  and 
the  method  therefore  gives  lower  efficiencies  at  light  loads  than 
would  be  expected.  In  general,  however,  it  is  the  most  economi- 
cal method  of  governing  yet  devised.  As  considerable  intervals 
of  time  may  intervene  between  "working"  cycles,  a  very  heavy 
flywheel  is  needed  on  engines  governed  by  this  method. 

Hit-and-miss  governing  is  very  satisfactory  for  engines  where 
close  speed  regulation  is  not  necessary,  and  is  commonly  used 
on  the  smaller  sizes,  say  up  to  25  or  50  horse  power.  Wliere 
close  regulation  is  required,  as  for  the  operation  of  alternators 
in  parallel,  it  is  practically  never  used. 


INTERNAL-COMBUSTION  ENGINES  429 

(e)  In  quantity  governing,  the  number  of  cycles  and  the  pro- 
portions of  the  mixture  are  maintained  constant,  but  the  amount 
of  mixture  admitted  per  cycle  is  varied  to  suit  the  power  demand. 
This  is  generally  done  in  one  of  two  ways,  —  by  "cut-off  gov- 
erning," or  by  "  throttling  governing." 

In  cut-off  governing,  after  the  amount  of  mixture  necessary  to 
produce  the  required  power  has  been  taken  in,  the  inlet  valve 
is  closed,  and  the  charge  expanded  as  the  out  stroke,  or  suction 
stroke,  continues.  The  cycle  is  then  completed  as  usual,  produc- 
ing under  low  load  a  diagram  like  that  of  Fig.  290,  in  which  the 
lower  loop  is  exaggerated  for  clearness. 


Fig.  290.  Fig.  291. 

In  throttling  governing,  except  at  the  maximum  load,  the 
charge  is  throttled  during  the  entire  suction  stroke  to  reduce 
the  amount  of  mixture  entering  the  cylinder.  This  gives  a  dia- 
gram like  Fig.  291,  in  which  the  lower  loop  is  again  exaggerated. 

In  both  of  these  methods  'of  governing,  the  reduction  in  quan- 
tity of  mixture  with  decrease  in  load  is  accompanied  by  a  lower- 
ing of  the  compression  curve.  If  not  carried  too  far,  this  is 
desirable  from  a  mechanical  standpoint,  as  it  tends  to  produce 
more  uniform  turning  effort,  and  reduces  the  necessary  weight 
of  flywheel. 

Of  the  two  methods  the  cut-off  is  the  better  because  it  gives 
a  smaller  lower  loop  and  less  lost  work.  It  also  has  the  advan- 
tage that  the  governor  action  is  delayed  to  the  latest  possible 
instant  in  the  cycle,  and  hence  each  working  cycle  more  nearly 
meets  the  power  demand. 

(f)  In  quality  governing  the  number  of  cycles  and  quantity  of 
material  per  cycle  are  maintained  constant,  but  the  proportion 
of  gas  to  air,  or  quality  of  the  mixture,  is  varied,  so  that  the 
power  developed  in  the  cylinder  just  meets  the  power  demand. 

Since  the  same  volume  of  mixture  is  drawn  in  each  cycle  and 
is  compressed  to  the  same  pressure,  the  efficiency  is  theoretically 


430  HEAT-POWER  ENGINEERING 

constant  at  all  loads.  In  practice,  however,  each  fuel  has  an 
air-to-gas  ratio  that  gives  best  results;  thus  it  follows  that  this 
method  of  regulation  gives  maximum  efficiency  only  at  one 
particular  load.  With  some  fuels  it  is  exceedingly  difficult  to 
obtain  satisfactory  ignition  of  the  very  "  weak  "  mixtures  intro- 
duced at  low  loads,  and  such 
mixtures  also  burn  very  slowly, 
the  combustion  continuing  in 
extreme  cases  throughout  the 
entire  expansion  stroke. 
—  A  group  of  indicator  diagrams 

jrjg  2Q2  from  a  quality-governed  engine 

is  given  in  Fig.  292.      The  slow 

burning  of  the  weak  charges  is  shown  by  the  gradual  tilting  of 
the  combustion  line  as  the  load  decreases. 

The  constant  compression  pressure  has  an  undesirable  effect 
on  the  crank  effort  (see  (e)  of  this  section),  as  the  m.e.p.  of  the 
compression  line  does  not  change  with  the  m.e.p.  of  the  expansion 
line. 

(g)  Combined  systems  are  sometimes  used  in  an  effort  to 
obtain  the  advantages  of  the  different  methods  previously 
described  with  as  few  as  possible  of  their  disadvantages.  Thus 
hit-and-miss  governing  may  be  used  at  low  loads  and  quality 
governing  at  the  higher  loads  which  call  for  sufficient  gas  to 
make  a  readily  ignitable  mixture.  Or  quality  governing  may  be 
used  at  the  higher  loads,  gradually  merging  into  quantity  govern- 
ing as  the  load  decreases. 

All  these  combinations  tend  to  complicate  the  valve  gear  and 
call  for  more  or  less  sensitive  and  intricate  adjustments.  They 
are,  therefore,  commercially  handicapped,  though  theoretically 
desirable. 

(h)  As  the  form  and  area  of  the  card  may  be  changed  by 
altering  the  time  of  ignition,  this  might  be  used  for  governing. 
It  is  actually  used  for  that  purpose  to  a  certain  extent  in  marine 
and  auto  engines.  Since  there  is  some  best  time  of  ignition  for 
each  mixture  in  each  engine  running  at  each  speed,  it  is  generally 
better  to  change  the  time  of  ignition  to  suit  the  conditions 
brought  about  by  governing  rather  than  govern  by  changing  the 
time  of  ignition. 

In  some  combination  systems  an  ignition  timing  device  under 


IN  TERN  A  L-COMB  USTION  ENGINES 


431 


control  of  the  governor  has  been  incorporated,  but  it  has  gener- 
ally been  found  more  satisfactory  to  trust  to  hand  timing. 

213.  Gas  Valves,  Mixing  Valves,  etc.  (a)  When  gas  is  sup- 
plied an  engine  under  pressure,  as  is  generally  the  case  in  all 
except  "  suction  gas-producer  "  plants  (see  Fig.  5),  a  gas  valve  of 
some  sort  is  necessary  to  shut  off  the  gas  supply  during  all  but 
the  suction  stroke  of  the  engine. 

(b)  This  valve  may  be  combined  with  the  inlet  valve  of  the 
engine,  giving  the  arrangement  shown  diagrammatically  in 
Fig.  293.  The  air  and  gas  cocks  shown  are  used  for  proportion- 
ing the  mixture  by  hand,  and  the  gas  cock  is  also  used  as  a 
permanent  shut-off  valve.  Such  an  arrangement  can  be  used 
with  hit-and-miss  or  with  quantity  governing,  but  is  obviously 
unsuited  for  quality  governing  because  of  the  hand  regulation 
of  the  proportions. 


Inlet 
Valve 


Cylinder 
Fig.  293. 


Cylinder 
Fig.  294. 


(c)  The  gas  valve  is  more  commonly  a  separate  valve,  although 
it  may  be  carried  loosely  on  the  same  stem  as  the  inlet  valve, 
as  a  in  Fig.  294.     When  thus  made  separate  from  the  inlet  valve, 
it  can  be  put  under  governor  control,  so  that  any  kind  of  govern- 
ing can  be  adopted,  at  the  option  of  the  designer.     In  all  cases 
it  is  common  practice  to  supply  gas  and  air  cocks  or  their  equiva- 
lent so  that  the  proportions  of  the  mixture  can  be  roughly  regu- 
lated by  hand  and  so  that  the  gas  can  be  permanently  shut  off 
from  the  engine. 

(d)  The  terms  mixing  valve  and  proportioning  valve  are  used 
rather  loosely  to  designate  anything  which  has  to  do  with  the 
mixing  of  air  with  gas  already  measured  out,  or  with  the  measur- 
ing and  mixing  of  the  constituents  of  the  charge.     In  the  strictest 


432 


HEAT-POWER  ENGINEERING 


sense  a  proportioning  valve,  and  to  a  certain  extent  a  mixing 
valve,  precedes  the  inlet  valve,  measures  the  combustible  part 
of  the  charge,  and  mixes  it  with  the  air.  A  gas  valve  under 
governor  control,  combined  with  surfaces,  or  passages,  which  will 
mix  the  gas  with  the  air  before  or  during  passage  through  the 
inlet  port,  is  properly  a  mixing  or  proportioning  valve.  One 
example  of  this  sort  of  arrangement  is  shown  in  Fig.  294. 

The  small  gas  valve  a  is  guided  by  the  sleeve  sliding  on  the  stem 
of  the  inlet  valve  b.  It  is  operated  by  separate  linkage  under 
governor  control,  so  that  the  time,  or  extent,  of  its  opening  can 
be  varied  to  suit  the  load.  In  operation,  the  inlet  valve  opens 
first,  allowing  fresh  air  to  enter  the  cylinder  and  blow  away  hot 
burned  gases.  The  gas  valve  a  then  opens,  admitting  gas, 
which,  traveling  downward,  is  thoroughly  mixed  with  the  air 
as  it  issues  from  the  small  holes  shown.  The  valve  a  closes 
before  the  inlet  valve  b,  so  that  the  mixing  chamber  becomes 
filled  with  pure  air  before  being  shut  off  from  the  cylinder. 

Such  a  device  is  commonly  known  as  a  combined  mixing  and 
inlet  valve,  although  the  gas  valve  is  occasionally  designated  as  a 

mixing    valve    or    a    proportioning 
valve. 

(e)  The  elements  of  another  type 
of  mixing  valve  are  shown  in  Fig. 
295.  The  inner  cylinder  is  supposed 
to  be  under  governor  control,  so  that 
it  can  be  rotated  more  or  less  as  the 
load  varies,  thus  changing  the  effect- 
ive openings  of  the  gas  and  air  ports 
to  suit  the  demand  for  power.  By 

properly  proportioning  the  gas  and  air  ports,  their  areas  may  be 
made  to  change  at  the  same  rate  under  the  action  of  the  governor, 
thus  giving  throttling  regulation;  or  the  areas  may  be  made  to 
change  differentially,  giving  quality  governing  or  mixed  quality 
and  quantity  regulation. 

(f)  Experience  has  shown  that  proportioning  valves  of  the  type 
shown  in  Fig.  295,  and  others  using  sliding  surfaces,  are  per- 
fectly satisfactory  when  used  with  such  fuels  as  natural  gas  and 
illuminating  gas.  Producer  gas  and  blast-furnace  gases,  how- 
ever, carry  impurities  which  quickly  foul  such  sliding  surfaces 
and  impair  the  action  of  the  valve.  For  such  gases,  mixing  and 


INTERNAL-COMBUSTION  ENGINES 


433 


proportioning  valves  made  without  sliding  surfaces,  such  as  that 
shown  in  Fig.  294,  must  be  used.  Even  the  valve  shown  in  this 
figure  might  give  trouble  because  of  deposits  on  the  stem  of  the 
main  valve,  and  a  design  eliminating  this  possibility  would  prob- 
ably give  better  results. 

214.  Methods  of  Ignition,     (a)  In  the  early  development  of 
gas  engines  the  charge  was  ignited  by  opening  communication 
at  the  proper  time  between  the  compression  space  of  the  engine 
and  a  small  chamber  containing  an  open  flame.     This  method 
was  complicated  mechanically,  and  had  so  many  objectionable 
features  that  it  did  not  survive. 

(b)  The  methods  at  present  used  are: 

(a)  Hot- tube  ignition ; 

(b)  Spontaneous  ignition   by  heat  of  compression  (as- 

sisted, or  not  assisted,  by  the  action  of  a  hot  cham- 
ber, such  as  a  vaporizer  or  hot  bulb) ; 

(c)  Electric  ignition. 

215.  Hot-Tube  Ignition,     (a)  A  simple  type  of  hot- tube  igni- 
tion is  shown  schematically  in  Fig.  296.     The  tube  a,  generally 
made  of  metal,  is  closed  at  one  end,  while 

the  other  end  opens  into  the  cylinder. 
By  moving  the  burner  and  chimney  &, 
the  hot  zone,  which  is  at  about  red  heat, 
can  be  located  anywhere  along  the  tube. 

At  the  end  of  the  exhaust  stroke  the  hot 
tube,  like  the  rest  of  the  clearance  space, 
is  filled  with  burned  gases  at  a  pressure 
slightly  above  atmospheric.  During  the 
suction  stroke  these  gases  are  partly  ex- 
panded, and  during  the  compression 
stroke  they  are  compressed  into  the  tube 
by  the  combustible  mixture  until  the  lat- 
ter finally  reaches  the  hot  zone,  where  it 
is  ignited.  By  moving  the  hot  zone  along  the  tube,  the  time  in 
the  compression  stroke  at  which  the  mixture  is  ignited  can  be 
varied. 

(b)  By  this  method  ignition  is  generally  certain,  but  the  timing 
is  untrustworthy  because  of  variations  in  the  condition  of  the 


Fig.  296. 


434  HEAT-POWER  ENGINEERING 

tube  or  of  the  mixture.  Hence,  despite  its  simplicity  and  lack 
of  moving  parts,  hot-tube  ignition  is  not  now  very  widely  used. 
"  Timing  valves  "  have  been  used  to  close  the  cylinder  end  of 
the  tube  and  to  thus  control  ignition,  but  few  have  survived. 

Hot-tube  ignition  involves  a  constant  supply  of  gas  to  the 
burner,  and  this  of  course  adds  to  the  fuel  consumption  of  the 
engine. 

216.  Spontaneous   Ignition.     In   many   engines   using   liquid 
fuels  heavier  than  gasoline,   ignition  is  produced  by  the  tem- 
perature  attained   during   compression.     In   the   Diesel   engine 
the  compression  pressure  is  so  high  that  the  resulting  temperature 
alone  causes  ignition.     In  other  engines,  like  the  hot-bulb  type 
(Fig.  289) ,  ignition  results  from  the  combined  action  of  compres- 
sion and  a  hot  vaporizing  chamber. 

This  method  of  igniting  has  not  proved  applicable  to  the  more 
volatile  liquid  fuels  and  to  the  gaseous  fuels  because  of  the  diffi- 
culty of  timing. 

217.  Electric  Ignition,     (a)  The  most  satisfactory  method  of 
igniting  is  by  an  electric  spark. 

All  electrical  ignition  systems  in  use,  with  few  exceptions, 
fall  under  either  "  make-and-break  "  or  "jump-spark  "  ignition. 
The  less  descriptive  terms,  "  low- tension  "  ignition  and  "  high- 
tension  "  ignition,  are  often  used  in  place  of  these. 

(b)  In  the  make-and-break  ignition  system,  two  "  electrodes  " 
are  brought  together  within  the  combustion  space  to  "  make,"  or 
close,  the  circuit,  and  are  separated  suddenly  to  "break  "  the 
circuit  and  produce  a  spark. 

One  arrangement  of  such  a  system  is  shown  in  Fig.  297,  the 
"  igniter  block,11  or  "plug''  entering  the  combustion  space  through 
the  center  of  the  cylinder  head.  The  "  stationary  electrode  " 
is  designated  by  i  and  the  "movable  electrode"  by  j.  The  wir- 
ing diagram  is  shown  in  Fig.  298.  In  this  figure,  B  represents 
a  battery  or  other  low- voltage  generator,  C  an  "  induction  "  or 
"  intensifier  coil"  E  the  stationary  electrode,  which  is  insulated 
from  the  igniter  block  and  engine  frame,  and  5  a  stud  or  other 
convenient  screw  fastening  on  the  engine..  The  movable  elec- 
trode is  in  electrical  contact  with  the  igniter  block  and  engine 
frame,  as  shown  in  Fig.  297. 

(c)  The  operation  is  as  follows:  The  cam  a,  Fig.  297,  pushes 


INTERNAL-COMBUSTION  ENGINES 


435 


the  rod  b  toward  the  igniter  and  the  strike  block  d,  engaging  the 
flipper  e  on  lever  /,  moves  the  latter  toward  the  left.  As  / 
moves,  it  draws  g  after  it  by  means  of  the  one-turn  spring  shown. 
As  g  moves  it  rotates  the  movable  electrode  until  the  arm  j 
inside  of  the  cylinder  is  brought  into  contact  with  the  stationary 


Fig.  297. 

electrode  i.  The  circuit  is  then  made  and  current  flows  until 
the  circuit  is  broken  by  the  block  d  traveling  past  the  edge  of  the 
flipper  e.  When  this  occurs,  the  spring  h  pulls  the  arm  j  out  of 
contact  with  i,  and  the  circuit  is  broken.  The  spark  results 
from  the  action  of  the  induction  coil  at  the  instant  of  breaking 
the  circuit.  The  rapid  change  in  the  number  of  lines  of  force 


Fig.  298. 

through  the  core  causes  sufficient  self-induction  to  generate  an 
electromotive  force  of  such  intensity  as  to  bridge  the  gap  between 
the  separating  electrodes. 

(d)  The  timing  of  the  spark  is  effected  by  moving  guide  C 
across  the  path  of  the  bar  b  in  Fig.  297,  thus  changing  the  time 
at  which  block  d  releases  flipper  e. 

(e)  The  type  of  igniter  just  described  is  known  as  a  "  hammer 
make-and-break  igniter  "  to  distinguish  it  from  another  known 


436 


HEAT-POWER  ENGINEERING 


as  a  "  wipe-spark  "  or  "  wipe  make-and-break  igniter,"  in  which  a 
movable  electrode  periodically  wipes  or  slides  across  a  station- 
ary electrode.  The  wipe  spark  automatically  cleans  the  contact 
surfaces  within  the  cylinder,  which  is  in  a  way.  advantageous, 
but  it  is  not  so  extensively  used  as  the  hammer  type. 

(f)  The  make-and-break  system  has  the  advantages  of  being 
electrically  simple  and  operating  with  low  e.m.f.,  so  that  short 
circuits  are  not  so  apt  to  occur  as  in  the  systems  described  in 
following  sections.  It  is,  however,  complicated  mechanically,  and 
because  of  friction  and  inertia  of  parts  is  not  generally  used  on 
engines  operating  at  speeds  above  500  to  600  r.p.m.  The 
movable  electrode  is  very  apt  to  stick  or  to  work  loose,  causing 
trouble  because  of  no  spark  or  because 
of  loss  of  compression  by  leakage. 

(g)  In  the  jump-spark  system  there 
are  within  the  cylinder  two  fixed  termi- 
nals, with  short  intervening  gap,  across 
which  a  spark  jumps  when  sufficient 
difference  of  potential  has  been  devel- 
oped. In  its  simplest  form  the  apparatus 
has  two  circuits,  as  shown  in  Fig.  299, 


Fig.  299. 


with  heavy  lines  representing  the  u  low- tension  circuit  "  and  the 
light  lines  the  "  high-tension  circuit." 


Fig.  300. 

In  the  figure,  B  is  the  source  of  electromotive  force,  T  is  a 
rotating  "timer,"  C  a  "condenser,"  K  a  "coil,"  and  S  a 
"  spark  plug,"  several  examples  of  which  are  shown  in  Fig.  300. 


INTERNAL-COMBUSTION  ENGINES  437 

(h)  In  operation  the  primary  circuit  is  closed  by  the  timer  T 
and  then  suddenly  opened,  with  the  result  that  a  spark  jumps 
between  the  terminals  of  the  plug.  The  action  of  the  coil  is 
as  follows:  When  the  primary  circuit  is  closed  by  rotation  of 
the  timer,  the  magnetic  field  induces  an  electromotive  force  in 
the  secondary  circuit.  This  is  not  great  enough,  however,  to 
cause  a  spark  to  pass  between  the  plug  terminals.  But  when 
the  primary  circuit  is  quickly  broken,  the  sudden  collapse  of  the 
magnetic  field  about  the  core  of  the  coil  induces  for  the  instant 
in  the  secondary  circuit  a  very  high  potential  difference,  which 
may  be  made  sufficient  to  cause  the  passage  of  a  spark,  with 
resultant  ignition. 

The  function  of  the  condenser,  which  bridges  the  timer  in  the 
primary  circuit,  is  to  prevent  sparking  at  the  contact  points  of 
that  apparatus.  Such  sparking  would  cause  rapid  deterioration 
of  the  contact  surfaces  and  is  therefore  undesirable. 

(i)  A  more  common  type  of  jump-spark  apparatus  uses  a 
"  trembler  coil  "  instead  of  the  plain  induction  coil  shown  in 
Fig.  299.  This  apparatus  is  so  arranged  that  the  trembler  forms 
part  of  the  primary  circuit,  and  is  in  such  position  that  it  is  at- 
tracted to  the  core  of  the  coil  when  this  is  magnetized,  and  thus 
breaks  the  primary  circuit.  This  in  turn  demagnetizes  the  core, 
hence  the  trembler  flies  back  and  makes  the  circuit  once  more; 
thus  the  core  is  again  magnetized  and  attracts  the  trembler, 
breaks  the  circuit,  and  so  on,  as  long  as  the  timer  is  in  position 
to  close  the  primary  circuit.  This  intermittent  making  and 
breaking  of  the  primary  circuit  causes  a  succession  of  sparks 
at  the  spark  plug  in  the  secondary  circuit,  which  action  is  generally 
supposed  to  insure  more  certain  ignition.  The  great  advantage 
achieved  is  really  quick  action  and  accurate  timing,  though 
these  are  often  counterbalanced  by  considerable  trouble  with  the 
trembler  which  may  call  for  almost  constant  adjustment. 

(j)  Both  of  these  high-tension  or  jump-spark  systems  are 
easily  timed  by  shifting  the  phase  relation  of  timer,  or  commuta- 
tor, and  engine  crank,  and  they  are  particularly  satisfactory  for 
high  speed.  Recently  there  has  been  a  tendency  to  adopt  these 
systems  for  ordinary  slow-speed  stationary  work;  but  as  the 
spark  does  not  seem  to  have  the  same  igniting  power  as  that  of 
the  make-and-break  system,  most  applications  have  been  limited 
to  the  more  easily  ignitable  fuels  like  natural  and  illuminating 


438 


HEAT-POWER  ENGINEERING 


gas  and  gasoline.     Few  simple  high-tension  systems  have  yet 
been  used  with  producer  gas  and  "  blast-furnace  gas." 

218.  Internal-Combustion  Engine  Valve  Gear,  (a)  The  slide 
valve,  so  common  in  steam-engine  practice,  is  never  used  in  its 
simple  form  on  internal-combustion  engines  for  admission  or 
exhaust.  It  is  sometimes  used  for  mixing  purposes,  as  was 
indicated  in  Sect.  213.  The  high  temperatures  to  which  inlet 
and  exhaust  valves  are  subjected  make  lubrication  difficult  and 
cause  warping  of  the  valve  and  seat,  and  the  high  pressures  make 
it  difficult  to  keep  the  valve  on  its  seat  to  prevent  leakage.  When 
the  fuel  used  contains  sulphur,  which  is  not  an  uncommon 
occurrence,  the  valve  and  seat  are  often 
quickly  pitted  and  corroded. 

(b)  Some  highly  specialized  slide  valves 
are,  however,  in  use  and  give  good  satis- 
faction. The  control  of  ports  by  the 
piston  of  the  two-stroke-cycle  engine  is 
the  most  common  example.  Recently  a 
number  of  "  sleeve  motors  "  have  been 
designed  for  use  on  automobiles  and  seem 
to  promise  very  satisfactory  operation. 

One  example  of  this  type  is  shown 
semi-diagrammatically  in  Fig.  301.  The 
two  sleeves,  reciprocating  vertically  un- 
der the  action  of  eccentrics  or  cranks  on 
a  side  shaft,  act  in  conjunction  with  the 
/  cylinder  head  and  external  cylinder  to 

control  admission  and  exhaust  by  means 
of  the  ports  shown.     The  advantages  of 

this  type  are  rapid  opening  and  closing  of  valves,  long  period  of 
approximately  maximum  opening,  and  silent  operation. 

(c)  The  success  of  this  type  of  valve  has  caused  the  appear- 
ance of  a  number  of  different  varieties  of  slide-valve  and  piston- 
valve  auto-engine  designs.      Few  of  these  have  been  tested  to 
any  extent,  and  it  is  therefore  too  early  to  draw  conclusions  as 
to  their  ultimate  success. 

(d)  With  the  exception  of  the  cases  cited  above,  the  poppet 
or  mushroom  valve  is  in  practically  universal  use  for  internal- 
combustion    engines.     It    maintains    its    correct    shape    under 


INTERNAL-COMBUSTION  ENGINES  439 

changing  temperatures  more  perfectly  than  other  types;  it  re- 
quires a  minimum  of  contact  surface  between  valve  and  seat; 
it  opens  inward  and  is  therefore  forced  to  its  seat  by  the  high 
pressures  in  such  engines;  it  requires  no  lubrication;  and  it  and 
its  seat  are  easily  kept  comparatively  true  by  grinding. 

(e)  In    modern   designs,    inlet    valves    are    practically    never 
water-cooled,  as  the  ingoing  charge  cools  them  sufficiently  during 
each  suction  stroke.     Exhaust  valves,  on  the  other  hand,  are 
practically  always  water-cooled   when  larger  than  five  inches 
in  diameter,  and  often  in  smaller  sizes.     This  is  deemed  necessary 
because  of  the  high  temperature  of  the  exhaust  gases  in  which 
the  valve  is  immersed  during  the  entire  exhaust  period,  but  it 
should  be  noted  in  this  connection  that  one  European  builder 
is  obtaining  satisfactory  operation  with  simple  uncooled  cast  iron 
exhaust  valves  in  the  largest  sizes  of  horizontal  engines. 

(f)  In   some    four-stroke-cycle  engines    the  operating   condi- 
tions of  the  exhaust  valve  have  been  improved  by  the  use  of 
"  auxiliary  exhaust  ports"     These  are  ports  in  the  cylinder  wall 
which  are  uncovered  by  the   piston  when  near  the  end  of  its 
stroke.     The  first  discharge  of  exhaust  gases  takes  place  through 
these  ports,  so  that  a  smaller  quantity  of  cooler  gases  is  handled 
by  the  exhaust  valve. 

This  construction  necessitates  the  use  of  a  larger  cylinder  for 
a  given  power  than  is  required  without  the  use  of  auxiliary 
ports,  and  it  complicates  the  cylinder  casting.  It  is  practically 
never  used  on  double-acting  engines  because  of  these  reasons,  and 
because  of  the  additional  fact  that  it  would  necessitate  the  use 
of  an  enormously  long  piston,  similar  to  that  shown  in  Fig.  280, 
thus  materially  increasing  the  weight  of  the  reciprocating  parts. 

(g)  Two  types  of  inlet  valve  are  in  use,  —  the  automatic  valve 
and  the  positively  actuated  valve.     The  automatic  valve  is  held  to 
its  seat  by  a  weak  spring,  and  is  raised  by  the  difference  between 
atmospheric  and   suction   pressures  during  the  suction  stroke. 
The  positively  actuated  valve  is  opened  mechanically  and  gen- 
erally closed  by  spring  pressure. 

Automatic  valves  are  uncertain  in  their  action,  opening  only 
after  a  considerable  pressure  difference  has  been  created,  antf 
then  more  or  less  slowly.  After  opening  they  do  not  remain 
wide  open  during  the  remainder  of  the  suction  stroke,  buf 
"chatter"  more  or  less,  thus  materially  decreasing  the  voln- 


440  HEAT-POWER  ENGINEERING' 

metric  efficiency  of  the  engine.  For  these  reasons  they  are 
seldom  used  on  the  better  types  or  on  the  larger  engines. 

Positively  actuated  valves,  on  the  other  hand,  can  be  made 
to  open  at  the  time  desired,  can  be  given  an  amount  of  opening 
approximately  equal  to  that  theoretically  required  at  each  piston 
position,  and  can  be  made  to  close  very  nearly  at  the  right  time. 

(h)  The  valves  of  internal-combustion  engines  are  generally 
operated  by  means  of  cams,  or  eccentrics,  on  a  side  shaft,  or 
auxiliary  shaft,  driven  by  gearing  from  the  crank  shaft.  On 
the  smaller  engines  cams  are  most  often  used,  but  on  the  larger 
engines  the  eccentrics  seem  to  be  preferred,  particularly  in  this 
country.  Closure  practically  always  occurs  by  spring  pressure, 
the  valve  being  released  by  the  opening  mechanism. 

The  cam  can  be  manufactured  more  cheaply  than  the  eccentric, 
and  when  properly  designed  it  is  not  very  noisy  in  operation  and 
wears  slowly.  In  general,  however,  it  is  rather  difficult  to 
obtain  as  perfect  valve  operation  with  cams  as  it  is  with  eccentrics 
unless  linkage  is  introduced,  which  complicates  the  mechanism 
and  increases  the  cost. 


F »g-  3°3-  Fig.  304. 

Cams  may  be  used  to  operate  the  valves  by  direct  contact 
with  the  valve  stem  (Fig.  302) ;  or  by  contact  with  one  end  of  a 
pivoted  lever,  the  other  end  of  which  contacts  with  the  valve 
stem  (Fig.  303) ;  or  through  rolling,  rocking,  or  floating  levers,  one 
arrangement  of  which  is  shown  in  Fig.  304. 

The  eccentric  always  operates  in  conjunction  with  such  levers 
as  are  shown  in  Fig.  304. 


INTERNAL-COMBUSTION  ENGINES  441 

(i)  The  time  (with  reference  to  crank  and  piston  positions) 
at  which  valves  open  and  close  varies  widely  with  the  location 
of  the  valve  and  with  the  type  of  engine.  The  exhaust  valve 
universally  opens  early,  generally  when  the  piston  is  at  about 
0.9  stroke.  It  may  close  before  the  end  of  the  return  stroke,  or 
on  dead  center,  or  it  may  remain  open  until  after  the  suction 
stroke  has  started.  The  object  of  leaving  it  open  after  dead 
center  has  been  passed  is  to  take  advantage  of  the  inertia  of  the 
moving  exhaust  gases  and  thus  get  more  perfect  discharge. 
Where  the  valves,  manifolds,  and  cylinders  are  so  arranged  that 
this  can  be  done,  it  represents  good  practice.  The  inlet  valve 
very  commonly  opens  after  the  beginning  of  the  suction  stroke, 
though  it  is  sometimes  opened  just  before,  or  on  dead  center,  in 
order  to  obtain  a  wider  opening  by  the  time  suction  actually 
starts.  It  is  very  generally  closed  after  the  end  of  the  suction 
stroke  in  order  to  take  advantage  of  the  inertia  of  the  moving 
column  of  gas,  thus  increasing  the  volumetric  efficiency. 

In  general,  the  higher  the  speed  of  an  engine  the  later  may  the 
valves  close,  and  the  greater  may  be  the  overlap  of  exhaust 
closure  and  inlet  opening  if  the  valves  are  widely  sepa- 
rated. 

(j)  Because  of  the  heavy  springs  necessary  to  close  the  valves 
of  internal-combustion  engines  in  the  short  time  available,  and 
because  of  the  relatively  great  weight  of  the  valves,  the  parts 
actuating  the  latter  are  generally  very  strong  and  heavy.  This 
is  particularly  true  of  exhaust-valve  gear.  This  valve  must  be 
opened  against  the  combined  action  of  high-pressure  gas  and  a 
very  powerful  spring. 

Many  designers  have  attempted  to  reduce  the  size  and  wear 
of  the  actuating  parts  by  building  balanced  exhaust  valves.  As 
a  general  rule  these  have  not  survived,  probably  because  they 
simplify  the  external  gear  by  complication  of  the  inclosed  part 
of  the  valve  system. 

Because  of  the  great  weight  of  the  valves  and  actuating 
mechanisms  in  large  engines  and  because  of  the  great  magnitude 
of  the  forces  transmitted  by  these  mechanisms,  it  is  generally 
undesirable  or  even  impossible  to  construct  governors  which 
can  operate  in  any  such  direct  manner  as  is  common  in  the 
average  steam  engine.  Governors  could  not  be  constructed 
powerful  enough  to  operate  directly  unless  made  with  such 


442  HEAT-POWER  ENGINEERING'' 

heavy  parts,  and  to  transmit  such  great  forces,  that  their  sensi- 
tiveness would  be  considerably  impaired. 

In  very  large  engines  a  differential  governing  device  is  now 
commonly  used.  In  such  cases  the  governor  operates  upon  the 
equivalent  of  a  small  engine  of  some  kind,  which  engine,  in  turn, 
supplies  such  power  as  is  necessary  for  moving  the  valve  gear. 
As  an  example,  the  governor  might  actuate  a  small  pilot  valve 
which  by  its  motion  admitted  oil  under  pressure  to  one,  or  the 
other,  end  of  a  cylinder  fitted  with  a  piston  suitably  linked  to 
the  inlet-  or  mixing- valve  gear.  The  motion  of  the  piston  in  the 
proper  direction  and  to  the  right  extent,  as  controlled  by  the 
governor  through  the  pilot  valve,  would  then  serve  to  give  the  re- 
quired adjustment  of  the  main  valves. 

In  smaller  engines  it  is  customary  to  connect  the  governor 
to  some  light  form  of  mixing  valve,  to  a  balanced  or  floating 
valve  of  some  kind,  or  to  a  light  link  or  equivalent  which  is 
easily  moved  and  causes  the  necessary  adjustment  by  the  shifting 
of  a  fulcrum  or  the  like  in  the  main  gear. 


CHAPTER  XXVI. 


INTERNAL-COMBUSTION  ENGINES  (cont.). 

EFFICIENCY,  PERFORMANCE,  AND  POWER. 

219.  Efficiencies  of  Otto  Four-Stroke  Cycle  Engines,  (a)  Not 
only  does  the  thermal  efficiency  of  the  Otto  cycle  engine  theo- 
retically vary  with  the  ratio  of  compression,  increasing  as  the 
final  volume  is  decreased  with  respect  to  the  initial  volume, 
but  real  engines  also  show  a  similar  gain.  The  rapid  improvement 
in  the  efficiency  of  this  type  of  engine  during  the  past  twenty 
years  has  been  largely  due  to  this  increase  in  compression  pres- 
sure. It  is  well  shown  by  the  following  table :  * 

TABLE  XII.  —  EFFICIENCIES   OF  OTTO   FOUR-STROKE  CYCLE 

ENGINES. 


No. 

Year. 

Type  of 
Engine. 

Cylinder 
Size. 

Indicated 
Thermal 
Efficiencies. 

Brake  Thermal 
Efficiencies. 

Mechanical 
Efficiencies. 

Inches. 

Per  cent. 

Per  cent. 

Per  cent. 

I 

1882 

Deutz 

6-75  X  13-7 

16 

14 

87.6 

2 

1888 

Crossley 

9-5     X  18 

22 

18.9 

86.1 

3 

1898 

National 

10        X  18 

28.7 

25 

87.0 

4 

1908 

Crossley 

II.  S      X   21 

36.8 

32.2 

87.5 

(b)  It  should  not  be  assumed,  however,  that  by  an  indefinite 
increase  of  compression  pressure  the  thermal  efficiency  of  the 
real  engine  can  be  raised  without  limit.  For  even  if  the  ten- 
dency of  the  fuel  to  preignition  could  be  overcome,  calculations 
based  upon  actual  performances  show  that  with  the  Otto  type 
of  engine  the  maximum  practical  thermal  efficiency  would 
probably  be  attained  with  a  compression  pressure  of  from  250 
pounds  to  300  pounds  per  square  inch. 

Blast-furnace  gas  engines  operating  with  compression  pressure 
as  high  as  200  pounds  have  given   thermal  efficiencies  on  the 
brake  of  32  to  34  per  cent.     But  the  tendency  with  this  fuel  is 
*  The  Gas,  Petrol  and  Oil  Engine,  D.  Clerk,  page  243. 
443 


444  HEAT-POWER  ENGINEERING 

now  toward  the  use  of  compression  pressures  in  the  neighborhood 
of  1 60  to  1 80  pounds  because  of  the  mechanical  difficulties 
encountered  with  the  higher  pressures;  and  in  this  case  a  little 
under  30  per  cent  is  extremely  good  thermal  efficiency  on  the 
brake  for  modern  engines,  while  the  average  operating  value  for 
good  standard  American  types  of  stationary  engines  is  about  25 
to  27  per  cent  at  rated  load,  and  of  course  decreases  with  reduc- 
tion in  the  load. 

(c)  Besides  the  compression  ratio,  the  thermal  efficiency  in 
general  can  also  be  increased  by 

(1)  Mixing  the  incoming  charge  more  perfectly; 

(2)  Producing  fairly  rapid  and  complete  combustion  at  the 

compression  end  of  the  stroke  (note,  however,  that 
too  rapid  combustion  is  not  desirable) ; 

(3)  Preventing  loss  of  heat  from  the  charge  to  surrounding- 

metal  during  combustion  and  expansion. 

Many  modern  engines  have  elaborate  mixing  valves  which 
cause  thorough  intermixing  of  gas  and  air  before,  or  just  at  the 
time  of,  entering  the  cylinder. 

In  high-efficiency  engines  the  combustion  space  is  made  as 
nearly  as  possible  spherical,  hemispherical,  or  in  the  form  of  a 
short  cylinder;  and  all  pockets  leading  out  of  this  space  are 
avoided  as  far  as  possible.  This  results  in  less  surface  for  the  vol- 
ume inclosed,  and  thus  reduces  heat  loss  to  the  metal  and  makes 
the  combustion  more  rapid  and  complete  for  a  similar  reason. 

In  pockets  connecting  with  the  combustion  space  the  gases 
often  burn  long  after  combustion  of  the  main  part  of  the  charge 
is  complete.  This  can  be  prevented  by  placing  the  igniter  in 
the  pocket,  and  igniting  the  gas  there  first,  in  which  case  the  rapid 
increase  of  temperature  will  cause  a  sudden  pressure  rise,  blowing 
some  of  the  burning  gas  into  the  main  charge,  thus  causing  very 
complete  inflammation. 

Large  engines  generally  have  slightly  higher  thermal  efficien- 
cies than  small  engines  of  the  same  type  and  proportions,  because 
large  cylinders  have  less  wall  surface  per  unit  of  volume  inclosed 
than  have  small  cylinders  of  the  same  proportions.  This,  how- 
ever, may  be  counteracted  by  difficulty  of  mixing  the  charge  in 
the  larger  cylinder  and  difficulty  in  effecting  rapid  and  complete 
combustion. 

When  large  cylinder  diameters  are  used,  two  or  more  igniters 


INTERNAL-COMBUSTION  ENGINES 


445 


at  different  points  are  often  operated  simultaneously  in  each 
combustion  space  in  order  to  reduce  the  distance  through  which 
inflammation  must  progress  from  each  igniter. 

Piston  speeds  of  high-efficiency  engines  are  carried  as  high  as 
is  mechanically  feasible  in  order  to  reduce  the  time  of  contact 
between  hot  gases  and  walls. 

(d)  The  values  of  all  the  different  efficiencies  enumerated  in 
Sect.  105  will  vary  considerably  with  the  conditions,  fuel,  mix- 
ture, type  of  engine,  etc.  ;  but  for  the  purpose  of  giving  a  gen- 
eral idea  of  the  order  of  these  values  a  certain  type  and  set  of 
conditions  will  be  assumed. 

The  engine  is  supposed  to  operate  with  "producer  gas"  as 
fuel  and  (in  the  ideal  case  for  drawing  the  air  card)  to  have  a 
suction  pressure  equal  to  atmospheric,  a  pressure  of  150  pounds 
per  square  inch  absolute  at  the  end  of  compression,  a  temperature 
at  the  end  of  suction  stroke  equal  to  520°  F.  abs.,  a  tempera- 
ture at  the  end  of  compression  of  1000°  F.  abs.,  and  a  tempera- 
ture at  the  end  of  combustion  of  about  6500°  F.  abs.  These  figures 
are  obtained  by  neglecting  all  losses  in  the  real  engine  and  by 
considering  the  specific  heats  constant. 

(e)  The  thermodynamic  or  Carnot  efficiency  is  then 


_,- 

Efc  =  ~ 


I  —  T2      6500  — 


6500 


92  per  cent. 


(f)  The  cycle  efficiency  for  this  Otto  cycle  is  from  Eq.  (80), 


=  48  per  cent. 


CEf  =  1  -        =  1  - 

Ta  1000 


Then  in  Fig.  305,  drawn  to 
scale  for  the  assumed  engine, 
the  distance  AB  is  48  per  cent 
of  AC* 

Thus  the  Otto  cycle  upon 
which  this  engine  is  to  operate 
is  less  efficient  than  reversible 
cycles,  and  the  real  engine  is  ini- 
tially handicapped  to  that  extent. 

(g)  The  relative  efficiency  is 


D     G       J  M  P 


Fig.  305- 


cent. 


446  HEAT-POWER  ENGINEERING" 

This  shows  that  the  real  Otto  engine,  if  absolutely  perfect,  could 
only  make  available  a  little  more  than  half  the  mechanical  energy 
obtainable  with  the  ideal  Carnot  engine. 

(h)  The  indicated  efficiency  measures  the  amount  by  which 
the  cylinder  of  the  real  engine  falls  short  of  developing  the 
48  per  cent  of  the  supplied  energy. 

The  weight  (Wi)  of  mixture  that  this  engine  would  probably 
use  is  about  9  to  10  pounds  per  i.h.p.-hour,  and  the  heat  AQ 
supplied  by  each  pound  of  mixture  is  about  940  B.t.u.  Then 
the  theoretical  Otto  engine  would  make  available  940  X  0.48  = 
451.2  B.t.u.  per  pound  as  AE.  One  horse  power  is  equivalent 
to  2545  B.t.u.  per  hour,  and  the  heat  theoretically  available  for 
doing  work  is  (9  or  10)  X  451.2  B.t.u.;  hence 


lEf  =  -=  =  -.  --         ~      -  =  62.6  to  56.4  per  cent. 
(9  to  10)  X  451.2 


That  is,  the  area  of  the  upper  loop  of  the  real  indicator  card 
divided  by  the  area  of  the  ideal  air  card  would  give  a  value 
between  62.6  per  cent  and  56.4  per  cent.  This  measures  the 
proportion  of  the  maximum  energy  of  this  cycle  that  is  made 
available  by  the  real  engine.  In  Fig.  305,  DE  should  be  62.6  per 
cent  to  56.4  per  cent  of  DF. 

(i)  The  thermal  efficiency  on  the  i.h.p.  is  easily  determined  to  be 


(9  to  1C  X  940  -  3° 
which  shows  that  the  real  engine  actually  converts  into  mechani- 
cal energy  from  30  to  27  per  cent  of  all  the  heat  supplied  it. 
Some  of  this  is,  however,  lost  in  fluid  and  mechanical  friction,  and 
the  amount  of  such  loss  is  measured  by  the  mechanical  efficiency. 

The  TIE/  is  the  ratio  of  GH  to  AC  in  Fig.  305. 

(j)  The  mechanical  efficiency,  MEf,  of  an  engine  of  this  kind 
would  probably  be  about  85  per  cent,  thus  the  d.h.p.  would  be 
about  85  per  cent  of  the  i.h.p.  In  Fig.  305,  JK  is  therefore  85 
per  cent  of  JL. 

(k)  The  thermal  efficiency  on  the  d.h.p.  is  from  Eq.  (220) 
TDEf  =  TIEf  X  MEf  =  (27  to  30)  X  0.85  =  22.9  to  25.5  per  cent, 

showing  that  the  engine  actually  turns  into  useful,  available 
power  about  one  quarter  of  all  the  heat  energy  supplied  it.  In 
Fig-  305  the  TDEf  is  given  by  the  ratio  of  MN  to  AC. 


INTERNAL-COMBUSTION  ENGINES  447 

(1)  The  over-all  efficiency  would  be  by  Eq.  (221) 
OEf=  lEf  X  ME}  =  (56.4  to  62.7)  X  0.85  =  47.9  to  53.3  per  cent, 

showing  that  the  real  engine  losses  (cylinder,  fluid  friction,  and 
mechanical  friction)  consume  about  one-half  the  power  which  the 
ideal  engine  with  the  same  cycle  would  make  available.  In  Fig. 
305  the  OEf  is  the  ratio  of  MN  to  AB. 

220.  Efficiencies  of  other  Commercial  Engines,      (a)   Two- 
stroke-cycle   Otto   Engines,  because   of   greater   cyclinder   and 
friction  losses,  generally  have  over-all  efficiencies  of  from  0.7  to 
0.8  of  those  of  corresponding  four-stroke  engines.     The  indicated 
efficiency  and   mechanical   efficiency  may  both  be  lower   than 
in  four-stroke  engines,  or  the  indicated  efficiency  may  be  lower 
while  the  mechanical  efficiency  is  higher  because  of  the  absence 
of  valves  and  such. 

(b)  The  thermal  efficiency  of  the  Diesel  oil  engine  is  generally 
higher  than  that  of  engines  working  on  the  Otto  cycle.  This  is 
due  to  the  higher  compression  pressure  which  can  be  carried  in 
these  engines  (500  pounds  per  square  inch  or  more),  and  to 
the  fact  that  the  combustion  conditions  are  also  probably 
somewhat  better. 

Average  thermal  efficiencies  on  the  brake  with  Diesel  engines 
are  about  30  per  cent,  and  sometimes  run  as  high  as  35  per  cent. 

221.  Heat  Balance  for  Gas  Engines,     (a)  In  reporting  an 
engine  test,  it  is  customary  to  account  for  all  heat  supplied.     The 
statement  of  this  account  is  called  the  "  heat  balance."     There 
are  only  five  possible  destinations  for  heat  supplied  to  a  gas 
engine.     They  are: 

(1)  Useful  mechanical  energy; 

(2)  Loss  to  jacket; 

(3)  Heat  carried  away  in  the  exhaust  gases; 

(4)  Loss  due  to  incomplete  combustion; 

(5)  Radiation,  which  includes  energy  converted  into  heat  by 

friction. 

(b)  The  useful  mechanical  work  has  already  been  shown  to 
equal  from  15  to  30  per  cent  of  the  heat  supplied. 

(c)  The  relative  amount  of  heat  lost  to  the  water,   or  air, 
jacketing   the   cylinder  varies  in  different  engines,  and  in  the 


448  HEAT-POWER  ENGINEERING  > 

same  engine  under  different  conditions.  The  loss  to  jacket  is 
between  25  and  50  per  cent,  with  an  average  from  30  to  35  per 
cent.  In  the  case  of  air  jacketing,  it  is  not  generally  possible  to 
distinguish  between  jacket  and  radiation  losses. 

(d)  The  loss  due  to  heat  carried  away  by  the  exhaust  gases, 
owing  to  their  high  temperature,  generally  falls  between  25  and 
40  per  cent,  increasing  as  the  jacket  loss  decreases,  and  vice  versa. 

(e)  Combustion  is  almost  always  incomplete  to  a  small  extent 
and  may  at  times  be  imperfect  enough  to  account  for  a  consid- 
erable proportion  of  the  heat  available.     This  loss  should  not  be 
greater  than  I  to  2  per  cent  of  the  total  heat,  and  is  often  much 
less. 

(f)  Radiation  loss  is  supposed  to  include  all  heat  radiated  from 
the  outer  surfaces  of  the  engine,  and  in  the  heat  balance  it  would 
include  all  energy  converted   into   heat  by  friction  and   subse- 
quently lost  by  radiation  and  conduction.     It  is  generally  found 
by  subtracting  the  sum  of  the  other  four  quantities  of  heat  in 
per  cent  from  100;  and  when  this  method  is  used  this  difference 
includes  all  errors  of  the  other  results.     When  calculated  in  this 
way  it  may  have  a  value  of  from  10  to  20  per  cent,  with  an  aver- 
age of  about  15  per  cent. 

(g)  Another  heat-balance  method  puts  under  (i)  the  energy 
represented  by  the  upper  loop  of  the  diagram,  instead  of  the 
mechanical  energy  delivered.     Then  the  energy  loss  in  gas  and 
engine  friction  is  already  included  under  (i)  and  does  not  appear 
as  radiation  loss  under  (5).     The  latter  value  is  then  reduced 
to  about  5  to  8  per  cent  of  the  total  heat  supplied. 

(h)  The  total  heat  supplied  the  engine  may  be  taken  as  either 
the  higher  or  lower  heat  value  of  the  gas  (see  Chapter  XXVIII). 
Obviously  the  use  of  the  lower  value  results  in  a  higher  efficiency 
for  the  engine,  and  is  therefore  favored  by  gas-engine  builders. 
In  America  the  lower  value  is  universally  used,  although  in  some 
countries  of  Europe  the  higher  value  is  sometimes  adopted. 

(i)  It  is  important  to  note  that  the  thermal  efficiencies  of 
steam  and  internal-combustion  engines  are  not  strictly  compar- 
able unless  the  amounts  of  heat  available  are  measured  in  a 
truly  comparable  way.  This  is  usually  not  the  case,  for  the  fol- 
lowing reasons:  The  heat  supplied  a  steam  engine  is  generally 
figured  as  that  in  the  steam  above  some  datum,  such  as  32°  F., 
or  feed- water  temperature,  or  exhaust  temperature  and  is  not  in 


INTERNAL-COMBUSTION  ENGINES  449 

terms  of  the  fuel  used  or  its  cost.  On  the  other  hand,  the  heat 
supplied  an  internal-combustion  engine  is  based  upon  a  calori- 
metric  determination  of  the  fuel,  with  certain  corrections  in  case 
the  lower  calorific  value  is  sought.  This  amounts  to  figuring  the 
heat  supplied  above  a  datum  equal  to  the  existing  atmospheric 
temperature  for  all  the  constituents  of  the  exhaust  gas  excepting 
the  water  formed  by  the  combustion  of  hydrogen.  The  heat  value 
of  this  combustible  is  figured  above  a  datum  which  often  corre- 
sponds roughly  to  212°  F.  (See  Chapter  XXVIII  for  further 
discussion.) 

The  datum  used  is  thus  arbitrarily  chosen  for  convenience  in 
each  case,  and  the  results  are  not  strictly  comparable.  It  might 
seem  that,  since  the  steam  engine  is  given  credit  for  the  heat  of 
the  liquid  in  the  exhaust  steam,  or  for  that  part  of  it  above  feed- 
water  temperature,  some  sort  of  similar  device  might  be  adopted 
in  the  case  of  the  internal-combustion  engine.  This  is  incorrect, 
however,  because  the  exhaust  of  the  latter  engine  is  absolutely 
useless  so  far  as  the  engine  is  concerned.  Part  of  the  heat 
carried  may  be  abstracted  by  generating  steam,  heating  water, 
or  in  a  number  of  other  ways;  but  this  should  not  affect  the 
figure  for  heat  consumption  of  the  engine,  although  it  is  properly 
taken  account  of  in  determining  the  efficiency  of  the  plant  as  a 
whole. 

(j)  The  only  true  comparison  of  heat  expenditure  is  between 
heat-power  plants  as  a  whole  and  not  between  engines  only. 
If  the  fuel  is  the  same  in  both  cases,  the  ratio  of  the  amounts  of 
fuel  per  d.h.p.  may  be  used;  otherwise  relative  economy  is  shown 
by  the  ratio  of  the  costs  of  the  respective  amounts  of  fuel  con- 
sumed per  d.h.p.-hour. 

The  true  comparison  for  economic  purposes  should  include 
not  only  the  fuel  cost,  but  expenditure  for  labor,  lubricants, 
supplies,  repairs,  interest,  depreciation,  insurance,  and  all  other 
costs  involved  in  power  generation;  and  only  on  such  a  basis  are 
two  systems  truly  comparable. 

222.  Performance  of  Internal-Combustion  Engines,  (a)  There 
are  so  many  different  kinds  of  internal-combustion  engines  that 
it  is  difficult  to  make  broad  statements  to  fit  all  cases.  The  fol- 
lowing must,  therefore,  be  regarded  as  very  general,  and  appli- 
cable only  to  the  average  lines  of  engines. 


450 


HEAT-POWER  ENGINEERING 


(b)  American  engines  built  to  run  on  natural  gas  are  gener- 
ally guaranteed  to  deliver  a  brake  horse  power  on  from  10  to  n 
cubic  feet  of  gas  at  rated  load.  This  gas  is  commonly  assumed 
to  have  a  calorific  value  (lower)  about  1000  B.t.u.  per  cubic 
foot;  so  this  guarantee  is  from  10,000  to  11,000  B.t.u.  per  horse- 
power hour  at  rated  load,  corresponding  to  thermal  efficiencies 
of  from  23  to  25.5  per  cent  on  the  d.h.p.  Many  engines  at 
present  in  operation  give  better  results  than  these  by  several 
per  cent  at  rated  loads;  and  the  efficiencies  are  still  better  at 
loads  from  10  to  15%  greater  than  the  normal. 

At  three-quarter  load  they  are  generally,  guaranteed  at  1 1 ,000 
to  13,000  B.t.u.;  at  half-load,  13,000  to  15,000;  and  at  one-quarter 
load  20,000  to  23,000  B.t.u. 


\ 

/ 

// 

20,000 

ij 

15,000^ 

J3 
10,000-^ 

fq 

5,000 

^x 

^ 

5''xxX 

p 

pq 

x 

/^ 

<<4 

*^ 

—  ___-•  --* 

500,000 
250,000 

Fraction  of 
Develops 

X 

Rated  Load    H                    l/2                     $£                     *                      *% 
dH.P.       25                 50                75               100  '.  _       125 

Fig.  306. 

The  curves  of  the  total  consumption  and  rate  per  d.h.p.-hour 
for  average  100  horse-power  natural-gas  engines  are  given  in 
Fig.  306.  In  each  case  the  two  curves  correspond  to  the  limits 
above  given.  The  exact  shape  of  these  curves  will,  of  course, 
depend  upon  the  type  of  engine,  method  of  governing,  etc.,  but 
those  given  may  be  taken  as  representing  average  practice. 

It  is  convenient  to  remember  that  practically  all  internal- 
combustion  engines  (with  the  possible  exception  of  some  oil 
engines)  will  require  about  twice  as  many  thermal  units  per  horse- 
power hour  at  one-quarter  load  as  at  the  rated  load. 


INTERNAL-COMBUSTION  ENGINES  451 

(c)  Engines    intended    to    operate    on    illuminating    gas    are 
generally   guaranteed   with   lower   efficiencies   than   natural-gas 
engines.     The  B.t.u.  per  d.h.p.-hour  is  usually  from  12,000  to 
13,000  B.t.u.  at  full  load.     The  poorer  performance  is  principally 
due  to  the  fact  that  these  engines  are,  as  a  rule,  not  so  carefully 
designed,  as  they  are  not  built  in  large  sizes  or  in  great  numbers 
because  of  the  high  cost  of  this  gas.     Some  of  the  highest  thermal 
efficiencies  on  record  have,  however,  been  obtained  with  engines 
using  illuminating  gas. 

(d)  Producer-gas  engines  are  generally  guaranteed  on  a  basis 
of  coal  used  per  horse-power  hour  rather  than  cubic  feet  of  gas 
or  B.t.u.     The  average  figure  is  I  to  i.i  pounds  of  coal  per  horse- 
power-hour at  rated  load,  and  most  producer-gas  installations 
of  good  design  can  be  counted  on  to  produce  a  d.h.p.-hour  on 
less  than  1.2  pounds  if  operated  continuously  at  full  load.     Under 
accurate  test  many  of  them  have  developed  a  brake  horse-power 
hour  on  0.8  to  0.9  of  a  pound  of  coal. 

To  give  an  idea  of  the  meaning  of  these  figures,  it  is  sufficient 
to  state  that  a  consumption  of  only  0.8  pound  of  coal  per 
d.h.p.-hour  corresponds  to  a  thermal  efficiency  on  the  brake  for 
the  engine  alone  of  about  31  per  cent;  while  I  pound  corresponds 
to  about  25  per  cent. 

(e)  Gasoline  engines  (stationary)  are  generally  guaranteed  to 
deliver  a  d.h.p.-hour  on  one   pint  of  gasoline,   at  rated  load. 
This  corresponds  to  a  heat  consumption  of  about  14,000  B.t.u. 
per  d.h.p.-hour,  or  a   thermal  efficiency  of  about   18  per  cent. 
As  a  matter  of  fact,  all  of  the  better  types  are  capable  of  deliver- 
ing a  d.h.p.-hour  on  about  two-thirds  of  the  guaranteed  quantity, 
when  everything  is  in  perfect  adjustment. 

Between  rated  oad  and  maximum  load  the  efficiency  will 
first  increase  and  then  due  to  the  use  of  rich  mixture  will  slowly 
decrease. 

At  about  one  quarter  load  the  consumption  per  d.h.p.  will 
be  about  twice  that  at  full  load. 

(f)  Alcohol  engines  are  not  as  yet  a  commercial   product  in 
this  country,  and  very  few  figures  are  available  from  practice. 
Tests  show  that  such  engines  can  safely  be  guaranteed  on  the 
same  or  a  smaller  volume  consumption  than  gasoline.     It  is  safe 
to  assume  a  thermal  efficiency  of  25  per  cent  on  the  brake  with 
these  engines,  and  figures  as  high  as  32  per  cent  and  more  have 


452 


HEAT-POWER  ENGINEERING 


11 


13        15        17        19 
B.H.P.  and  I.H.P. 


23 


Fig.  307. 


Fig.  308. 


loo 
[» 


30  W 

t 


Fig.  309. 


INTERNAL-COMBUSTION  ENGINES 


453 


100 


80 


(50 


50000 
g  45000 

I 

1 
1 

B.t.u./  1.  H.  P.-or/  B.  H.  P.-Hour 

V 

1 

1 

^ 

\ 

S_ 

<fc 

| 

O 
^    30000 

°   30000 
25000 
20000 

\ 

% 

c 

500  H.P.  DOUBLE 
ACTING  TANDEM 
HORIZONTAL  ENGINE 
OPERATING  ON 
BITUMINOUS 
PRODUCER  GAS. 

X 

^ 

7  \ 

\ 

^ 

s^ 

i 

**&• 

fc> 

)         100  i       200    1    300        1UO       5 

)0        COO  B.H.I 

%  of  Rated  Load 

Fig.  310.. 


500  H.P.   DOUBLE  ACTING 
TANDEM  HORIZONTAL 

ENGINE  OPERATING  ON 
BITUMINOUS  PRODUCER  GAS 


100$    $>  of  Rated 
Load 


Fig.  3". 


3,000,000 
2,000,000 

1,000,000 
#  Nor  ma 

250  H.P.    MARINE  TYPE 
DIESEL  ENGINE. 

l^JUU 

11000 
10000 
9000 
8000 

ij 

A 

\ 

\ 

p 

CQ 

Nj£ 

^ 

/, 

O 

H 

#s 

><^ 

4 
—  ^~ 

? 

p 

D.h.p.50|       100  j    150      |200       250      300 
1  Load  25           50           75           100       120 

Fig.  312. 


454  HEAT-POWER  ENGINEERING 

been  obtained.  This  high  efficiency  is  largely  due  to  the  high 
compression  pressure  that  can  be  used  with  this  fuel. 

(g)  Oil  engines  (kerosene,  distillate,  and  crude)  differ  widely 
in  fuel  consumption,  but  the  newer  and  better  American  types 
are  capable  of  producing  a  d.h.p.-hour  on  from  0.7  to  as  low  as 
0.5  of  a  pound  of  oil.  These  figures  correspond  roughly  to 
thermal  efficiencies  of  from  1 8  to  28  per  cent  on  the  d.h.p. 

(h)  The  curves  given  in  Figs.  307  to  312  inclusive  show  results 
of  tests  of  several  different  types  of  engines  with  different  fuels. 
They  illustrate  in  a  general  way  how  the  various  efficiencies  of 
commercial  importance  vary  with  such  things  as  load,  size  of 
engine,  kind  of  fuel,  etc. 


CHAPTER  XXVII. 
FUELS. 

223.  Fuels,     (a)  In  the  discussion  of  ideal  engines  in  preceding 
chapters,  a  hot  body  was  assumed  to  be  available  and  it  was 
imagined  to  be  so  constituted  that  it  could  deliver  heat  at  any 
time  and  in  any  desired  quantity,  with  no  change  in  its  own 
temperature.     No   such  hot   body  is   really  available,   and   in 
practice  supplies  of  heat  are  obtained  by  burning  "  fuel." 

(b)  In  the  broadest  sense  fuel  is  any  material  which  can  be  made 
to  combine  with  other  material  in  such  a  way  as  to  liberate  heat.     In 
the  commercial  sense,  however,  fuel  is  any  material  the  greater 
part  of  which  can  be  made  to  combine  with  oxygen,  usually  from 
the  air,  so  as  to  liberate  heat,  and  which  is  purchasable  at  such  a 
price  that  its  use  will  yield  a  profit. 

(c)  Fuels   may   be   solid,   liquid   or   gaseous.     The   principal 
Natural  Fuels  are  Coal,  Wood,  Petroleum  Oil  or  Crude  Oil,  and 
Natural  Gas.     The  principal  Prepared  Fuels  are  Coke,  Briquets 
made  from  coal,  Charcoal,  Distillation  Products  of  Petroleum, 
Artificial  Gas  made  from  solid  or  liquid  fuel,  Hydrogen  Gas  and 
Acetylene  Gas  made  from  noncombustibles,  and  Alcohol.     There 
are  also  certain  kinds  of  municipal  refuse  and  manufacturing 
wastes  which  have  fuel  value. 

224.  Geology  of  Coal,     (a)  Formation.     Beds  of  coal  in  the 
different  stages  of  formation  are  scattered  over  the  earth's  sur- 
face.    Geologists  believe  that  coal  results  from  collections  of 
vegetable  matter,  deposited  in  swampy  places  or  under  water, 
which  are  subsequently  covered  by  silt  and  other  material  and 
during  geological  ages  are  gradually  changed  in  physical  and 
chemical  composition  until  they  finally  become  coal. 

(b)  Vegetable  matter  may  here  be  assumed  to  consist  of 
carbon,  hydrogen  and  oxygen  combined  in  definite  proportions, 
together  with  certain  incombustible  inorganic  salts  in  the  cell 
structure.  This  vegetable  matter  when  under  water  changes 

455 


456 


HEAT-POWER  ENGINEERING 


very  gradually,  losing  some  of  its  material  in  the  form  of  gas 
(usually  methane  or  marsh  gas,  CH^)  and  as  water.  These  trans- 
formations continue  after  the  deposit  has  been  deeply  covered 
with  earth,  and  eventually  only  the  carbon  and  the  inert  salts 
remain.  The  extent  of  these  changes  is  principally  dependent 
on  time,  measured  in  geological  ages,  on  temperature,  and  on  the 
pressure,  depth  and  porosity  of  the  overlying  material. 

The  combustible  part  of  coal  consists  principally  of  volatile 
matter  (which  is  released  upon  heating  to  a  high  temperature  in 


100      90 


%  Volatile  Matter 
70       60       50       40        30       20       10        0 


\ 


V 


Vegetable 
Matter 


JFeat 
Lignite 


0        10       20       30       10       50       60       70       80 
fi  Fixed  Carbon 

Fig.  313. 


90    100   f 


,Semi- 
Bituminous 


Anthracite 
Graphitic 


a  closed  crucible)  and  of  fixed  carbon  which  remains  after  such 
treatment.  As  the  formation  of  coal  progresses  the  percentage 
of  volatile  matter  and  moisture  decreases  with  corresponding 
increase  of  fixed  carbon. 

(c)  Classification.  In  the  early  stages  of  transformation  the 
material  is  called  (i)  Peat  or  Turf.  Later,  with  increased  pres- 
sure of  overlying  material  resulting  in  greatly  reduced  volume, 
it  becomes  (2)  brown  or  black  Lignite.  Later  still,  after  addi- 
tional physical  and  chemical  changes,  the  material  becomes 
(3)  Soft  Coal  or  Bituminous  Coal.  Subsequently,  it  becomes 


FUELS 


457 


successively  (4)  Semibituminous ,  then  (5)  Semianthracite,  (6) 
Anthracite,  and  finally  (7)  Graphitic  Coal.  The  last  is  practically 
pure  carbon.  These  are  the  seven  groups  into  which  coals  are 
generally  classified.* 

(d)  Fig.  313  shows  in  a  very  general  way  the  relation  of  fixed 
carbon  to  volatile  matter  during  the  transformation  of  vegetable 
matter  into  coal. 

The  horizontal  width  of  the  diagram  represents  the  sum  of 
fixed  carbon  and  volatile  matter.  The  inclined  line  divides  the 
horizontals  into  parts  which  represent  fixed  carbon  (at  the  left) 
and  volatile  matter  (at  the  right).  Percentages  may  be  read 
from  the  scales. 

The  progress  of  the  transformation  is  shown  by  the  classi- 
fication at  the  right  of  the  diagram.  This  grouping  would  seem 
to  indicate  well-defined  divisions  between  adjacent  classes;  but 
in  reality  the  groups  blend  into  each  other.  The  diagram  is 
simply  for  illustration  and  should  not  be  used  otherwise. 

(e)  There  is  as  yet  no  really  satisfactory  basis  for  the  classi- 
fication of  coal.     Formerly  the  classification  was  according  to 
the  percentage  of  fixed  carbon  in  the  dry  combustible,  as  given  in 
Table  XIII.     This,  however,  is  not  very  satisfactory  for  coals 
high  in  volatile  matter. 

TABLE  XIII.  —  OLD   CLASSIFICATION   OF  COALS. 


Kind  of  Coal. 

Fixed  Carbon. 

Volatile  Matter. 

Anthracite  
Semianthracite  

Per  cent. 
97.0  to  92.5 
92.5  to  87.5 

Percent. 
3.0  to    7-5 
7.5  to  12.5 

Semibituminous 

87.5  to  75.0 

12.5  to  25.0 

Bituminous   Eastern                                  .... 

75.0  to  60.0 

25.0  to  40.0 

Bituminous   Western                                  .... 

65.0  to  50.0 

35.0  to  50.0 

Lignite                                                         

Under  50.0 

Over  50.0 

(f)  A  recently  proposed  classification,  based  on  the  ratio  of 
volatile  carbon  to  total  carbon  and  known  as  Parr's  Classifica- 
tion^ appears  to  be  more  satisfactory.  Omitting  the  subgroups 
under  bituminous  coals  and  lignites,  this  classification  is  given  in 
Table  XIV. 

*  One  other  group  falling  between  (2)  and  (3)  above  and  known  as  "subbitumi- 
nous  "  is  sometimes  recognized. 

f  Bull.  No.  3  Illinois  State  Geol.  Survey. 


458  HEAT-POWER  ENGINEERING 

TABLE  XIV.  —  PARR'S  CLASSIFICATION   OF  COALS.     (Abbrev.) 


"K"itirl  of  Pnal 

Volatile  Carbon 

Inert  Volatile 

Total  Carbon 

Anthracite  
Semianthracite  
Semibituminous  
Bituminous  

Per  cent. 

Below  4 
Between  4  and  8 
Between  10  and  15 
22  to  44 

Per  cent. 
5  to  16 

Lignite 

27  and  up 

16  to  30 

(g)  Coal  Fields  in  the  United  States.*  The  main  deposits 
in  this  country  are  shown  in  a  very  general  way  in  Fig.  314,  in 
which  the  average  character  of  each  deposit  is  indicated  by  the 


FIELDS 

1-  R.I.  Graphitic  5-  Eastern  Interior 

2- Pa.  Anthracite  6 -Western       " 

3- Appalachian  7-S.W.  " 

4-Northern  Interior 


Fig.  314- 

kind  of  hatching.  In  Rhode  Island  there  is  a  little  graphitic 
coal.  Most  of  the  anthracite  is  found  in  beds  of  less  than  500 
square  miles  area  located  in  eastern  Pennsylvania.  The  princi- 
pal deposit  of  semibituminous  coal  is  about  three  hundred  miles 
long  by  twenty  wide  and  lies  along  the  eastern  edge  of  the 
Northern  Appalachian  Field.  The  bituminous  coals  extend  from 
this  deposit  westward.  Starting  with  the  graphitic  coal  in 

'    *  See  Coal  Fields  in  the  U.  S.  by  C.  W.  Hayes,  U.  S.  Geological  Survey,  and 
Kent's  "  Steam  Boiler  Economy." 


FUELS  459 

Rhode  Island,  broadly  speaking,  the  farther  west  a  coal  is  located 
the  less  advanced  it  is  in  the  process  of  transformation.  .It  is 
important  to  note,  however,  that  there  are  many  exceptions  to 
these  very  general  statements,  for  there  are  numerous  other  small 
fields,  not  shown,  scattered  over  the  country.  For  instance,  a 
little  anthracite  coal  is  found  in  Colorado  and  in  New^  Mexico, 
and  some  semibituminous  in  Arkansas. 

225.  Composition  of  Coal,  (a)  Coals  consist  principally  of 
the  elements  Carbon,  Hydrogen,  Sulphur,  Oxygen,  and  Nitrogen, 
together  with  moisture  and  ash.  The  elements  named,  par- 
ticularly Carbon,  Hydrogen  and  Oxygen,  seem  to  be  combined 
in  various  ways  in  the  solid  coal,  though  little  is  known  of  the 
formulas  of  the  compounds  in  which  they  exist.  The  ash  contains 
the  inert  salts  of  the  original  vegetable  matter,  together  with  silt 
and  similar  impurities  acquired  after  deposition  and  submersion. 

(b)  "Moisture  "  is  arbitrarily  defined  as  the  material  lost  when 
a  finely  powdered  sample  of  the  coal  is  maintained  from  half  an 
hour,  to  an  hour,  at  a  temperature  of  about  220°  Fahr.;  or,  more 
exactly,  as  the  maximum  loss  which  can  be  made  to  occur  at 
this  temperature.     The  material  driven  off  in  this  way  is  not 
necessarily  all  moisture,  for,  with  some  coals,  part  of  the  more 
volatile  combustible  material  may  distil  off.     Moreover,  all  the 
water  content  may  not  be  driven  off  by  maintaining  the  material 
at  this  temperature.     The  definition  is,  therefore,  only  an  arbi- 
trary one,  but  it  seems  to  be  the  best  that  can  be  devised. 

(c)  "Dry  Coal"  is  coal   from  which  the  moisture  has  been 
driven  by  heating,  as  above  described. 

(d)  "  Volatile  Matter"  (or  "  volatile  ")  is  the  name  given  to  all 
material  driven  off  when  "  dry  coal  "  is  maintained  at  a  very  high 
temperature  (between  a  "  red  "  and  "  white  heat ")  in  a  covered 
crucible  (out  of  contact  with  air)  until  there  is  no  further  loss  of 
weight.    This  definition  is  again  purely  an  arbitrary  one,  but  it  is 
useful  in  that  it  gives  a  measure  of  the  material  which  will  be 
similarly  given  off  in  a  furnace  or  in  a  coke  oven. 

(e)  "Fixed  Carbon  "  is  defined  as  the  portion  remaining  after 
subtracting  the  ash  from  the  material  left  in  a  crucible  after 
driving  off  the  volatile  matter. 

(f)  "Combustible  "  is  the  term  used  to  designate  the  part  of  the 
coal  other  than  moisture  and  ash.     It  is,  therefore,  the  sum  of 


46o 


HEAT-POWER  ENGINEERING 


fixed  carbon  and  "  volatile,"  as  above  defined.  It  is  composed 
principally  of  carbon  and  hydrocarbons  but  it  is  important  to 
note  that  it  also  contains  noncombustible  matter  such  as  Nitro- 
gen and  Oxygen  and  hence  the  term  is  a  misnomer.  When  the 
coal  contains  sulphur  a  large  part  of  this  is  also  found  in  the  so- 
called  combustible. 

226.  Coal  Analyses,  (a)  Two  types  of  analysis  are  in  common 
use  —  one  gives  what  is  known  as  an  "  Ultimate  Analysis,"  the 
other  a  "  Proximate  Analysis." 

(b)  In  an  ultimate  analysis  of  so-called  "dry  combustible" 
the  percentages  of  Carbon,  Hydrogen,  Oxygen,  Nitrogen,  and 
Sulphur  are  determined.  The  ultimate  analysis  of  "dry  coal " 
also  includes  the  percentage  of  ash,  and  in  some  cases  a  chemical 
analysis  of  the  ash  is  also  made.  Ultimate  analyses  are  seldom 
made  by  engineers,  being  more  often  obtained  from  chemical 
laboratories.  Table  XV  gives  in  a  general  way  the  approximate 
ranges  of  the  ultimate  analyses  of  the  combustible  in  different 
kinds  of  coals.  More  accurate  tables  of  analyses  of  coals  from  dif- 
ferent localities  can  be  found  in  text  books  on  fuels  and  on  boilers, 
in  engineer's  "  pocket  books  "  and  in  reports  and  publications 
of  the  geological  surveys  of  the  United  States  and  of  various 
states.  In  consulting  such  references  it  is  necessary  to  bear  in 
mind  that  ultimate  analyses  are  sometimes  incorrectly  made  on 
the  basis  of  coal  "  as  received,"  i.e.,  on  wet  coal.  In  such  cases 
the  percentages  of  H  and  0  include  the  hydrogen  and  oxygen 
of  the  moisture. 

TABLE  XV. —  ULTIMATE  ANALYSES  OF  COALS. 


Per  Lb.  of  Dry  Combustible. 

C 

H 

0 

N 

S 

Anthracite  

92-98 
90-5 
87.3 
75-83 
70-78 
61 

1-3-5 
5 
4-5-5-5 
5-6.8 

6 

2-3 
4-5 
3-4-8 
4-1  1 
10-15 
33 

I 

0-1.5 

Semianthracite  
Semibituminous 

0.9-1.8 

1-2 
2 

0.6-1.3 
0.4-3 

i-3 

Bituminous.  .  .    . 

Lignite.  . 

Peat  

(c)   The  proximate  analysis  divides  the  fuel  roughly  into  the 
several  parts  which  have  already  been  described  in  Section  225, 


FUELS  461 

as  Moisture,  Volatile  Matter,  Fixed  Carbon,  and  Ash.  While 
this  analysis  is  less  exhaustive  than  an  ultimate  analysis,  it  has 
two  marked  advantages  over  the  latter:  (i)  It  is  easily  made 
by  the  engineer  and  involves  the  use  of  very  simple  apparatus; 
and  (2)  it  indicates,  in  a  general  way,  the  behavior  which  may 
be  expected  of  the  coal  during  utilization  as  fuel. 

(d)  Proximate  analyses  are  given  both  on  the  basis  of  "dry 
coal  "  and  coal   "  as  received."     For  purposes  of  comparison 
with  other  fuels,  the  dry-coal  basis  is  the  better  because  the 
conditions  of  storage  and  transportation  may  materially  change 
the  moisture  content.     It  would  be  obviously  unfair,  for  instance, 
to  charge  against  a  coal,  in  comparison  with  others,  the  fact  that 
it  had  been  rained  on,  or  had  been  stored  under  water.     On  the 
other  hand,  when  coal  is  being  purchased  by  weight,  it  is  as  ob- 
viously unfair  to  pay  for  water  at  the  price  of  coal,  and  there- 
fore for  this  and  similar  purposes  analyses  should  be  on  a  basis 
of  coal   "  as  received,"  or  else,  in   addition  to  the  proximate 
analysis  of  dry  coal,  there  should  be  a  statement  of  moisture 
content. 

(e)  Table  XIII  gives  the  approximate  range  of  percentages 
of  fixed  carbon  and  volatile  in  the  combustible  of  the  different 
kinds  of  coal.     The  proximate  analyses  of  "  dry  coals  "  may  be 
obtained  by  introducing  average  ash  contents  and  altering  the 
percentages    accordingly.     Proximate    analyses    of    coal    from 
different  localities  may  be  found  in  the  books  and  reports  to 
which  reference  has  already  been  made. 

(f)  It  will  be  shown  in  later  chapters  that  such  data  as  are 
given  by  the  ultimate  analysis  can  be  used  for  calculating  the 
calorific  value,  and  that  they  are  also  needed  for  computing 
losses  occurring  in  furnaces  and  boilers.     For  these  reasons  ulti- 
mate analyses  are  often  desired,  even  though  their  actual  deter- 
mination is  outside  the  engineer's  field.     It  has  been  shown  by 
Professor  L.  S.  Marks*  that,  in  the  case  of  most  coals  occurring 
in  the  United  States,  the  ultimate  analysis  can  be  approximated 
from  the  proximate  analysis  with  sufficient  accuracy  for  deter- 
mining the  distribution  of  boiler  and  furnace  losses  and  for  general 
engineering  work.     The  results  which  Professor  Marks  gave  by 
curves  have  been  put  into  the  form  of  equations  by  Professor 

*  Power,  vol.  29,  p.  928,  Dec.,  1908. 


462  HEAT-POWER  ENGINEERING-' 

H.  Diederichs.     Only  the  principal  ones  of  these  equations  will 
be  given  here.* 

Letting  V  represent  the  weight-percentage  of  volatile  matter 
in  the  combustible,  then  the  approximate  weight-percentages  of 
hydrogen  (H),  of  volatile  carbon  (C),  and  of  nitrogen  (N)  are 
respectively 


(329) 


C  =  0.02  V2  )  for  anthracite  and  )  ,       . 

or          =  0.9  (V  —  10)  )  semianthracite.       ) 

C  =  0.9  (V  —  14)  for  bituminous  and  semibituminous  (331) 

C  =  0.9  (V  -  1  8)  for  lignites  .........  (332) 

N  =  0.07  V  for  anthracite  and  semianthracite.     .     .  (333) 

N  =  2.10  —  0.012  V  for  bituminous  and  lignite.  .     .  (334) 

The  occurrence  of  oxygen  and  sulphur  is  apparently  more  or 
less  accidental  in  character,  showing  no  uniformity,  and  is  not 
expressible  by  equations.  The  greater  part  of  all  the  sulphur 
and  some  of  the  oxygen  will  appear  in  the  proximate  analysis 
as  volatile,  and  will  therefore  be  accounted  for  as  hydrogen  and 
carbon  in  the  use  of  these  equations. 

227.  Fuel  Values  of  Coals,  (a)  The  methods  of  determining 
the  fuel  values  of  combustible  materials  will  be  discussed  in 
detail  in  the  next  chapter;  there  are  a  few  considerations,  how- 
ever, which  it  is  necessary  to  mention  briefly  at  this  point.  It 
is  customary  to  state  the  calorific  value  of  a  material  in  terms  of 
the  B.t.u.  made  available  by  burning  one  pound.  When  a 
material  containing  uncombined  hydrogen  is  burned,  this  hy- 
drogen unites  with  the  oxygen  and  forms  superheated  water 
vapor.  If  this  vapor  passes  off  without  surrendering  its  heat, 
the  calorific  value  of  the  fuel  is  less  than  if  that  heat  is  made 
available.  Hence  the  terms  lower  heat  value  and  higher  heat  value 
are  used  to  distinguish  between  the  two  conditions  of  combustion. 

(b)  As  will  be  explained  in  Chapter  XXVIII,  the  Calorific 
Value  of  a  coal  can  be  very  roughly  determined  from  the  ulti- 
mate analysis  by  the  use  of  Dulong's  Formulas.  These  are  given 

*  For  more  complete  explanations,  percentages  of  accuracy,  etc.,  see  Carpenter 
and  Diederichs'  "  Experimental  Engineering,"  p.  507,  and  the  original  article  in 
Power  referred  to  in  the  preceding  footnote. 


FUELS  463 

in  Section  243  as  Eqs.  (376)  and  (377)  and  are  stated  as  follows: 

Higher  B.t.u.  =  14,600  C  +  62,000  (H  -  O/8)  -f-  4000  S. 
Lower  B.t.u.    =  14,600  C  +  52,000  (H  —  0/8)  +  4000  S. 

If  for  C,  H,  O,  and  61  are  substituted  the  weights  of  these  elements 
per  pound  of  combustible,  the  results  will  be  B.t.u.  per^  pound  of 
combustible.  If  weights  per  pound  of  dry  coal  are  used,  the 
result  will,  of  course,  be  B.t.u.  per  pound  of  dry  coal. 

As  will  be  explained  more  in  detail  in  the  next  chapter,  Du- 
long's  formulas  are  only  approximate  because  they  assume  all 
the  oxygen  originally  present  in  the  fuel  to  be  combined  with 


16000 


15500 


50  60  70  80  90  100 

$  Eixed.Car.bon  ia  the  Combustible 

Fig-  3i5- 

hydrogen,  and  because  they  take  no  account  of  the  disappear- 
ance of  heat  accompanying  the  dissociation  of  hydrocarbons 
and  similar  obscure  phenomena  occurring  during  combustion. 
For  accurate  determination  of  the  calorific  value,  some  form  of 
fuel  calorimeter  should  be  used.  These  calorimeters  will  be  dis- 
cussed in  Section  244. 

(c)  Various  empirical  formulas  have  been  proposed  for  giving 
the  heat  value  per  pound  of  fuel  in  terms  of  the  proximate 
analysis.    These  usually  contain  "constants,"  which  are  given  in 
tables,  and  which  vary  with  the  locality  of  the  mine,  or  with  the 
ratio  of  certain  constituents,  such  as  volatile  matter  to  total  com- 
bustible.    These  formulas  will  not  be  given  in  this  brief  treatment. 

(d)  Fig.  315  gives  Mahler's  Curve*  which  shows  in  a  general 

*  Redrawn  from  curve  given  in  U.  S.  Geol.  Survey  Professional  Paper  No.  48. 


464  HEAT-POWER  ENGINEERING' 

way  how  the  heat  value  per  pound  of  combustible  varies  with  the 
percentage  of  fixed  carbon  present,  and  which  also  shows  the 
range  of  percentages  of  the  fixed  carbon  in  the  different  kinds  of 
coal  as  they  are  usually  classified.  This  curve  shows  clearly  that 
of  all  coals  the  semibituminous  has  the  combustible  of  the  highest 
heat  value;  and  in  connection  with  the  map  in  Fig.  314,  it  is  seen 
that  in  general  the  coals  are  of  decreasing  heat  value  the  farther 
they  are  located  from  the  main  semibituminous  bed.  It  is  also 
true,  generally,  that  the  difficulty  encountered  in  burning  a  coal 
efficiently  increases  with  the  distance  of  the  mine  from  this  same 
bed. 

(e)  Coal  when  mined  always  contains  moisture  and  often  takes 
up  more  afterward.     Moisture  is  generally  undesirable  because 
it  is  not  combustible  and  because  it  is  vaporized  and  superheated 
during  combustion,  thus  absorbing  heat  that  might  otherwise  be 
utilized.     Eastern  coals,  as  mined,  contain  from  one  to  five  per 
cent  of  moisture,  western  coals  from  three  to  fifteen  per  cent,  and 
lignites  from  ten  to  thirty  per  cent. 

(f)  Ash  not  only  decreases  the  heat  value  of  fuel,  but  it  also 
increases  the  cost  of  transportation  and  handling  of  the  coal  per 
unit  of  heat  produced,  and  in  addition  there  is  the  cost  of  its 
disposal  after  combustion.     The  presence  of  ash  also  interferes 
with  combustion,  especially  if  it  is  of  such  composition  as  to 
form  clinker.     The  percentage  of  ash  in  commercial  coals  ranges 
from  three  to  fifteen  ordinarily,  and  is  usually  greater  in  the 
smaller  sizes  than  in  the  larger. 

(g)  Sulphur,  although  combustible,  usually  makes  the  fuel  un- 
suitable for  use  under  boilers  and  for  many  other  purposes,  if 
present  in  large   quantities.     The  products  of   its  combustion 
may,  under  certain  circumstances,  form  acids  by  combining  with 
water  and  these  may  attack  the  metal  of  boilers,  etc.    The  pres- 
ence of  considerable  quantities  of  sulphur  is  supposed  to  indicate 
a  readily  fusible  ash  which  causes  trouble  in  the  boiler  furnace, 
or  in  the  "  gas  producer,"  by  the  formation  of  clinker. 

(h)  Peat,  in  its  natural  state,  is  a  poor  fuel  containing  a  large 
percentage  of  moisture.  Its  value  is  improved  by  drying,  but  it 
is  not  yet  generally  used  when  other  cheap  fuels  can  be  obtained.* 

*  As  an  indication  of  what  may  be  expected  when  other  fuels  become  scarcer, 
see  Bulletin  16,  U.  S.  Bureau  of  Mines,  "  The  Use  of  Peat  for  Fuel  and  Other 
Purposes." 


FUELS 


465 


(i)  Lignite  is  an  unsatisfactory  fuel  when  burned  in  furnaces, 
but  recent  investigations  seem  to  indicate  that  it  may  be  of  great 
value  for  the  making  of  "  producer  gas  "  for  which  there  is  a 
rapidly  growing  demand  for  power  purposes. 

(j)  Western  bituminous  coals  are  a  little  harder  to  burn  effi- 
ciently than  eastern  on  account  of  the  larger  proportion^of  volatile 
matter  contained.  The  higher  the  percentage  of  volatile  matter 
in  the  coal  the  more  difficult  it  is  to  burn  it  smokelessly  and 
efficiently  (see  Chapter  XXIX). 

(k)  Bituminous  coals  are  sometimes  classified  as  caking  and 
noncaking.  The  fragments  of  the  former  kind  coalesce  into  cakes 
while  burning,  which  is  desirable  in  the  making  of  coke  but  may 
interfere  with  the  supplying  of  air  for  combustion  when  the  coal  is 
burned  upon  grates. 

(1)  Cannel  coals  are  bituminous  coals  which  are  very  rich  in 
hydrocarbons  and  burn  like  a  candle,  hence  the  name.  These 
are  used  as  "  enrichers  "  in  gas  making. 

Coals  high  in  hydrocarbons  burn  with  a  long  flame  and  are 
more  difficult  to  burn  efficiently  than  short-flame  coals. 

(m)  Semibituminous  coals,  as  has  been  shown,  have  the  highest 
heat  value  per  pound,  and,  as  they  burn  with  a  comparatively 
short  flame,  they  are  the  most  desirable  coals  for  use  in  boiler 
and  similar  furnaces. 

TABLE  XVI.  — SIZES  OF   SOFT  COAL  — EASTERN    STATES.* 


Name. 

Through  Bars 
Spaced  Apart. 

Over  Bars  Spaced 
Apart. 

Lump  

Inches. 

Inches. 
If 

Nut  

I? 

3 

Slack 

| 

(n)  Anthracite  coal  has  an  advantage  over  the  other  classes 
in  burning  smokelessly,  and  consequently  is  in  great  demand 
where  smoke  is  not  permitted.  The  available  supply  in  the 
eastern  part  of  the  United  States  is  rapidly  diminishing  and  the 
price  is,  in  general,  higher  than  for  other  coals.  To  obtain  the  best 
results  with  anthracite  it  must  be  of  uniform  size.  As  the  price 
decreases  with  the  size,  only  the  smaller  grades,  usually  those  less 
than  f"  in  diameter,  are  used  for  power  purposes.  Table  XVII 
gives  the  usual  classification,  but  unfortunately  the  names  and 
sizes  in  some  instances  vary  with  the  locality. 

*  For  sizes  in  West  see  A.S.M.E.  Power  Test  Code.  o.  162. 


466 


HEAT-POWER  ENGINEERING 
TABLE  XVII.  — SIZES  OF  ANTHRACITE  COAL* 


Name. 

Through  (Dia.). 

Over  (Dia.). 

Chestnut  
Pea 

T 

I" 
& 

Buckwheat  No.  i. 
Buckwheat  No.  2. 
Buckwheat  No.  3. 
Culm 

A 

1 

A 

t 

A 

Run  of  mine 

Unscreened 

(o)  C0a/  dust,  produced  in  mining  the  material,  is  almost 
always  a  waste  product.  Such  dust  is  now  successfully  used  in 
firing  rotary  kilns  and  similar  apparatus,  but  is  seldom  used  for 
ordinary  power  purposes  although  special  devices  for  burning 
it  under  boilers  and  in  producers  have  been  used  to  a  limited 
extent. 

Coal  dust  and  similar  waste,  known  collectively  as  "  culm  " 
may  represent  from  10  per  cent  to  as  high  as  50  per  cent  of  all 
the  coal  recovered  from  the  mine.  It  is,  therefore,  apparent 
that  sooner  or  later  some  method  of  utilizing  this  waste  will 
have  to  be  adopted  because  of  the  decrease  in  the  available  supply 
of  coal.  Such  material  has  been  very  successfully  recovered  in 
Europe  by  forming  it  under  high  pressure  into  briquets  in  which 
such  materials  as  pitch,  resins,  wax  tailings,  starch,  and  several 
inorganic  salts  are  used  for  "  binders."  These  briquets  can 
often  be  used  more  efficiently  than  ordinary  lump  fuel,  because 
of  their  uniformity  of  size,  advantageous  shape,  and  general  good 
behavior  in  the  furnace;  hence  it  often  proves  to  be  economical 
to  purchase  briquets  at  a  slightly  higher  price  than  that  asked 
for  similar  lump  coal.f 

228.  Coke  is  the  solid  material  left  after  driving  off  the 
volatile  part  of  coal  by  heating  with  total  or  partial  exclusion  of 
air.  Only  certain  coals  yield  coke  of  commercial  value.  Nearly 
all  of  the  coke  made  is  used  in  metallurgical  processes,  and  but 
little  as  yet  for  power  purposes. 

*  There  are  other  sizes  such  as  "  Broken,"  "  Egg,"  and  "  Stove  "  which  need 
not  be  considered  here  as  they  are  not  commonly  used  in  heat-power  engineering. 
For  their  sizes  see  A.S.M.E.  Power  Test  Code,  page  15. 

t  For  investigations  relating  to  the  manufacture  and  utilization  of  briquets 
under  American  conditions  see  bulletins  of  the  U.  S.  Geol.  Survey  and  of  the  U.  S. 
Bureau  of  Mines. 


FUELS  467 

Coke  contains  from  80  to  93  per  cent  of  fixed  carbon,  from  5  to 
18  per  cent  of  ash,  from  0.5  to  1.5  per  cent  of  sulphur,  and  traces 
of  volatile.  It  is  interesting  to  note  that  the  volatile  is  not 
entirely  eliminated,  and  that,  as  all  the  ash  in  the  coal  remains  in 
the  coke,  the  percentage  of  inert  matter  present  in  the  product 
must  be  greater  than  that  in  the  original  material. 

The  calorific  value  per  pound  of  combustible  is  about  the  same 
as  for  carbon;  that  is,  it  is  in  the  neighborhood  of  14,600  B.t.u. 

229.  Wood,     (a)  As  wood  is  about  half  moisture  when  felled, 
it  must  be  dried  before  it  is  of  much  value  as  fuel.    Air-dried  wood 
generally  has  from  15  to  20  per  cent  of  moisture,  about  50  per 
cent  of  carbon,  from  J  to  2   per  cent  of  ash,  and  the  rest  is 
volatile  matter,  largely  inert.     The  heat  value  per  pound  of  dry 
material  is  from  6600  to  9800  B.t.u. 

When  other  cheap  fuel  is  available  wood  is  not  generally  used 
for  power  production.  However,  refuse  from  sawmills  and  other 
wood- working  factories  may  be  profitably  utilized. 

(b)  Charcoal  is  made  from  wood  in  much  the  same  manner 
that  coke  is  made  from  coal.  It  is  ordinarily  used  in  power 
plants  only  when  it  is  the  by-product  of  some  local  process,  such 
as  the  manufacture  of  turpentine  or  wood  alcohol.  It  may  con- 
tain from  80  to  97  per  cent  of  carbon,  depending  on  the  tempera- 
ture and  treatment  used  in  carbonizing  it. 

230.  Municipal  and  Industrial  Waste.     In  cities  and  indus- 
trial centers  there  is  a  constant  accumulation  of  combustible 
waste  and  in  some  cases  this  material  is  burned  directly  as  fuel, 
or  it  is  gasified  in  suitable  apparatus  and  the  resultant  combustible 
gas  used  as  fuel.     Installations  of  this  character  are  still  rare  but 
are  of  growing  commercial  importance. 

231.  Natural  Oil  and  Its  Products,     (a)  Petroleum,  or  Crude 
Oil,  has  come  into  extensive  use  as  fuel  in  the  last  twenty-five 
years.     It  is  a  more  or  less  viscous,  dark  brown  or  greenish 
colored  liquid  occurring  in  natural  reservoirs  in  the  earth's  crust. 
These  reservoirs  may  be  subterranean  pockets,  but  are,  in  general, 
oil-saturated  strata  buried  beneath  other  strata  which  are  prac- 
tically impervious  to  petroleum. 

(b)  Petroleum  in  its  crude  form  generally  has  a  specific  gravity 
between  0.82  and  0.92.  It  is  a  mixture  of  various  hydrocarbons 


4<58  HEAT-POWER  ENGINEERING  '' 

which  are  liquid  at  ordinary  temperatures  and  pressures,  and 
which  hold  in  solution  numbers  of  other  hydrocarbons  which 
otherwise  would  be  gaseous  or  solid  under  existing  conditions. 
In  general,  oils  from  one  field  are  composed  of  the  same  hydro- 
carbons in  about  the  same  proportions,  but  each  field  has  its  own 
characteristic  composition.  American  crude  oils  have  from  82 
to  87  per  cent  of  carbon,  from  12  to  15  per  cent  of  hydrogen,  and 
from  o  to  4  per  cent  of  oxygen  in  their  composition.  The  lower 
heat  value  per  pound  of  crude  petroleum  varies  from  18,000  to 
22,000  B.t.u. 

(c)  Many  of  the  more  highly  inflammable  volatile  components 
tend  to  distill  off  when  the  oil  is  brought  to  the  earth's  surface 
and  is  exposed  to  atmospheric  conditions.     These  volatiles,  some 
of  which  boil  at  temperatures  as  low  as  80°  F.,  are  usually  dis- 
tilled off  progressively  in  a  refinery.     The  distillation  products 
most  commonly  used  as  fuels  are  naphtha,  gasoline,  kerosene,  and 
distillate,  given  in  order  of  decreasing  inflammability  and  increas- 
ing density  and  distillation  temperature.     The  greater  part  of  the 
remainder  can  be  sold  as  "  fuel  oil." 

(d)  Gasoline  is  the  name  given  to  the  group  of  hydrocarbons 
which  distill  off  at  temperatures  between  150  and  300°  F.     Gaso- 
lines of  various  specific  gravities  are  obtained   by  fractionating 
the  material  obtained  between  these  temperatures,   the  lower 
gravities  corresponding  to  the  lower  temperatures.     The  com- 
monest grades  range  from  74  to  64  degrees  gasoline  as  measured 
by  a  Baume  hydrometer.     The  corresponding  specific  gravities 
are  0.686  and  0.722.     The  relative  proportions  of  carbon  and 
hydrogen  in  gasolines  are  roughly  85  per  cent  and  15  per  cent, 
and  the  lower  calorific  value  is  about  19,200  B.t.u.  per  pound. 
The  flash  point  of  gasoline,  that  is,  the  temperature  at  which 
readily  inflammable  vapors  are  given  off  from  an  exposed  surface, 
is  generally  well  b.elow  70°  F. 

(e)  Kerosene  is  the  name  of  the  next  important  group  of 
hydrocarbons    which    distill    over    after    the    gasolines.     Their 
specific  gravity  is  from  0.78  to  0.82  and  the  flash  point  is  from 
70°  to  about  150°  F.  for  the  different  grades.     The  B.t.u.  per 
pound  of  kerosene  is  about  18,500  lower  value. 

(f )  Fuel  Oil,  having  little  highly  volatile  matter,  can  be  handled 
without  danger  and,  being  very  cheap,  is  quite  widely  used  under 
boilers  and  in  furnaces.     The  lower  calorific  value  per  pound  is 


FUELS  469 

extremely  variable,  but  may  be  taken  roughly  at  18,000  B.t.u. 
per  pound. 

(g)  The  higher  calorific  value  of  U.  S.  petroleum  and  its  dis- 
tillates, ranging  from  crude  oil  to  gasoline,  varies  quite  regularly 
with  the  specific  gravity  of  the  material,  and  is  expressed  ap- 
proximately by  the  following  formula,*  which  may  be^  assumed 
correct  within  2  per  cent, 

B.t.u.  per  pound  =  18,650  +  40  (B  —  10),  .     .     (335) 

in  which  B  =  degrees  on  the  Baume  hydrometer.  Since  the 
Baume  scale  increases  as  the  density  of  the  material  becomes 
less,  this  formula  indicates  that  the  lighter  distillates  have 
greater  heat  values  than  the  heavier  ones,  when  figured  on  a 
weight  basis.  The  reverse  is  true  for  heat  value  per  gallon,  a 
unit  commonly  used  with  liquid  fuels;  hence  a  barrel  of  light 
petroleum  distillates  of  any  kind  will,  in  general,  have  less  heat 
value  than  a  barrel  of  heavier  distillates  or  of  the  original  oil 
free  from  water. 

232.  Alcohol,  (a)  Both  Methyl  ("  Wood  ")  and  Ethyl 
("  Grain  ")  alcohol  are  used  as  fuel  to  a  limited  extent.  Methyl 
alcohol  (CH*O)  is  poisonous  and  is  produced  during  the  dry  dis- 
tillation of  wood.  Ethyl  alcohol  (C^H^O)  is  made,  by  a  fermen- 
tation and  distillation  process,  from  grain,  fruit,  or  vegetable 
matter  containing  starch  or  stigar. 

(b)  The  material  known  as  Denatured  Alcohol  consists  of  ethyl 
alcohol  with  the  addition  of  from  I  to  10  per  cent  of  Methyl 
alcohol  and  other  substances  which  prevent  its  use  in  beverages 
and  give  it  an  unpleasant  odor.     Commercial  alcohol  generally 
also  contains  10  per  cent  or  more  of  water  by  volume. 

Denatured  alcohol  has  many  theoretical  and  practical  advan- 
tages over  gasoline  as  a  fuel  for  certain  purposes,  but  at  present 
its  relative  cost,  in  this  country  at  least,  is  so  great  as  to  prevent 
its  extensive  use. 

(c)  The  higher  calorific  value  of  Absolute  Ethyl  alcohol  (i.e. 
containing  no  water)  is  about  13,000  B.t.u. /lb.;   the  lower  value 
is  about  12,000  B.t.u./lb.     The  heat  value  of  "  Commercial  " 
alcohol,  containing  about  10  per  cent  of  water,  by  volume,  varies 
with  the  materials  used  in  denaturizing.     The  lower  heat  value 
is  generally  near  10,500  B.t.u./lb. 

*  H.  C.  Sherman  and  A.  H.  Kropff,  Jour.  Am.  Chem.  Soc.,  Oct.,  1908. 


470 


HEAT-POWER  ENGINEERING' 


233.  Natural  Gas.  (a)  This  material  is  found  in  various 
places,  but  particularly  in  certain  regions  of  the  United  States, 
either  escaping  through  cracks  and  faults  in  the  earth's  crust, 
or  held  at  high  pressure  in  huge  underground  reservoirs  which 
may  be  tapped  by  drilling  wells  similar  to  those  used  for  ob- 
taining oil;  in  fact,  most  oil  wells  yield  a  certain  amount  of 
natural  gas. 

(b)  Natural  gas  is  a  mixture  of  combustible  and  incombustible 
gases,  the  latter  generally  occurring  in  very  small  quantities. 
The  proportions  and  even  the  constituents  of  the  gas  are  seldom 
the  same  in  different  districts  and  occasionally  vary  unaccount- 
ably even  in  the  same  well. 

The  principal  combustible  constituents  are  Methane  (CH*),  and 
Hydrogen  (H^.  The  former  generally  occurs  in  far  greater  pro- 
portion than  the  latter.  The  other  combustible  gases  which 
usually  occur  in  very  small  proportions  are  Carbon  Monoxide, 
(CO),  sulphur  compounds  such  as  Hydrogen  Sulphide  (H^S),  and 
certain  hydrocarbon  gases,  such  as  Ethylene  (CzH*),  and  others. 

The  principal  incombustible  constituents  are  generally  small 
proportions  of  Carbon  Dioxide  (CO2),  Nitrogen  (Nz),  and  Oxy- 
gen (O2),  if  this  latter  may  be  considered  an  incombustible. 

(c)  Natural  gas  is  an  ideal  form  of  fuel  for  many  industrial 
purposes,  and  is  readily  piped  distances  of  one  hundred  miles  and 
more  for  use  in  industrial  centers  far  from  a  natural  supply. 
Unfortunately  many  of  the  wells  are  becoming  exhausted  and 
the  price  is  rising  in  proportion. 

TABLE  XVIII.*- TYPICAL  ANALYSES  OF   NATURAL  GAS. 


Location  of  Field. 

Analyses  in  Volumes,  Per  Cent. 

a 

>, 

w 

Methane, 
CH4. 

Ethylene, 

C*ff4- 

Illuminants, 
C6tf«.  etc. 

* 

Carbon 
monoxide, 
CO. 

jb 

O 

rT 

Sulphuretted 
hydrogen, 
H2S. 

Anderson,  Ind  

1.86 
1.31 

93-07 
87.75 
96.50 
92.60 
80.  ii 
96.34 
72.18 
77-03 
92.49 

0.47 

0.26 
6  60 

0.73 

0.42 

3.02 

4.34 

0.15 

0.20 

Louisville,  Ky  

Olean,  N.  Y  

5-72 

1.  00 

0.31 

trace 
6.30 
4.80 
4.  ii 

0.26 
0.66 
3.64 
0.80 
3.6o 
0.93 

0.50 
0.50 

2.00 
0.34 

Findlay,  Ohio  

2.18 
13.50 

Harvey  Well,  Pa  
Creighton  ,  Pa  

Pittsburgh,  Pa  
Pechelbrown,  Germany  

20.02 

1.  00 

3-50 

0.80 
1.  80 

'&.*>' 

2   13 

Aspharon  Peninsula,  Russia  

0.34 

•  Abstracted  from  Table  in  "Calorific  Value  of  Fuels,"  Herman  Poole,  p.  241. 


FUELS  47 ! 

Table  XVIII  gives  some  typical  analyses  of  natural  gas  from 
several  different  districts.  The  lower  calorific  value  generally 
varies  from  about  950  to  1000  B.t.u.  per  cubic  foot. 

234.  Artificial  Gases,  (a)  The  principal  artificial  gases  are 
made  from  coal  or  crude  oil,  but  there  are  also  many-  processes 
for  producing  combustible  gases  from  vegetable  and  animal  by- 
products and  wastes.  Many  of  the  latter  are  successful  in  iso- 
lated cases  but  they  are  not  yet  of  great  commercial  importance. 

(b)  Most  of  the  artificial  gases  are  made  either  by  destructive 
distillation,  by  partial  combustion,  by  chemical  decomposition, 
or  by  various  combinations  of  these  processes. 

Destructive  distillation  occurs  when  the  gas-making  material 
is  heated  in  a  chamber  from  which  air  is  more  or  less  perfectly 
excluded.  Illustrations  of  gases  made  by  this  process  are 
"  Illuminating,"  "  Retort,"  or  "  Town  Gas,"  used  for  illumi- 
nation, and  gas  made  in  "  By-product "  or  "  Retort  Coke 
Ovens  "  used  for  illumination  and  power. 

"  Producer  Gases  "  are  the  best  examples  of  those  which  in 
theory  are  made  by  a  process  of  incomplete  combustion.  Practi- 
cally this  is  always  more  or  less  combined  with  chemical  de- 
composition. These  gases  have  become  so  important  of  late 
in  connection  with  the  internal  combustion  engine  that  they 
will  be  discussed  later  in  a  separate  chapter. 

(c)  The  use  of  artificial  gases  as  fuel  in  internal  combustion 
engines  results  generally  in  a  greater  output  of  available  energy 
than  would  the  use  of  the  solid  fuels,  from  which  the  gases  are 
made,  in  other  heat-power  apparatus;   hence  these  gases  may  be 
expected  to  become  more  and  more  important  with  the  depletion 
of  the  natural  stores  of  fuel  and  with  the  growth  of  the  spirit  of 
conservation  of  the  earth's  resources. 


CHAPTER  XXVIII. 
COMBUSTION. 

235.  Definitions,     (a)  To  the  engineer  Combustion  means  the 
chemical  combination  of  certain  elements  with  oxygen  at  such  a 
rate  as  to  cause  an  appreciable  rise  of  temperature. 

Practically  all  chemical  reactions  are  accompanied  by  libera- 
tion or  absorption  of  heat.  When  heat  is  liberated  the  reaction 
is  called  exothermic;  when  heat  is  absorbed  the  reaction  is 
called  endothermic. 

(b)  During  these  reactions,  with  other  conditions  constant, 
(i)  the  amount  of  heat  energy  liberated  or  absorbed  is  independ- 
ent of  the  time  occupied;   and  (2)  for  any  material  taking  part 
in  the  reaction,  the  heat  change  is  directly  proportional  to  the 
mass  of  that  material. 

(c)  Materials  which  can  be  caused  to  unite  with  oxygen  to 
produce  heat  are  known  as  Combustibles.     For  engineering  pur- 
poses they  are  limited  to  Carbon  and  Hydrogen;    these,  either 
pure  or  in  various  combinations,  constitute  practically  the  entire 
stock  of  available  combustibles,  although   a   trace  of  sulphur 
usually  appears  as  an  impurity. 

(d)  In  heat-power  engineering  the  object  of  combustion  is 
either  the  production  of  heat  directly,  or  the  formation  of  a  more 
suitable  kind  of  combustible,  such  as  gas  or  coke,  from  the 
original  material. 

Useful  combustion  data  are  given  in  Table  XIX.  In  it  the 
values  of  specific  densities  and  volumes  are  given  for  an  average 
atmospheric  temperature  of  62°  F.  as  well  as  for  32°  F. 

236.  Combustion  of  Carbon,    (a)  Carbon  is  the  principal  com- 
bustible in  nearly  all  engineering  fuels.     This  element  combines 
with  oxygen  to  form  two  oxides,  —  Carbon  monoxide  (CO),  and 
Carbon  dioxide  (C02).     If  CO  is  formed,  the  combustion  is  said 
to  be  "  incomplete  " ;  if  C02  is  formed,  it  is  said  to  be  "  complete  " 
or  "  perfect." 

472 


COMBUSTION 


473 


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M     2       £        £  -£    -£  2-S-2     ^     -§,.2 

SP                                r£                     &*i     '™H             rrt     C^     rrt  T^             ^           '""'  *^3 

o2o      Wwoo      &   £ 

474  HEAT-POWER  ENGINEERING 

(b)  The  reactions  occurring  during  combustion  may  be  ex»- 
pressed  by  chemical  equations,  the  symbols  used  standing  for 
definite  proportions  by  mass  or  weight.     For  engineering  pur- 
poses the  atomic  weight  of  Carbon  may  be  taken  as  12,  that  of 
Nitrogen  as  14,  and  that  of  Oxygen  as  16. 

(c)  When  carbon  and  oxygen  combine  to  form  Carbon  Dioxide 
the  reaction  is  expressed  by 

C  +  02  =  C02;     ......     (336) 

the  weights  combined  are 

12  of  C  +  (2  X  1  6)  of  0  =  44  of  C02, 
and  dividing  this  by  12  gives 

lof  C  +  2f  of  0  =  3fof  C02.       .     .     .     (337) 

Thus  if  1  pound  of  carbon  unites  with  2§  pounds  of  O  the  result 
is  3§  pounds  of  C02.  It  is  also  found  that  heat  equal  to  about 
14,600  B.t.u.  is  liberated  per  pound  of  carbon  when  this  reaction 
occurs. 

(d)  When  carbon  is  burned  to  Carbon  Monoxide,  the  reaction 

is  expressed  by 

2  =  2CO;  ......     (338) 


the  weights  combined  are 

(2  X  12)  of  C  +  (2  X  1  6)  of  0  =  56  of  CO, 
and  dividing  this  by  24  gives 

1  of  C  +  ij  of  0  =  2j  of  CO.  .  .  .  (339) 
The  heat  liberated  is,  in  this  case,  about  4500  B.t.u.  per  pound 
of  carbon. 

(e)   The  gaseous  CO  formed  as  above  can  be  burned  to  CO2. 
The  reaction  is 

2  CO  +  02  =  2  CO2;    .....     (340) 

the  weights  combined  are 

\2  X  (12  +  i6)|  oiCO  +  (2X  1  6)  of  0  =  88  of  CO,, 
and  dividing  this  by  24  gives 

2j  of  CO  +  ij  of  0  =  3!  of  C02.     .     .     .     (341) 

Thus  the  2j  pounds  of  CO,  which  would  result  from  the  com- 
bination of  1  pound  of  carbon  as  in  Eq.  (339),  would  combine 
with  ij  pounds  of  0  to  form  3§  pounds  of  CO*. 

This  reaction  is  accompanied  by  the  liberation  of  heat  equal  to 
about  10,100  B.t.u.  per  pound  of  carbon.     Therefore  the  heat 


COMBUSTION  475 

liberated  per  pound  of  carbon  monoxide  gas  must  be  ioioo/2§  = 
4300  B.t.u. 

The  specific  volume  of  CO  is  12.81  cu.  ft.  at  32°  F.  and  14.7 
pounds  pressure.  Hence  the  heat  liberated  per  cu.  ft.  of  CO  under 
these  conditions  is  4300  -T-  12.81  =  335  B.t.u.  As  CO  is  a  con- 
stituent of  many  commercial  fuel  gases  and  as  these  are  usually 
measured  volumetrically  instead  of  gravimetrically,  this  value 
is  convenient  for  determining  the  heat  available  due  to  the  CO 
present. 

(f)  Equations  expressing  both  the  reaction  and  the  libera- 
tion of  heat  per  pound  of  material*  may  be  written  as  follows: 

C  +  02  =  C02  +  (  14,600  B.t.u.  per  pound  C)     .     .     (342) 
2  C  +  02  =  2  CO  +  (4500  B.t.u.  per  pound  C)      .     .     (343) 

2  CO  +  O   --2  CO  4-1      (I°'IO°  B-t>u<  per  P°Und  C)      (344) 
|  or  (4300  B.t.u.  per  pound  CO)      (345) 

Noting  that  4500  +  10,100  =  14,600,  it  is  evident  from  these 
equations  that  when  carbon  is  burned  to  C02,  the  ultimate 
results  are  the  same  whether  the  process  takes  place  in  one  or 
in  two  steps. 

Further,  if  part  of  the  pound  of  carbon  (say  Cx  pounds)  is 
burned  to  C02  and  the  rest  (Cv  pounds)  to  CO,  the  heat  liberated 

is 

B.t.u.  =  14,600  Cx  +  4500  Cy.       ...     (346) 

(g)  If  heat  is  the  object  of  combustion,  the  carbon  should  of 
course  be  burned  to  carbon  dioxide  rather  than  to  carbon  mon- 
oxide.    If  CO  is  formed  instead  of  C02,  the  proportion  of  the  heat 
lost  is  (10,100/14,600)  =  .69  +,  or  about  70  per  cent.     If,  how- 
ever, the  CO  is  burned  later,  the  rest  of  the  heat  may  be  recovered. 

*  As  will  be  seen  later,  it  is  sometimes  more  convenient  to  modify  Equation  (342) 
so  that  the  heat  quantity  as  well  as  symbol  C  will  correspond  to  1 2  Ibs.  of  carbon 
(the  pounds  being  taken  as  numerically  equal  to  the  molecular  weight  of  C  involved). 
The  equation  then  becomes 

C  -f  O2  =  CO2  +  175,200 (342a) 

where  175,200  =  12  X  14,600. 

Similarly,  for  the  24  Ibs.  of  carbon  represented  by  2  C  and  by  2  CO,  Eqs.  (343) 
and  (344)  become 

2  C  +  O2  =  2  CO  +  108,000 (343a) 

and  2  CO  +  O2  =  2  CO2  +  242,400    ....:...     (344a) 

in  which  108,000  =  24  X  4500,  and  242,400  =  24  X  10,100. 


476  HEAT-POWER  ENGINEERING- 

When  there  is  less  than  enough  oxygen  to  burn  the  carbon  to 
carbon  dioxide,  both  C02  and  CO  will  be  formed  and  the  relative 
amounts  of  each  can  be  determined  in  the  following  manner: 
Assume  first  that  there  is  1  per  cent  deficiency  in  the  oxygen 
supply  needed  to  form  C02  and  that  in  consequence  99  per  cent 
of  the  carbon  is  burned  to  C02  and  1  per  cent  remains  C;  then 
assume  that  this  1  per  cent  of  C  combines  with  some  of  the  CO2 
according  to  the  equation  C  +  CO*  =  2  CO',  thus  it  is  seen  that 
there  is  finally  2  per  cent  of  the  carbon  present  in  CO  and  98  per 
cent  in  C02.*  In  general,  then,  if  there  is  y  per  cent  deficiency 
of  oxygen  there  will  be  2y  per  cent  of  the  carbon  burned  to 
carbon  monoxide  instead  of  to  C02.  Hence  from  the  preceding 
paragraph  it  follows  that  with  y  per  cent  deficiency  of  oxygen 
there  is  (2  X  .7)  y  per  cent,  or  1 .4  y  per  cent  less  heat  developed 
than  if  all  the  carbon  were  burned  to  C02.  The  great  importance 
of  having  a  sufficient  supply  of  oxygen  is  thus  apparent. 

The  discussion  in  the  preceding  paragraph  presupposes  that 
the  oxygen  supply  is  at  least  sufficient  to  burn  all  the  carbon  to 
CO,  —  that  is,  that  the  deficiency  is  not  more  than  50  per  cent 
on  a  basis  of  combustion  to  C02.  Should  y  be  greater  than  50 
per  cent,  some  of  the  carbon  will  not  be  burned  at  all.  The  per- 
centage not  affected  will  be  2  (y  —  50) . 

(h)  It  is  sometimes  possible  to  reverse  chemical  reactions, — 
in  the  present  case,  for  instance,  to  break  up  one  of  the  oxides 
into  the  original  elements.  When  this  is  done  the  same  amount 
of  heat  will  be  absorbed  during  the  decomposition  as  was  origi- 
nally liberated  during  combination. 

Thus,  if  it  is  possible  to  break  up  the  quantity  of  C02  con- 
taining a  pound  of  carbon  into  the  elements  C  and  O,  it  will 
require  an  expenditure  of  14,600  B.t.u.  Similarly,  it  will  require 
10,100  B.t.u.  to  reduce  to  the  monoxide  CO  an  amount  of  COi 
containing  one  pound  of  carbon,  and  4500  B.t.u.  per  pound  of 
carbon  will  be  consumed  in  separating  CO  into  its  elements. 

237.  Weights  of  Oxygen  and  Air  Necessary  for  Combustion 
of  Carbon.  It  was  shown  that  for  each  pound  of  carbon  burned 
to  CO2  there  are  required  2§  pounds  of  oxygen,  or  ij  pound  of 

*  These  statements  should  be  limited  to  take  account  of  certain  "  equilibrium  " 
conditions  which  will  be  discussed  in  a  later  chapter.  For  the  present  purpose, 
however,  they  are  sufficiently  exact. 


COMBUSTION 


477 


0  if  CO  is  formed.  If,  as  before,  Cx  and  Cv  are  the  weights  of 
carbon  burned  respectively  to  C02  and  to  CO,  then  the  number 
of  pounds  of  oxygen  used  are 

Pounds  of  0  =  2f  Cx  +  ii  Cy.      .     . 


(347) 


TABLE  XX.  —  PROPERTIES   OF  AIR. 


Relative  Propor- 
tions. 

Ratio  of  Air 
toO. 

Ratio  of  2V 
toO. 

Spec.  Wt. 
at  Atm. 
Pres. 

Spec.  Vol. 
at  Atm. 
Pres. 

Exact. 

Approx. 

Exact. 

Approx. 

Exact. 

Approx. 

32° 

62° 

32° 

62° 
13-14 

By 

Weights. 

By 

Volumes. 

jo.  766  2V 
{  0.2340 

Jo  791  N 
\  0.209  O 

0.77  AT 
0.230 

0.79  TV 

0.21  O 

4  27 
4.78 

4-35 
4.76 

3.27 
3  78 

3-35 
3-76 

0.08072 

0.07609 

12.39 

Specific  Heats. 

CP  =0.238 

Cv  =0.169 

Since,  in  ordinary  engineering  work,  pure  oxygen  cannot,  in 
general,  be  conveniently  obtained,  it  is  customary  to  utilize  the 
oxygen  of  the  atmosphere.  Table  XX  shows  that  air  is  composed 
by  weight  of  about  23  parts  of  oxygen  and  77  of  nitrogen;  *  thus 
the  ratio  of  air  to  the  oxygen  it  contains  is  about  100/23=  4.35, 
and  of  nitrogen  to  oxygen  is  about  77/23  =  3.35.  Hence,  for  each 
pound  of  oxygen  supplied  there  must  be  used  4.35  pounds  of  air 
containing  3.35  pounds  of  inert  nitrogen.  An  equation  for 
finding  the  weight  of  air  required  to  burn  Cx  pounds  of  carbon 
to  CO2  and  Cy  pounds  to  CO  can  therefore  be  found  by  multi- 
plying both  sides  of  Eq.  (347)  by  4.35.  This  gives  (approxi- 
mately)! 

Pounds  of  Air  =  n.6  C,  +  5.8  Cy.    .     .     .     (348) 

238.  Volumes  of  Gases  Involved  in  Combustion  of  Carbon. 

(a)  The  combustion  formulas,  like  other  chemical  formulas 
involving  gases,  can  be  read  in  terms  of  molecules  and  of  volumes 
as  well  as  in  terms  of  weights.  Thus 

2  C  +  02  =  2  CO 

may  be  read,  "  two  atoms  of  carbon  unite  with  one  molecule  of 
oxygen  to  form  two  molecules  of  carbon  monoxide."    But  accord- 

*  This  is  the  common  engineering  assumption.  Atmospheric  air  always 
contains  carbon  dioxide  and  water  vapor  as  well  as  a  few  rare  gases  such  as  argon. 

f  The  quantity  n.6  (often  taken  as  12),  representing  the  weight  of  air  required 
for  complete  combustion  of  one  pound  of  C,  will  be  frequently  used  by  the  student 
hereafter;  hence  it  should  be  remembered. 


478  HEAT-POWER  ENGINEERING 

ing  to  Avogadro's  law  the  same  number  of  molecules  are  con- 
tained in  equal  volumes  of  all  the  different  gases  when  at  the 
same  temperature  and  pressure.  Therefore,  since  every  molecule 
of  oxygen  in  a  given  volume  of  gas  is  capable  of  yielding  two 
molecules  of  carbon  monoxide,  it  follows  that  one  volume  of 
oxygen  will  yield  two  volumes  of  CO,  both  being  measured  at  the 
same  temperature  and  pressure. 
Similarly  the  equation 

C  +  02  =  C02 

shows  that  one  volume  of  oxygen  yields  one  volume  of  carbon 
dioxide;    and  the  equation 

2  CO  +  02  =  2  C02 

shows  that  two  volumes  of  carbon  monoxide  combine  with  one 
volume  of  oxygen  to  form  only  two  volumes  of  carbon  dioxide. 

(b)  In  the  first  case  cited  there  was  an  increase  of  gas  volume, 
in  the  second  there  was  no  change,  and  in  the  third  there  was  a 
diminution.     If  the  gases  appear  in  terms  of  molecules  (02,  7V2, 
Hz,  CO,  etc.)  in  the  chemical  equations,  the  coefficients  of  the 
molecule  symbols  represent  relative  volumes. 

(c)  Since  air  is  composed  of  about  21  parts  of  oxygen  and 
79  parts  of  nitrogen  by  volume,  every  volume  of  atmospheric 

oxygen  will  carry  with  it—  =  3.76  volumes  of  nitrogen. 

When  air  is  used  to  support  combustion  the  nitrogen  takes  no 
chemical  part  in  the  reactions  considered  but  simply  mixes  with 
the  products  of  the  combustion  and  is  known  as  a  diluent* 

A  simple  relation  can  now  be  shown:  Since  the  volume  of 
CO2  formed  by  combustion  of  carbon  equals  the  volume  of  the 
oxygen  used  in  the  process  and  since  oxygen  forms  21  parts  of 
air  by  volume,  it  follows  that  with  "  complete  "  combustion  the 
products  will  consist  of  21  parts  C02  and  79  parts  N  by  volume 
when  not  diluted  by  the  presence  of  excess  air. 

(d)  Then  if  the  carbon  is  burned  in  air  and  if  analysis  of  the 
"  flue  "  gas  shows  that  the  volume  of  CO2  is  less  than  21  per  cent, 
it  follows  that  either  (1)  there  is  more  air  present  than  is  required 
for  complete  combustion,  the  excess  acting  as  a  diluent,  or  (2) 
that  there  is  a  deficiency  of  air,  with  the  result  that  only  a  part 

*  Under  some  conditions  part  of  the  nitrogen  burns  to  ah  oxide,  but  the  quantity 
thus  consumed  is  small  in  all  the  ordinary  engineering  processes. 


COMBUSTION 


479 


of  the  carbon  is  burned  to  CO2,  the  rest  appearing  in  CO.  If  the 
percentage  of  C02  is  less  than  21  and  no  CO  is  found  in  the  flue 
gas  it  indicates  that  there  is  excess  air;  and  if  CO  is  present 
there  is  a  deficiency.* 

(e)  The  percentage  of  COZ  by  volume  in  the  flue  gas  mixture 
can  be  computed  for  any  condition  of  combustion,  by -using  the 
following  formula, 

vol.  of  CO2 


Per  cent  of  CO2  by  vol.  = 

wV  . 

etc. 


total  vol.  of  gas 

wV 


X  ioo 


ioo 


X  ioo,  .    (349) 


-  (  T7A       t  \r\  ,  Tr. 

(wV)  +  OV)i  +  etc.  S  (wV) 

in  which  w  =  weight  of  C02  present  in  the  mixture, 

Wi,  Wz,  etc.  =  weights  of  the  other  gases  present, 

V  =  specific  volume  of  C02, 
Vi,  V2,  etc.  =  specific  volumes  of  the  other  gases. 

The  specific  volumes  of  gases  are  given  in  Table  XIX. 

(f)  If  an  excess  of  air  is  supplied,  say  x  per  cent  more  than  is 
required  for  perfect  combustion,  the  maximum  per  cent  of  C02 
by  volume  which  could  be  present  in  the  flue  gas  can  be  computed 
in  the  following  manner,  based  on  the  combustion  of  one  pound 
of  carbon.  In  this  case  the  combustion  of  the  pound  of  carbon 
will  result  in  3§  pounds  of  CO2  ;  it  will  theoretically  require  1  1  .6 
pounds  of  air;  there  will  be  0.77  X  1  1.6  =  8.9  pounds  of  nitrogen 
accompanying  the  oxygen  used  for  combustion;  and  there  will 

be  (  1  1  .6  X  —  -  )  pounds  of  excess  air.    The  following  table  gives  ihv 
\  ioo/ 

weights  (w)  of  gas  present  per  pound  of  C  burned  to  C02,  theif 
specific  volumes  (V)  at  62°  F.,  and  the  products  of  these  quan 
tities  OV). 

TABLE  XXL  —  FLUE  GAS  CONSTANTS. 


Gas. 

•w 

V62 

wV 

C02 

3f 

8.62 

31-6 

N  (theoretical) 

8.9 

13.60 

121.  0 

Air 

ii  .6  x 

I3-I4 

1.52  x 

IOO 

*  These  statements  should  be  limited  to  take  account  of  certain  "  equilibrium  " 
conditions  discussed  in  a  later  chapter.  For  the  present  purpose,  however,  they 
are  sufficiently  exact. 


480 


HEAT-POWER  ENGINEERING 


The  sum  of  the  last  column  is, 

S  (wV)n  =  31.6  +  I2i.o  +  1.52*  =  152.6  -f  1.52  x 


Then  from  Eq.  (349) 
Per  cent  CO2  by  vol.  = 


31.6 


153 


X  ioo,  approx.,      (350) 


which  gives  the  proportion  of  C02  in  the  flue  gas. 

(g)    Again,  since  the  per  cent  of  C02  by  volume  decreases 
directly  as  the  quantity  of  total  air  is  increased,  it  is  evident  from 

(c)  that 

Per  cent  C02  by  volume  =  21  -r-  (l  -f-  #/ioo),      -.     (351) 

in  which  x,  as  before,  represents  percentage  of  excess  aif.  Sim- 
plifying Eq.  (350)  results  in  the  same  equation  (approximately). 
The  relation  of  the  CO 2.  to  x  is  shown  in  Fig.  316  by  the  curve  to 
the  right  of  oO. 


X 


50      40      30       20       10       0        50      100     150     200     250 
V  #  Deficiency 


Fig.  316. 

(h)  The  expression  (l  -f  #/ioo)  is  known  as  the  excess 
coefficient  X.  In  words,  —  the  excess  coefficient  is  the  number 
by  which  the  theoretical  amount  of  oxygen,  or  air,  required  must 
be  multiplied  to  find  that  actually  supplied. 

If  the  C02  percentage  is  known,  and  if  the  combustion  is 
complete  (and  only  in  that  case)  the  per  cent  of  excess  air  x, 
can  be  found  from  Eq.  (351).  Thus 

x  =  (T 7-7^ — 1)100 (352) 

\per  cent  CO2        / 

(i)    For  the  case  of  complete  combustion,  the  percentage  of 


COMBUSTION 


481 


excess  air  can  also  be  found  when  both  the  total  volume  (N)  of 
nitrogen  and  the  volume  (Ox)  of  that  part  of  the  oxygen  which 
remains  free  after  combustion  are  known.  The  volume  of 
nitrogen  accompanying  the  excess  oxygen  is  79/21  X  Ox  =  3.76  Ox, 
and  that  corresponding  to  the  oxygen  used  in  combustion  is 
N  —  3.76  Ox.  Hence,  since  the  nitrogen  undergoes  no  change, 
the  percentage  of  excess  air  is 

x  =  100  (3.76  Ox)  +  (N-  376  Ox),      .     .     (353) 
and  the  excess  coefficient  is 


X  = 


_x_    =       i       376  Ox 
zoo          r  N  -  3.76  Ox ' 


(354) 


(j)  In  most  cases  it  is  possible  to  have  incomplete  combustion 
of  part  of  the  carbon  although  sufficient  air  is  present,  since  the 
air  may  not  be  properly  distributed.  In  such  cases  x  and  X 
can  be  determined  if  the  volume  per  cent  of  CO  is  known  in 
addition  to  the  N  and  0.  Since  each  volume  of  CO  present  could 
have  combined  with  half  its  volume  of  oxygen  to  form  C02,  it 
follows  that,  on  the  basis  of  complete  combustion,  the  excess 
oxygen  is  equal  to  0  —  CO/2.  The  nitrogen  accompanying  this 
is  3.76  (0  —  CO/ 2} ,  and  that  corresponding  to  the  oxygen  required 
for  complete  combustion  is  N—  3.76  (0  —  J  CO).  The  percentage 
of  excess  air  for  this  case  is,  then 


_  376  (0  -  i  CO)  X  IPO 
N  -  3.76  (0  -  \  CO) ' 


and  the  excess  coefficient  is 


100 


-i 
~ 


376(0-^  CO) 


(355) 


(356) 


(k)  In  case  there  is  a  deficiency  of  air  amounting  to  y  per  cent, 
there  is  2y  per  cent  of  the  carbon  burned  to  CO,  as  has  already 
been  shown  (in  Sect.  236  g) ;  in  burning  one  pound  of  carbon 
there  will  result  2^/100  X  2\  pounds  of  CO,  (l  -  2y/ioo)  X  3§ 
pounds  of  C02,  and  the  nitrogen  present  will  be  (l  —  y/ioo)  X 
(0.77  X  1 1. 6)  pounds.  Tabulating  these  values  gives: 

TABLE  XXII. —  FLUE  GAS  CONSTANTS. 


Gas. 

IV 

V62 

tt-V 

C02 

(l-2y/ioo)X3i 

8.62 

31.6  (1  —  2y/ioo) 

CO 

(2y/IOo)  X21 

13  .60 

31  .7  (zy/ioo) 

N 

(l-y/ioo)X8.9 

13.60 

121.  o  (1—  y/ioo) 

482  HEAT-POWER  ENGINEERING- 

The  summation  of  the  last  column  gives 

Then,  from  Eq.  (349), 

Per  cent  C02  by  vol.  =  ^A'lV'J*!?    X  IO° 


and       Per  cent  CO  by  vol.  =  J  X  '  100.    .     .     (358) 

The  relation  of  the  percentage  volumes  of  COz  and  CO  in  the 
flue  gas  to  the  percentage  deficiency  of  air,  is  shown  in  Fig.  316 
by  the  curves  to  the  left  of  oO. 

239.  Temperature  of  Combustion,  (a)  When  combustion 
occurs,  the  heat  energy  liberated  tends  to  be  dissipated.  But  if 
the  combustion  can  be  imagined  to  occur  within  a  vessel  perfectly 
impervious  to  heat,  then  all  the  liberated  heat  must  remain 
within  the  vessel,  and  the  products  of  combustion  would  be  raised 
to  a  high  temperature.  This  temperature  is  known  as  the  theo- 
retical temperature  of  combustion  and  is  readily  calculated. 

(b)  First,  assuming  only  one  gas  as  the  product  of  combustion, 
and  no  heat  absorbed  by  the  surrounding  vessel,  the  theoretical 
temperature  rise  will  be  obtained  by  dividing  the  available  heat 
by  the  product  of  the  weight  and  the  specific  heat  of  the  gas 
formed.  If  the  vessel  is  assumed  not  to  change  in  size,  the  specific 
heat  for  constant  volume  must  be  used;  but  if  the  vessel  is  the 
equivalent  of  one  fitted  with  a  movable  piston  so  arranged  as 
to  maintain  constant  pressure,  the  specific  heat  would  be  that 
for  constant  pressure. 

For  example  take  the  reaction 

2  C  +  02  =  2  C0]+  (4500  B.t.u.  per  pound  of  C). 

Since  2j  pounds  of  CO  are  formed  per  pound  of  carbon,  the 
theoretical  rise  of  temperature  with  the  theoretical  supply  of 
pure  oxygen  will  be 


in  which  Cn  is  either  the  specific  heat  at  constant  volume  (Cv), 
or  at  constant  pressure  (Cp),  as  the  case  may  be. 

(c)    If  air  is  used  to  furnish  the  oxygen,  the  nitrogen  must  also 
be  heated.     Then,  since  the  weight  of  N,  accompanying  the  O 


COMBUSTION  483 

used  per  pound  of  C,  is  ij  X  77/23  =  4-47,  the  resulting  temper- 
ature rise  is 

Rise  =  c   X2l|5<g,  . 

in  which  the  primed  specific  heat  is  for  the  nitrogen,  and^the  other 
for  CO  as  before.  Similar  equations  may  be  written  for  other 
combustibles  and  other  products  of  combustion. 

(d)  The  temperature  theoretically  attained  will  be  the  sum  of 
temperature  to  existing  before  the  start  of  the  reaction  and  the 
temperature  rise  as  found  above. 

In  general,  for  any  number  of  products  of  combustion, 

AC 


-{-  CiWi  +  CzWz  +  CsWs  -f-  etc. 
.            AQ 
=  fe  +  S(Cw)n'     •••'••••• (359) 

in  which 

/o  =  initial  temperature, 
A<2  =  heat  liberated, 

Co,  Ci,  Cz  =  the  specific  heats  of  the  products  of  combustion, 
at  constant  volume  or  pressure,  as  the  case  may 
be,  and 

WQ,  Wij  Wz  =  the  weights  of  the  products  of  combustion. 
The  specific  heats  of  the  products  of  combustion  *  are  given  in 
Table  I  on  pages  40  and  41. 

(e)  It  is  evident  that  the  larger  the  denominator  of  the  frac- 
tion in  Eq.  (359)  the  lower  will  be  the  theoretical  temperature  of 
combustion.     If,  then,  an  inert  gas  such  as  nitrogen  is  carried 
through  the  heating  process,  as  when  air  is  used  instead  of  pure 
oxygen,  the  theoretical  temperature  will  be  lowered;  and  should 
more  air  be  supplied  than  is  needed  for  complete  combustion, 
the  temperature  will  be  still  further  reduced.     Diluents,  though 
taking  no  essential  chemical  part  in  the  reaction,  thus  play  a  very 
important  part  from  the  physical  side;    they  always  reduce  the 
theoretical  maximum  temperature  attainable  by  the  combustion. 

The  way  the  temperature  rise  theoretically  varies  with  excess 
or  deficiency  of  air,  when  carbon  is  burned  at  constant  pressure, 
is  shown  in  Fig.  317. 

(f)  If  any  heat  is  lost  during  the  period  of  combustion,  as, 

*  See  also  (g)  of  this  section, 


484 


HEAT-POWER  ENGINEERING 


for  -instance,  by  radiation,  the  numerator  of  Eq.  (359)  will  be 
diminished  by  the  amount  lost  and  the  theoretical  temperature 
0  rise  will,  of  course,  .  be 

decreased.  This  indicates 
the  advisability  of  caus- 
ing combustion  to  take 
place  as  rapidly  as  pos- 
sible, because,  despite  the 
fact  that  the  same  a- 
mount  of  heat  is  liberated 
during  slow  as  during 
rapid  combustion,  the  ac- 


5000 
4000 
3000 
2000 
1000 
0 

j 

s 

^ 

-" 

\ 

/ 

/ 

\ 

^v 

>s 

^V 

x"v»v 

•^*». 

—    — 

0    40    30    20    10     0       50       100     150     200     250    3(X 
y  ^Deficiency                    *  %  Excess 

Fig.  317- 


tual  time  allowed  for  radiation  in  the  latter  case  is  less,  and 
hence,  other  things  being  equal,  the  temperature  attained  will 
be  greater. 

(g)  In  the  chapters  on  the  theory  of  the  ideal  gas  it  was  stated 
that  for  ordinary  work  the  specific  heats  of  real  gases  might  be 
considered  constant.  They  are,  however,  really  not  constants, 
and  some  of  them  increase  rapidly  in  value  at  high  temperatures. 
From  the  previous  consideration  of  the  behavior  of  superheated 
steam  this  is  just  what  would  be  expected. 

There  is  still  considerable  lack  of  agreement  between  the 
values  of  the  high  temperature  specific  heats  of  gases  as  deter- 
mined by  different  investigators.  The  later  work  in  this  field 
does,  however,  give  sufficiently  concordant  results  to  definitely 
settle  the  fact  that  such  increase  with  the  temperature  does 
occur,  and  to  warrant  the  engineer  in  assuming  some  of  the  values 
obtained  as  sufficiently  accurate  for  practically  all  engineering 
calculations. 

The  values  for  mean  specific  heats  given  in  Fig.  318,  taken 
from  curves  prepared  by  Prof.  G.  B.  Upton  and  published  in 
"Experimental  Engineering"  by  Carpenter  and  Diederichs,  repre- 
sent the  most  probable  values  for  the  different  gases  named. 
It  will  be  noted  that  no  account  is  apparently  taken  of  variation 
of  the  specific  heat  with  pressure.  Such  variation  is  negligible 
for  most  gases  with  which  the  engineer  ordinarily  deals,  —  the 
principal  exceptions  being  water  vapor  and  ammonia.  For  water 
vapor  the  variation  with  pressure  is  rapid  at  low  temperatures 
but  becomes  less  so  at  higher  temperatures,  as  was  shown  in 
Fig.  40. 


COMBUSTION 


485 


(h)  Since  the  specific  heat  increases  with  temperature,  the 
value  of  the  denominator  of  Eq.  (359)  must  increase  when 
the  numerator  becomes  greater,  other  things  being  equal;  thus 
the  higher  the  temperature  the  less  effective  is  a  given  quantity  of 
heat  in  causing  a  rise  of  one  degree.  It  follows  that  in  practical 
work,  even  if  all  radiation  could  be  prevented,  the  temperature 
will  never  rise  as  high  as  Eq.  (359)  would  indicate  when  the 
ordinary  values  of  the  specific  heat  are  used. 


Mean_SpecificJEIea1i 
(Q  )  at  Constant 
p  Pressure 


—472-0:30  -0;66 


-4.lJ-0.29  -0.64 


— 4.0L-Or28LOi62 


—3.9 


To  Obtain  Mean  Specific  Heat(Cv.) 
At  Constant  Volume  Substract 
From  Cp  The  Following  Constants :- 

O        N       Air     CO2  H2O     CO     H 
0.063  0.072  0.069   0.045   0.112   0.009  1.00 


0       200    400     600     800    1000    1200    1400   1600  1800    2000   2200  2400    2600  2800  3000 
Temp.  Deg.  Fahr. 

Fig.  318. 


To  determine  the  real  temperature  rise  (neglecting  radiation 
loss)  for  any  given  heat  supply,  the  mean  specific  heats  must  be 
used  in  the  denominator  of  the  equation.  The  only  satisfactory 
way  of  doing  this  would  be  to  guess  at  the  temperature  expected, 
choose  the  corresponding  mean  specific  heats,  determine  the  re- 
sultant temperature  and  compare  with  the  value  assumed.  If 
the  difference  is  great  a  closer  approximation  can  be  made,  and 
so  on.  This  is  similar  to  many  of  the  calculations  used  in 
nection  with  superheated  steam. 


486  HEAT-POWER  ENGINEERING 

240.  Combustion  of  Hydrogen,  (a)  Hydrogen  burns  accord- 
ing to  the  following  equation: 

2  H2  +  <92  =  2  H£> (360) 

The  weights  combined  are 

(2X2)  of  H+(2  X  1 6)  ofO=36  of  H*>O, 
and  dividing  this  by  4  gives 

i  of  H  +8  of  O  =  9  of  HzO (361) 

Then)  for  each  pound  of  hydrogen  burned,  8  pounds  of  oxygen 
must  be  supplied,  and  9  pounds  of  water  will  result.  It  is  also 
found  that  about  62,000  B.t.u.  are  liberated  per  pound  of  hydro- 
gen burned. 

(b)  Problems  involving  the  combustion  of  hydrogen  are  often 
complicated  by  the  fact  that  many  of  the  real  combustibles 
contain  some  oxygen,  which  may  exist  as  a  constituent  of  a 
CxHyOz  compound,  or  in  combination  with  some  of  the  hydrogen 
as  H^Oj  or  in  a  number  of  other  different  ways.  Obviously,  to 
calculate  the  heat  that  would  be  liberated  by  a  pound  of  such 
material  would  require  a  knowledge  of  the  condition  of  all 
oxygen  present;  but  unfortunately  such  knowledge  is  seldom 
available,  hence  it  is  customary  to  consider  that  all  oxygen  present 
is  combined  with  hydrogen  as  HzO  and  that  only  the  remainder 
of  the  hydrogen  can  burn  to  liberate  heat.  This  combustible 
part  of  the  total  hydrogen  is  known  as  available  or  uncombined 
hydrogen. 

According  to  the  assumption  just  given,  the  "available" 
hydrogen  can  be  determined  in  any  case  by  subtracting  from 
the  total  hydrogen  the  amount  which  could  be  combined  with  all 
the  oxygen  present.  Equation  (361)  above  shows  that  a  given 
weight  of  oxygen  could  be  combined  with  one-eighth  its  weight 
of  hydrogen  and  it  follows  from  this  that  the  weight  of  the 
unavailable  hydrogen  must  be  one-eighth  of  the  weight  of  oxygen 
present  in  a  compound. 

Then  if  //  represents  the  total  weight  of  hydrogen  present  and 
if  there  are  0  pounds  of  oxygen  which  are  assumed  to  be  already 
combined  with  part  of  this  hydrogen,  the  available  hydrogen 
must  weigh  ( H  -  0/8)  pounds.  The  oxygen  required  for  the 
combustion  of  the  available  hydrogen  is 

Pounds  of  0  =  8  (H  -  0/8), .     ,     „•    .     (362) 


COMBUSTION  487 

and  the  weight  of  air  required  to  supply  this  oxygen  is  found  by 
multiplying  this  equation  by  4.35;    thus 

Pounds  of  air  =  34.8  (H  -  0/8)  (approx.).      .     (363) 

(c)  If  hydrogen  at  60°  F.  is  burned  to  H%0  and  the  latter  is 
afterwards  cooled  to  60°,  the  quantity  of  heat  obtained  varies 
according  to  the  conditions  of  cooling.     If  the  material  is  con- 
tained in  a  vessel  equivalent  to  a  cylinder  closed  with  a  movable 
piston  exerting  a  constant  pressure  and  if  at  the  end  of  the  cool- 
ing process  all  the  water  exists  as  liquid,  a  certain  amount  of 
heat  equal  to  about  62 ,000  B.t.u.  (experimental  value  61,950)  per 
pound  of  available  hydrogen  will  be  obtained.     In  this  book  this 
will  be  called  the  "  higher  heat  value  "  of  hydrogen. 

On  this  basis  the  higher  heat  value  may  be  defined  as  the 
quantity  of  heat  obtained  when  the  products  of  combustion  are 
cooled  in  such  manner  that  the  water  vapor  resulting  from  the 
combustion  of  one  pound  of  hydrogen  (initially  at  60°  F.)  is  com- 
pletely condensed  at  constant  pressure  to  a  liquid  at  a  tempera- 
ture of  60°  F.  Then,  when  a  combustible  containing  H  pounds 
of  hydrogen  and  0  pounds  of  oxygen  is  burned,  the  heat  obtained 
from  the  available  hydrogen,  on  the  basis  of  this  higher  heat 
value,  would  be 

B.t.u.  =  62,000  (H  -  0/8). 

(d)  Other  definitions  of  higher  heat  value  are  sometimes  given. 
Instead  of  cooling  to  60°,  some  other  (higher)  temperature,  such 
as  212°,  may  be  used,  in  which  case  the  amount  of  heat  involved 
is  slightly  less. 

Should  the  cooling  be  conducted  in  a  vessel  inclosing  a  greater 
volume  than  that  occupied  by  the  liquid  water,  only  a  part  of 
the  vapor  will  condense,  the  rest  remaining  to  fill  the  surplus 
space  at  the  existing  temperature.  This  vapor  will  of  course 
have  associated  with  it  its  latent  heat  of  vaporization,  and  there- 
fore the  heat  value  found  will  be  less  than  that  obtained  when 
all  the  water  is  condensed. 

(e)  Another  calorific  quantity,  known  as  the  "lower  heat 
value,"  is  used  by  engineers  but  is  not  very  accurately  defined. 
It  is  generally  assumed  to  be  the  heat  obtained  if  all  the  water 
formed  remains  saturated  or  superheated  vapor  at  the  tempera- 
ture of  the  products  of  combustion.     This  would  be  numerically 


488  HEAT-POWER  ENGINEERING' 

less  than  the  higher  heat  value  already  given,  by  an  amount 
equal  to  the  heat  above  60°  per  pound  of  vapor  in  the  flue  gas. 

The  accurate  determination  of  the  heat  which  could  be  ob- 
tained by  cooling  and  condensing,  under  constant  pressure,  the 
water  vapor  contained  in  flue  gases  is  more  or  less  complicated 
in  most  cases.  It  is  first  necessary  to  determine  the  weight  of 
vapor  per  cubic  foot  of  gas,  its  partial  pressure,  and  its  tempera- 
ture. From  this  data  its  state  can  be  determined  either  from 
steam  tables,  or  from  a  diagram  similar  to  that  of  Fig.  34  drawn 
for  water  vapor.  With  the  state  known,  the  heat  which  would 
be  liberated  per  pound  during  cooling  and  condensing  under 
constant  pressure  can  be  found  from  the  steam  tables.  The 
same  result  can  be  closely  approximated  by  the  use  of  the  follow- 
ing formula,*  which  gives  very  closely  the  heat  above  32°  F.  per 
pound  of  water  vapor  in  the  air,  or  in  products  of  combustion, 

A<2  =  1058.7+0455  fc  B.t.u.,      ..';•..     ;.    (364) 
in  which 

AQ  =  B.t.u.  per. pound  above  32°  F.;  and 
/i  =  temperature  of  vapor  in  products  of  com- 
bustion ( =  temperature  of  gas) . 

If  it  is  assumed  that  the  liquid  resulting  from  condensation 
could  be  cooled  only  to  the  temperature  /2°  F.  (say  the  room 
temperature  of  about  60°,  instead  of  to  32°),  then, 

Aft,  =  (1058.7  +  0.455  /O  -  (/2  -  32) 

=  1090.7  +  0.455  ti  -  tz.         .     .     .     .     (365) 

Thus,  every  pound  of  water  vapor  which  escapes  uncondensed  in 
the  products  of  combustion  will  carry  with  it  an  amount  of  heat 
equal  to  Aft2,  which  is,  therefore,  unavailable  for  other  pur- 
poses. Since  every  pound  of  hydrogen  burns  to  nine  pounds 
of  water,  it  follows  that  the  lower  heat  value  per  pound  of 
available  hydrogen  is 

L.H.V.  =  62,000  -  9  (1090.7  +  0.455  /!  -  /2).  .     (366) 

This  expression  shows  that  the  lower  heat  value  is  really  a 
variable,  depending  for  its  value  on  the  lowest  temperature  /i 
attained  by  the  products  of  combustion  before  leaving  the 
apparatus  which  they  are  supposed  to  heat,  and  also  on  the  tem- 

*  For  explanation  of  this  formula  and  further  details  see  "  Experimental  En- 
gineering," Carpenter  and  Diederichs,  p.  467. 


COMBUSTION  489 

perature  J2,  which  is  generally  assumed  as  about  60°.  For  a 
value  of  /i  equal  to  1500°  F.,  and  /2  equal  to  60°,  the  difference 
between  the  lower  and  higher  heat  values  is  about  15,000  B.t.u.; 
for  ti  equal  to  500°  F.  the  difference  equals  about  n,ooo  B.t.u. j 
and  for  ti  and  /2  both  equal  to  60°  F.  the  difference  is  still  about 
9500. 

(f)  The  value  ordinarily  used  for  engineering  purposes,  and 
which  may   therefore  be   called  the  "engineering  lower  heat 
value,"   is  generally  taken  at  52,000,   which  corresponds  to  a 
value  of  /i  equal  to  about  530°  F.  with  /2  =  60°  F.     It  is  evident 
that  this  may  be  merely  a  very  rough  approximation  in  many 
cases. 

When  this  value  is  used,  the  lower  heat  value  of  the  hydrogen 
in  a  fuel  which  contains  H  pounds  of  that  element  and  0  pounds 
of  oxygen  is 

B.t.u.  =  52,000  (H  -  0/8) (367) 

(g)  In  some  cases  it  is  more  convenient  to  use  heat  values  per 
cubic  foot  of  hydrogen  rather  than  per  pound.     These  can  easily 
be  obtained  by  dividing  the  values  already  given  by  the  specific 
volume  of  hydrogen.     There  will  obviously  be  as  many  different 
.values   as   there   are   temperature  and   pressure   combinations; 
hence  the  conditions  under  which  the  cubic  foot  of  gas  is  to  be 
measured   should   always   be   specified.     At   a   temperature   of 
32°  F.  and  under  a  pressure  of  14.7  pounds  per  square  inch  the 
specific  volume  of  hydrogen  is  178  cubic  feet.     Therefore,  the 
heat  values  per  cubic  foot  under  these  conditions  are 


and 


Higher  heat  value  =  -        -  =  348  B.t.u.  .     .     (368) 
170 

r^  OOO 

Lower  heat  value  =  —     -  =  292  B.t.u.  .     .     (369) 
170 


(h)  In  this  connection  it  should  be  noted  that  although  the 
heat  value  per  pound  of  hydrogen  is  considerably  higher  than 
the  heat  value  per  pound  of  carbon  monoxide,  the  values  per 
cubic  foot  of  material  are  more  nearly  equal.  Thus  the  value 
per  cubic  foot  of  CO  at  32°  F.  and  at  atmospheric  pressure 
is  about  335  B.t.u.,  which  is  but  slightly  less  than  the  upper 
value  for  hydrogen  and  is  considerably  greater  than  the  lower 
value. 


4QO 


HEAT-POWER  ENGINEERING 


This  relation  is  of  particular  importance  in  engineering, 
because : 

(1)  There  are  a  large  number  of  commercial  gases  containing 
both  hydrogen  and  carbon  monoxide  and  it  is  possible  to  regu- 
late the  relative  proportions  of  the  two  to  a  certain  extent. 

(2)  It  is  generally  the  volume  of  the  gas  which  is  to  be  handled, 
and  not  its  weight,  which  determines  the  dimensions  and  cost 
of  apparatus  and  cost  of  operation ;  and 

(3)  Under  most  engineering  conditions  it  is  the  lower  heat 
value  of  hydrogen,  not  the  higher,  that  is  made  available. 

241.  Hydrocarbons,  (a)  Combustibles  composed  of  hydro- 
gen and  carbon  in  combination  are  known  as  "  hydrocarbons." 
There  are  many  kinds  which  differ  as  to  the  relative  proportions 
of  H  and  C  contained.  They  burn  to  form  the  ultimate  products 
C02  and  H*0,  but  the  process  is  often  very  complicated.  The 
exact  combustion  behavior  of  all  the  common  hydrocarbons  is 
not  yet  well  known  but  experiment  shows  that  in  many  cases  a 
number  of  reactions  go  on  before  the  actual  combustion  process 
is  completed. 

(b)  It  is  very  common  practice  to  assume  that  when  a  hydro- 
carbon containing  C  pounds  of  carbon  and  H  pounds  of  hydrogen 
is  burned  it  should  liberate 

(C  X  14,600)  +  (H  X  62,000)  B.t.u.,     .     v    (370) 

but  such  calculations  seldom  check  with  the  actual  values.  This 
is  explained  in  part  by  the  fact  that  the  hydrocarbon  is  already 
a  chemical  compound  and  must  be  broken  up  to  enable  the  indi- 
vidual elements  to  combine  with  oxygen.  When  this  occurs 
a  quantity  of  heat  must  be  absorbed  or  liberated,  thus  diminish- 
ing or  increasing  the  amount  liberated  during  the  formation  of 
COz  and  HZO.  Many  empirical  formulas  have  been  developed 
to  take  account  of  such  effects,  but  none  of  them  are  entirely 
satisfactory  for  all  cases. 

(c)  In  many  instances  the  approximate  calculation  by  Eq. 
(370)  is  sufficiently  exact,  but  when  great  accuracy  is  desired  a 
determination  should  be  made  by  using  a  "  Fuel  Calorimeter," 
which  will  be  briefly  described  in  Section  244. 

The  experimentally  determined  and  calculated  calorific  valifes 
of  several  of  the  principal  hydrocarbons  are  given  in  Table  XXIII. 


COMBUSTION 


491 


TABLE  XXIII.  —  CALORIFIC  VALUES  OF  HYDROCARBONS. 


Name. 

Molecular 
Formula. 

Weight  in 
Lbs./Cu.  Ft., 
Atm.  Pres.  and 
32°  F. 

Calorific  Value  Experimentally 
Determined,  B.t.u./Lb. 

Calorific  Value 
Calculated, 
B.t.u./Lb. 

Higher. 

Lower. 

Higher. 

Methane  .... 
Ethane 

CH< 

Cs%fl6 

CiH% 

C^HZ 

o  .  04464 

0.08329 

0.07809 
0.07251 

23,842 
22,399 
21,429 
21,429 

21,385 
20,434 
20,025 
20,673 

26,455 
24,080 
21,370 
18,240 

Ethylene.  .  . 
Acetylene..  . 

242.  Combustion    of    Sulphur.     Sulphur    burned    in    oxygen 
forms  sulphur  dioxide.     The  reaction  is  given  by  the  equation 

S  +  02  =  S02 (371) 

The  weights  combined  are 

32  of  S  +  (2  X  16)  0/0  =  64  of  S02, 
and  dividing  by  32  gives 

iofS  +  iofO  =  2ofS02 (372) 

Then,  for  each  pound  of  sulphur,  one  pound  of  oxygen  is  needed 
for  complete  combustion  and  2  pounds  of  SOz  result.  To  furnish 
the  pound  of  oxygen  approximately  4.35  pounds  of  air  are 
required.  The  reaction  is  accompanied  by  the  liberation  of 
about  4000  B.t.u.  per  pound  of  sulphur. 

243.  Combustion  of  a  Mixture  of  Elements,     (a)  If  the  sym- 
bols represent  the  pounds  of  each  of  the  respective  elements 
present  in  a  mixture,  and  if  it  is  supposed  that  the  oxygen  present 
is  already  in  combination  with  hydrogen,  then,  from  the  pre- 
ceding paragraphs,  it  is  evident  that  for  complete  combustion 
there  are  needed 

Pounds  of  Oxygen  =  2§  C  +  8  (H  -  0/8)  +  S;        (373) 
to  furnish  this  would  require  4.35  times  as  much  air,  or 

Pounds  of  Air  =  1 1.6  C  +  34.8  (H  -  0/8)  +  4-35^;  (374) 

and  the  volume  of  this  air  at  a  temperature  of  62°  F.  and  at 
atmospheric  pressure  is  found  by  multiplying  by  the  specific 
volume  13.14  (from  Table  XX),  giving 

Cubic  Feet  of  Air  =  153  C  +  454  (H  -  0/8)  +  57  S.   (375) 


49 2  HEAT-POWER  ENGINEERING, 

The  volumes  at  other  temperatures  and  pressures  can  be  found 
from  the  relation  (PV/T)1  =  (PV/T)* 

•  (b)  The  heat  liberated  when  such  mixtures  are  burned  can  be 
conveniently  determined  by  the  use  of  what  are  known  as 
Dulongs  formulas.  These  are: 

Higher  B.t.u.  =  14,600  C  +  62,000  (H  -  0/8)  +  4000  5.  (376) 
Lower  B.t.u.  =  14,600  C  +  52,000  (H  -  O/8)  -f  4000  5.  (377) 

It  will  be  noted  that  these  formulas  are  merely  the  summations 
of  the  heat  values  given  before  for  the  individual  elements. 

As  already  explained,  if  there  are  chemical  combinations 
which  must  be  broken  up,  the  heat  associated  with  the  separa- 
tion must  be  considered  besides  that  given  by  Dulong's  formula. 
Thus  Eqs.  (376)  and  (377)  do  not  apply  to  hydrocarbons,  al- 
though their  use  will  give  the  approximate  heat  values. 

244.  Fuel  Calorimeters  and  Heat  Value,  (a)  In  the  absence 
of  satisfactory  methods  of  calculating  the  heat  liberated  during 
combustion,  the  scientist  and  the  engineer  have  developed  in- 
struments, known  as  Fuel  Calorimeters,  for  measuring  the  energy 
as  liberated. 

Practically  all  of  them  operate  in  the  following  way :  A  known 
weight,  or  volume,  of  the  combustible  is  burned  within  the  in- 
strument under  such  conditions  as  to  insure  as  nearly  as  pos- 
sible complete  combustion,  and  the  heat  liberated  is  absorbed  by 
water  or  similar  liquid  in  an  enveloping  jacket.  By  measuring 
the  temperature  rise  of  the  liquid,  and  correcting  for  radiation 
loss  from  the  instrument,  the  heat  liberated  is  obtained;  and  from 
the  known  weight  of  the  material  burned,  the  heat  which  would 
be  liberated  per  unit  weight  may  be  calculated.  This  value  is 
known  as  the  Heat  Value,  Calorific  Value,  or  Heat  of  Com- 
bustion of  the  material.  In  engineering  work  it  is  generally 
expressed  in  B.t.u.  per  pound  of  material,  or,  in  the  case  of  gases,* 
per  cubic  foot  at  standard  conditions. 

(b)  In  all  calorimeters  the  jacket  temperature  is  near  that  of 
the  room  and  the  products  of  combustion  are  cooled  to  approxi- 

*  It  is  almost  standard  practice  to  use  weight  as  the  basis  for  solid  fuels  and 
volume  as  the  basis  for  gases.  For  liquids  both  weight  and  volume  are  used, 
though  weight  is  probably  givea  the  preference.  Whenever  there  is  a  possibility 
of  confusion  the  unit  should  be  given  in  the  statement  of  results.  If  a  cubic  foot 
of  gas  "  at  standard  "  is  used,  the  so-called  standard  should  be  denned. 


COMBUSTION  493 

mately  the  temperature  of  the  jacket  before  leaving  the  instru- 
ment; thus  the  heat  measured  is  generally  assumed  to  be  that 
obtained  by  bringing  the  products  of  combustion  down  to  the 
initial  temperature  of  the  combustible  material.  This  is  seldom 
really  accomplished  and  an  error  from  this  source  is  therefore 
introduced  into  practically  all  commercial  calorific  determina- 
tions. This  method  gives  what  is  commercially  called  the 
"  higher  heat  value,"  when  the  combustible  contains  available 
hydrogen. 

It  has  already  been  pointed  out  that  even  with  the  tempera- 
ture of  the  combustion  products  reduced  to  60°  F.  there  may  be 
a  considerable  discrepancy  between  the  values  thus  obtained 
and  the  true  higher  value. 

An  accurate  method  of  stating  calorific  values  would  be  to 
give  the  heat  liberated  when  material  at  32°  F.,  or  60°  F.,  is 
burned  and  the  products  are  cooled  to  the  original  temperature, 
allowance  being  made  in  each  case  for  humidity  in  the  products 
of  combustion.  In  the  present  state  of  the  art,  however,  such 
refinements  are  not  warranted. 

245.  Flue  Gas  Analysis,  (a)  In  connection  with  tests  of 
furnaces,  boilers,  and  similar  apparatus  in  which  fuel  is  burned, 
it  is  often  necessary  to  analyze  the  flue  gases  in  order  that  certain 
efficiencies  and  losses  can  be  calculated  and  that  the  conditions 
of  combustion  can  be  determined.  In  these  analyses  the  quanti- 
ties of  gases  present  are  generally  expressed  in  "  volume  per- 
centages." For  example,  gases  a,  b,  and  c  may  be  said  to  con- 
stitute respectively  10  per  cent,  20  per  cent,  and  70  per  cent  of 
the  total  volume  (=  100  per  cent)  resulting  from  their  mixture. 

(b)  In  making  the  analysis,  a  measured  volume  of  the  mixed 
gases  at  atmospheric  temperature  and  pressure  is  successively 
brought  into   contact  with   appropriate  reagents,   each  one  of 
which  absorbs  but  one  constituent  gas;    then,  by  noting  the 
corresponding  decreases  in  volume  under  atmospheric  conditions, 
the  volume-percentages  of  the  various  constituent  gases  can 
readily  be  determined. 

(c)  To  give  a  clearer  idea  of  this  process,  assume  that  the 
cubical  vessel  shown  in  Fig.  319  (a)  incloses  a  volume  of  100  units, 
that  it  is  filled  with  a  mixture  of  gases,  say   C02,  CO  and  N, 
and  that  the  pressure  of  the  mixture  is  atmospheric.     Each  of 


494 


HEAT-POWER  ENGINEERING 


(b) 


Fig.  3i9- 


the  constituents  evidently  occupies  the  entire  volume,  that  is, 
each  is  evenly  distributed  throughout  the  vessel;  each  exerts  a 
definite  "  partial  pressure  ";  and  the  sum  of  these  partial  pres- 
sures equals  the  atmospheric  pressure.  If  it  were  possible  to 
collect  each  of  the  constituents  and  isolate  it  from  the  others  by 
flexible  diaphragms,  as  shown  in  Fig.  319  (b),  and  if  each  of  the 

constituents  were  decreased  in  volume 
until  its  pressure  became  equal  to 
atmospheric,  then  the  sum  of  all  the 
volumes  would  equal  the  original  vol- 
ume, provided  the  temperature  re- 
mained the  same.  That  this  is  true 
will  be  shown  in  the  following  para- 
graphs. 

(d)  Assume,  for  instance,  that  in  Fig.  319  (a)  the  partial  pres- 
sures are  aPat  bPa,  and  cPa,  a,  b,  and  c  being  fractions  and  Pa 
being  atmospheric  pressure.     If  the  total  pressure  of  the  mixture 
is  atmospheric,  the  sum  of  the  three   partial   pressures  must 
equal  Pa,  that  is 

aPa  -f-  bPa  +  cPa  =  Pa,  or  a  +  b  +  c  =  1. 

If  the  volume  of  the  vessel  is  V,  then  the  constituent  with 
partial  pressure  aPa  will  have  to  be  given  a  volume 

Fi  =  (V  X  aPa)  +  Pa  =  aV, 

in  order  to  raise  it  to  atmospheric  pressure  when  isolated ;  the 
constituent  with  partial  pressure  bPa  will  have  to  be  given  a 
volume  Vz=  bV\  and  the  remaining  constituent,  a  volume 
F3  =  cV. 

From  the  relations  between  a,  6,  and  c  it  is  obvious  that 

Vi  +  F2  +  V3  =  V  ( =  100  by  assumption). 

(e)  Thus  a,  b,  and  c  not  only  represent  the  partial  pressure 
fractions,  but  also  give  the  fractions  of  the  total  volume  that 
would  be  occupied  by  the  constituents  when  reduced  to  the 
volumes  they  would  have  when  isolated  and  raised  to  atmos- 
pheric pressure  without  change  of  temperature.     As  was  stated, 
the  so-called  percentage  by  volume  of  any  constituent  is  there- 
fore merely  the  percentage  of  the  original  volume  of  the  mixture 
which  that  constituent  would  occupy  if  existing  alone  at  the 


COMBUSTION  495 

same  pressure  as  that  exerted  by  the  mixture  and  at  the  same 
temperature. 

(f)  It  is  important  to  note  in  connection  with  flue  gas  analyses 
that  the  water  vapor  content  is  never  determined  in  ordinary 
engineering  apparatus.  The  greater  part  of  this  water  is  con- 
densed and  disappears  by  mixing  with  water  contained  in  the 
apparatus  used  in  making  the  analysis.  The  gaseous  mixture 
is,  however,  practically  always  saturated  with  water  vapor  during 
the  entire  analysis,  and  although  this  water  exerts  a  partial 
pressure,  this  latter  affects  each  of  the  constituents  proportion- 
ately, hence  its  influence  is  really  negligible.  Though  water 
vapor  is  present  the  results  on  the  percentage  basis  are  therefore 
the  same  as  those  for  dry  gas. 

246.  Weight  of  Flue  Gases,  (a)  In  many  engineering  com- 
putations it  is  necessary  to  determine  the  weights  of  the  gases 
resulting  from  the  combustion  of  a  given  fuel  under  given  con- 
ditions. Such  calculations  are  simple  when  one  knows  (i)  the 
analysis  of  the  flue  gases,  (2)  the  analysis  of  the  fuel,  and  (3)  the 
moisture  content  of  the  air. 

(b)  As  was  seen  in  the  preceding  section,  the  volumetric 
analysis  of  the  flue  gas  is  the  equivalent  of  isolating  the  con- 
stituent gases  and  reducing  them  to  the  same  pressure  and 
temperature.  Then  from  Avogadro's  hypothesis  it  follows  that 
the  number  of  molecules  of  each  of  the  gases  present  must  be 
directly  proportional  to  the  volumes  (V)  which  the  gases  occupy, 
hence  the  products  (mV)  of  these  volumes  by  the  respective 
molecular  weights  (m)  of  the  gases,  give  measures  of  the  rela- 
tive proportions  by  weight  of  the  gases  present  in  the  mixture; 
the  sum  (2w  V)  of  these  products  gives  a  measure  of  the  weight 
of  the  whole  mixture ;  and  the  weight  percentage  of  any  con- 
stituent is  evidently 

Per  cent  weight  =  mV  -^  SwF.      .     .     .     (378) 

Thus,  if  the  mixture  is  composed  of  COz,  0,  CO,  N,  H,  and  502, 
and  if  the  relative  volumetric  proportions  of  the  constituents 
are  represented  by  their  chemical  symbols,  then  the  equivalent 
molecular  weight  of  a  unit  volume  of  the  mixture  is 

SwF  =  (44  CO*  +  J20  +  28CO  +  28N  +  2H  +  64  50,),  (379) 


496  HEAT-POWER  ENGINEERING 

and  the  weight  percentage  of  COz  for  example  is  found  by  divid- 
ing 44  CO2  by  Eq.  (379). 

(c)  It  is  generally  most  convenient  to  express  the  constituents 
in  terms  of  their  weight  per  pound  of  carbon  burned.     The  weight 
corresponding  to  the  m  V  value  of  the  carbon  represented  in  Eq. 
(379)  is  evidently 

Weight  of  C  =  12  (COz  +  CO) ;  i'^V  .  (380) 
hence  the  weight  of  any  constituent  per  pound  of  carbon  is  found 
by  dividing  its  mV  value  by  12  (COz  +  CO).  Thus,  the  weight 
of  nitrogen  is 

WN  =  28  N  '-5-  12  (COz  +  CO) ;  per  Ib.  of  C    .     .     (381) 
the  weight  of  free  hydrogen  is 

wH  =  2  H  -J-  12  (COz  +  CO)  ;•'.".     .     (3810) 
and  similarly  for  the  other  constituents. 

The  total  weight  (w)  of  dry  gas  mixture  per  pound  of  carbon 
actually  burned  is  given  by  dividing  Eq.  (379)  by  Eq.  (380). 
When  simplified  this  becomes 

=  u  CO,  +  80  +  7  (CO  +  N)  +H/2  +  16  SOz  *. 

3  (COz  +  CO) 

in  which,  as  before,  the  symbols  represent  the  relative  volumes 
of  the  gases  they  symbolize. 

(d)  To  find  the  total  weight  of  "wet"  gases  per  pound  of  car- 
bon, it  is  necessary  to  add  three  more  items: 

(1)  The  weight  of  water,  in  the  fuel  per  pound  of  carbon,  as 
found  by  analysis; 

(2)  The  weight  of  water  carried  by  the  air  supplied  for  com- 
bustion, per  pound  of  carbon,  which  can  be  found  from  psy- 
chrometric  observations ;  and 

(3)  The  weight  of  water  formed  by  the  hydrogen  burned,  per 
pound  of  carbon.     This  can  be  found  as  follows,  when  the  fuel 
analysis  is  known:  Let  w#'be  the  weight  of  free  hydrogen,  per 
pound  of  carbon  in  the  fuel,  and  letfl",  as  before,  be  the  volume  of 
hydrogen  not  burned  (per  pound  of  C),  as  found  in  the  analysis 
of  the  flue  gases;    then  WH'-  \2  H  -±  12  (COz  +  CO)}  is  the 
weight  of  hydrogen  burned,  and  the  resulting  weight  of  water  is 

Weight  of  HzO  =  9  \WH'-  [2  H  -5- 12  (COz  +  CO)]  j     (383) 

*  If  the  gases  CH4  and  CnHm  are  present,  this  expression  should  have 
4  CHt  +  7  CnHm  added  to  the  numerator,  and  the  parenthesis  in  the  denominator 
should  include  Cff4  +  2  Cn#m,  it  being  assumed  that  the  CnHm  is  all  Ethylene 

(Off*). 


COMBUSTION  497 

247.  Percentage  of  Excess  Air.  It  is  now  possible  to  derive 
perfectly  general  expressions  for  the  percentage  of  excess  air 
and  for  the  excess  coefficient,  —  that  is,  expressions  which  are  not 
limited,  as  are  Eqs.  (352)  to  (355),  to  the  case  of  the  combustion 
of  carbon  alone. 

If  the  symbols  represent  relative  volumes  as  before,  then,  accord- 
ing to  Eq.  (381)  the  total  weight  of  nitrogen  in  the  flue  gases  per 
pound  of  carbon  is  28  N  -s-  I2(C02  +  C0),or  7^-5-  3(C02+  CO); 
hence,  the  oxygen  which  accompanied  this  nitrogen  must  be 

Total  oxygen  =  ^  X  3  (aJ2  +  C0)  Pounds.      .     (384) 

The  weight  of  oxygen  not  used  is,  similarly, 

32  0  -M2  (C02  +  CO)  =  8  0  +  3  (C02  +  CO), 
where  0  is  its  volume,  which  is  assumed  to  be  known  from  the 
volumetric  analysis  of  the  flue  gas.     But  part  of  this  unused 
oxygen  could  have  been  utilized  had  combustion  been  perfect. 

-ru  •  -t*  l6^          28  C0  4  CO 

Thus  a  weight  equal  to    -  X  ^  (CQf  +  CQ}  =  z(co^co} 

might  have  been  used  for  burning  the  CO  to  C02;  and  a  weight 


to  8  X  CO)  -  3  (CO,  +  CO)    ™ght  have  been 


used  for  burning  the  free  hydrogen  in  the  flue  gas.     The  true 
weight  of  excess  oxygen  per  pound  C  is,  therefore, 

Excess  0  =  [8  0-4(CO+tf)]  -^  [3  (C02  +  CO)]      (385) 
Subtracting  this  from  the  total  oxygen  (Eq.  (384))  gives  the 
weight  of  required  oxygen,  per  pound  of  C  as 


Required  oxygen  =  -  3  (CO2  +  CO)  -  '  (386) 
Then,  since  the  percentage  of  excess  air,  x,  is  equal  to  excess  air 
(or  O)  divided  by  the  total  required  air  (or  0),  it  follows  that 

I00.f         (38;) 


*  If  the  gases  C#4  and  CnHm  are  present,  4  CH,  +  7  CnHm  should  be  added 
to  the  parenthesis  in  the  numerator  and  C#4  +  2  CnHm  should  be  included  in  that 
in  the  denominator.  This  .neglects  any  N  in  the  fuel. 

t  To  account  for  the  gases  mentioned  in  the  two  preceding  footnotes, 
4  CH*  +  7  CnHm  should  be  added  in  the  parentheses  in  the  numerator  and 
denominator. 


HEAT-POWER  ENGINEERING 


The  excess  coefficient,  X,  is  therefore 

80- 


(388) 
100 


* 


x  7^~  [80- 

248.  Stack  Losses,  (a)  In  connection  with  tests  of  furnaces, 
boilers  and  similar  apparatus  it  is  customary  to  determine  the 
amount  of  heat  carried  away  by  the  gases  passing  up  the  stack, 
or  as  it  is  often  called  the  "  heat  lost  in  flue  gases." 

(b)  Before  taking  up  the  complete  method  of  calculating  these 
losses,  a  simplified  theoretical  discussion  will  be  considered  in 
order   to   bring   out   certain   fundamental   relations.     For   this 
purpose  the  case  of  dry  carbon  only,  burned  with  dry  air,  will 
be  analyzed.     In   connection   therewith   the   combustion   may 
occur  under  any  one  of  three  sets  of  conditions,  as  follows: 

Case  i.    Complete  combustion  with  theoretical  air  supply; 
Case  2.    Complete  combustion  with  excess  air;   and 
Case  3.    Incomplete  combustion  with  deficiency  of  air. 
It  is  obvious  that  Case  I  is  merely  a  limiting  value  between 
Cases  2  and  3,  and  hence  need  not  be  considered  separately. 

(c)  With  Excess  Air  (Case  2)  the  only  loss  to  the  stack  under 
the  assumed  conditions  is  that  due  to  sensible  heat  of  the  CC>2, 
the  nitrogen,  and  the  excess  air  in  the  flue  gases. 

It  was  shown  in  Sect.  238  (f),  that  with  x  per  cent  excess  air 
the  so-called  "products  of  combustion"  resulting  from  the 
complete  burning  of  one  pound  of  carbon  would  consist  of  3.67 
pounds  of  COz,  8.9  pounds  of  N  and  0.116^:  pounds  of  air; 
hence  the  total  weight  of  flue  gas,  per  pound  of  carbon,  is  given 
by  the  equation, 

Pounds  of  flue  gas  =  3.67  +  8.9  +  0.116  x  .     .     (389) 

As  this  waste  gas  leaves  at  a  temperature  considerably  higher 
than  that  at  which  the  constituents  entered  the  furnace,  it 
carries  with  it  sensible  heat  which  should  have  been  used. 
With  weight  determined  the  corresponding  loss  of  heat  can 
readily  be  computed  when  the  specific  heat  and  the  temperature 
of  the  flue  gas  are  known. 

As  flue  gases  of  boiler  furnaces  generally  leave  with  a  tempera- 
ture less  than  700°  F.,  it  is  customary  to  neglect  the  variations 
of  the  specific  heats  with  temperature,  and  as  the  specific  heat 
of  the  flue  gas  is  nearly  the  same  as  that  of  air,  it  is  also  customary 
*  See  last  footnote  on  page  497. 


COMBUSTION  499 

to  neglect  the  change  with  variations  in  x.  The  specific  heats 
assumed  for  the  mixture  by  different  writers  generally  fall 
between  0.22  and  0.24;  with  average  excess  coefficients,  0.24 
is  a  satisfactory  figure.  With  this  assumption,  the  approximate 
formula  for  loss  of  heat  in  the  flue  gas,  per  pound  of  carbon 
burned,  for  Case  2  is 

B.t.u.  loss  =  0.24  (3.67  -f-  8.9  +  o.iidx]  (tf  —  ta),      (390) 

where  //  is  the  temperature  of  the  flue  gas  and  ta  is  the  atmos- 
pheric temperature.  Since  each  pound  of  carbon  should  liberate 
14,600  B.t.u.  the  per  cent  loss  of  heat  is  given  by 


0.24(3.67  +  8.9  +  o.n6x)  X(tf-ta)  ,  ,       N 

Per  cent  loss  =  —  ^VJ    '   '  —  ^—^  --  1  —  ±>  -  aJ.  x  100.     (391) 

14^000 

Values  obtained  from  this  equation  are  plotted  in  the  upper, 
right-hand  quadrant  of  Fig.  320  and  the  resulting  curves  serve 
to  show  how  the  stack  loss  varies  with  different  values  of  x  and 
of  (I/  —  ta).  Actually,  because  of  increases  in  the  specific  heats 
with  temperature  and  excess  air,  the  losses  would  increase  some- 
what more  rapidly  than  these  curves  show. 

(d)  With  Deficiency  of  Air  (Case  3  above)  there  are  two  stack 
losses  to  be  considered  —  that  due  to  sensible  heat,  and  that  due 
to  the  heat  value  of  the  CO  (or  of  the  CO  and  C)  not  burned. 

The  weights  of  gas  (per  pound  C)  present  with  y  per  cent 
deficiency  of  air  will  be  given  by  (from  (k)  of  Sect.  238) 

Pounds  of  Flue  Gas  =  3.67(1  -  —}of  COZ  +  2.  33  —  of  CO 

\  IOO/  IOO 

(392) 


+  8.9(1  - 


Assuming  the  specific  heat  0.24,  this  would  give,  per  pound  of 
carbon,  a  stack  loss  due  to  sensible  heat  of 


(393) 

Since  each  pound  of  CO  could  give  4300  B.t.u.  if  burned,  there 
is  also,  per  pound  of  C,  a  loss  due  to  the  CO  equal  to 

(B.t.u.)co  =  2.33  X         X  4300     .     .     .     (394) 


provided  the  deficiency  (y)  is  not  greater  than  50  per  cent. 


HEAT-POWER  ENGINEERING' 


The  total  loss  with  deficiency  of  air  less  than  50  per  cent  is 
evidently  equal  to  (B.t.u.)s  +  (B.t.u.)Co-  This  has  been  plotted 
in  the  lower  right-hand  quadrant  of  Fig.  320  for  different  tem- 
peratures of  gas. 

If  y  exceeds  50  per  cent  some  of  the  carbon  is  not  burned  at  all 
and  the  losses  would  therefore  be  still  greater.  However,  as  this 
is  a  case  not  ordinarily  approached  in  practice  it  need  not  be 
considered  here. 


Fig.  320. 

The  losses  resulting  from  a  deficiency  of  air  are  shown  in  the 
lower  right-hand  quadrant  of  Fig.  320. 

(e)  The  completed  chart  of  Fig.  320  includes  the  curves  pre- 
viously given  in  Fig.  316,  and  serves  to  show  in  a  general  way  how 
the  losses  vary  with  different  temperatures,  different  quantities 
of  air  and  different  flue  gas  analyses.  It  must  be  borne  in  mind 
that  certain  broad  assumptions  were  made  to  simplify  the  deriva- 
tion of  this  chart  and  it  is  therefore  only  approximately  correct. 
From  an  inspection  of  the  curves  it  at  once  becomes  apparent 
that  losses  due  to  excess  air  are  much  less  than  those  due  to 
deficiencies,  for  example,  with  flue  gas  at  500  degrees,  the  loss 
occasioned  by  100  per  cent  excess  air  is  equalled  by  that  due  to 
only  about  8  per  cent  deficiency. 


COMBUSTION  501 

In  using  the  chart,  however,  it  is  important  to  note  that  com- 
parisons of  losses  incident  to  using  different  percentages  of  excess 
air  should  not  necessarily  be  made  on  the  basis  of  the  same 
temperature  —  for,  ordinarily,  larger  amounts  of  air  bring  about 
a  reduction  in  temperature  of  the  flue  gas. 

(f)  The  foregoing  applies  to  the  combustion  of  carbon  alone. 
In  the  actual  case  the  "  flue  gas  "  usually  contains  C02,  CO,  N, 
0,  H,  hydrocarbons  and  water  vapor  and  therefore  differs  some- 
what from  the  case  just  considered.     The  stack  losses  in  the 
actual  case  may  be  conveniently  divided  into  three  distinct 
parts  : 

(1)  That  part  represented  by  the  sensible  heat  of  the  dry  flue 
gas,  not  including  the  moisture  that  may  be  present; 

(2)  That  part  due  to  incomplete  combustion  of  some  of  the 
constituents  of  the  fuel  —  this  includes  the  potential  heat  of  the 
unburned  C  (in  the  smoke) ,  CO,  H  and  hydrocarbons ; 

(3)  That  part  represented  by  the  latent  and  sensible  heat  of 
the  water  vapor  (moisture)  in  the  flue  gas. 

The  methods  of  determining  each  of  these  losses  will  now  be 
considered. 

(g)  The  weight  (w)  of  dry  flue  gas  (per  pound  of  carbon)  in  the 
fuel  can  be  found  by  Eq.  (382)  in  Sect.  246  and  it  is  common 
practice  to  use  0.24  for  the  Cp  of  the  mixture.     Hence  the  approxi- 
mate loss  in  the  sensible  heat  in  the  dry  flue  gas  (per  pound  of 
carbon  burned)  is 

(B.t.u.)s  =  0.24  w(tf-ta) (395) 

(h)  A  more  accurate  method  of  finding  this  loss  is  to  first 
determine  (as  in  Sect.  246)  the  weight  (wn),  per  pound_pf  C,  of 
each  of  the  constituent  gases,  get  its  mean  specific  heat  CPn  from 
Fig.  318  for  the  temperature  range,  then  compute  the  sensible 
heat  it  carries  away;  and  finally  take  the  summation  for  all  the 
constituents.  Thus  the  total  sensible  heat  carried  away  by  the 
dry  flue  gases  is  (per  pound  of  carbon  burned) 

(B.t.u.)s  =  S  (wCp)n  X  (//-/«)-     -     -     •     (396) 
(i)    The  stack  loss  due  to  incomplete  combustion  is  (per  pound 

of  C)* 

(B.t.u.)I=CXi4,6oo  +  COX430o+H(52,i8j -4.005  tf+()ta), 

(397) 
*  Neglecting  hydrocarbons. 


502  HEAT-POWER  ENGINEERING  , 

in  which  the  symbols  represent  weights  (per  pound  of  C)  of 
the  respective  substances,  and  the  parenthetical  quantity  is  ob- 
tained by  subtracting  from  62,000  (which  is  the  higher  heat 
value  of  H)  the  value  9  (i 090.7  +  0.455  h  ~  O  as  previously 
given  in  Eq.  (366). 

(j)  The  heat  loss  due  to  the  moisture  in  the  flue  gas  depends 
on  the  source  of  this  water  vapor.  That  moisture  which  is 
humidity  in  the  air  used  for  combustion  is  already  vapor  and 
merely  becomes  superheated  in  the  furnace;  hence  the  heat  it 
carries  away  is,  per  pound  of  C, 

(B.t.u.)A  =AXCP(t,-ta),* (398) 

where  A  is  the  weight  of  moisture  in  the  air  used  per  pound  of  C. 
The  loss  of  heat  due  to  the  moisture  (M  pounds  per  pound 
of  C)  originally  in  the  coal  and  due  to  the  water  formed  by  the 
combustion  of  hydrogen  (Mr  pounds  per  pound  C)  is,  from  Eq. 
(366), 

(B.t.u.M  =  (M  +  M')  (1090.7  +  0.455  tf  -Q      •     •     (399) 

per  pound  of  C. 
The  total  loss  of  heat  per  pound  of  carbon  in  the  fuel  is 

therefore,     (B.t.u.)s  +  (B.t.u.)j  +  (B.t.u.}  ±  +  (B.t.u.)M. 


CHAPTER  XXIX. 

ACTUAL  COMBUSTION  OF    FUELS  —  FURNACES  AND   STOKERS  — 

OIL  BURNERS. 

249.  Introductory.     In  a  preceding  chapter  the  physics  and 
chemistry   of  combustion  were  discussed   for   theoretical  cases 
only.     The  study  of  the  actual  process  of  combustion  in  furnaces, 
which  will  now  be  taken  up,  is  more  complicated  because  of 
the  wide  variation  in  composition  of  the  fuels  and  because  there 
is  a  great  diversity  of  conditions  under  which  the  combustion 
takes  place.     In  fact,  there  are  so  many  variables  involved  that 
it  is  substantially  true  that  in  no  two  distinct  cases  does  com- 
bustion occur  under  identical  conditions;    and  even  in  the  same 
furnace  the  conditions  are  constantly  varying.     It  is,  therefore, 
impossible  to  give  detailed  discussion  of  all  the  possible  cases 
which  might  occur.     There  are,  however,  certain  broad  general 
principles,  which,  if  understood,  will  be  of  great  value  in  the 
solution  of  problems  of  combustion  which  arise  in  actual  furnace 
operation  and  these  will  be  brought  out  in  the  discussion  which 
follows. 

250.  Air  Supply,     (a)  In  the  actual  case,  as  in  the  theoretical 
one,  it  is  essential  that  there  be  furnished  a  proper  amount  of 
air  to  supply  the  oxygen  needed  for  combustion.     The  exact 
quantity  necessary  depends  on  the  composition  of  the  fuel  and 
can  readily  be  computed  by  the  method  given  in  Sect.  243,  if 
the  chemical  analysis  is  known.     The  approximate  amount  of 
air  required  is  often  determined,  however,  by  assuming  that  the 
combustible  part  of  the  fuel  is  pure  carbon,  each  pound  of  which 
requires  n.6  pounds  of  air  for  complete  oxidation  and  results 
in  12.6  pounds  of  flue  gas.     But,  for  most  practical  purposes  it 
is  sufficiently  accurate,  and  is  on  the  side  of  liberality,  to  assume 
the  entire  weight  of  coal  to  be  composed  of  carbon,  and  then  use 
these  same  values  as  per  pound  of  coal.     It  should  be  noted, 
however,  that  the  richer  the  fuel  is  in  combustible  hydrogen  the 

503 


504  HEAT-POWER  ENGINEERING 

greater  will  be  the  proportion  of  air  needed,  since  one  pound  of 
hydrogen  requires  34.6  pounds  of  air  or  about  three  times  as 
much  as  is  needed  per  pound  of  C. 

(b)  In  the  ideal  case,  with  fuel  containing  only  carbon,  each 
per  cent  deficiency  of  air  has  been  seen  to  result  in  1 .4  per  cent 
loss  of  heat  because  of  incomplete  combustion  (Sect.  236  (g)). 
As  the  same  thing  is  substantially  true  in  the  actual  case,  great 
care  must  be  exercised  to  insure  an  adequate  supply  of  air  at  all 
points  in  the  fuel  bed.  As  the  bed  usually  varies  in  thickness 
and  in  compactness  and  texture,  the  air  will  meet  with  less 
resistance  in  passing  through  certain  portions  than  through 
others.  Hence  to  insure  against  a  deficiency  at  any  point,  it  is 
necessary  to  furnish  an  amount  of  air  somewhat  in  excess  of  what 
would  theoretically  be  required  if  it  were  uniformly  distributed 
and  properly  mixed  with  the  combustible  material.  Excess  air 
is  not  without  its  disadvantages,  however,  as  it  dilutes  the 
furnace  gases  and  lowers  their  temperature,  which  results  in  a 
decrease  in  the  boiler  efficiency.  Although  its  presence  is  thus 
detrimental,  it  is  much  less  so  under  ordinary  conditions  than  is 
a  deficiency,  as  was  made  clear  in  Fig.  320.  Hence  excess  air 
should  always  be  present  but  in  as  small  amount  as  is  consistent 
with  satisfactory  combustion.  Usually  an  excess  coefficient 
X  of  from  1.5  to  2  times  the  theoretical  amount,  on  a  basis  of 
carbon,  is  used,  i.e.,  from  18  to  24  pounds  of  air  per  pound  of 
combustible.  And,  as  before,  it  is  usually  sufficiently  accurate 
to  assume  the  whole  of  the  coal  to  be  carbon,  and  to  use  these 
values  as  per  pound  of  coal.  Experience  shows  that  if  less  than 
1.3  times  the  theoretical  quantity  is  used,  the  amount  of  CO 
formed  is  generally  prohibitive  even  if  the  greatest  care  is 
exercised  in  operating  the  furnace.*  But  even  if  the  air  supply 
is  adequate  it  does  not  follow  that  the  combustion  is  complete, 
as  will  be  seen  in  the  next  section. 

(c)  With  pure  carbon  as  the  fuel  and  with  the  theoretical  air 
supply,  there  would  be  about  21  per  cent  by  volume  of  CO2  in  the 
flue  gas,  as  was  shown  in  Sect.  238  (c).  Excess  air  will  result  in 
a  decrease  of  the  volume  per  cent  of  CO2  in  the  manner  shown  by 

*  Even  when  considerable  excess  air  is  furnished  there  may  be  some  CO  formed 
in  the  thicker  and  more  compact  portions  of  the  fuel  bed  because  of  local  deficiency 
of  air.  Further,  flue  gas  analyses  may  also  show  CO  which  was  formed  by  processes 
which  will  not  be  discussed  until  later. 


ACTUAL  COMBUSTION  OF  FUELS 


505 


\ 

\ 

\ 

\ 

V 

s 

X 

j, 



•*^. 

%  CO2  in  Flue  Gas  by  Volume 


Fig.  321. 


the  curve  in  Fig.  321.  As  the  combustible  part  of  the  coal  is 
mostly  carbon  these  same  percentages  hold  substantially  in  the 
actual  case.*  Thus,  a  knowledge  of  the  CO2  content  in  the  flue 
gas  indicates  in  a  general  way  the  operating  conditions  within 
the  furnace  and  enables  the  boiler  attendant  to  intelligently 
adjust  the  air  supply. 

Experience  has  shown  that  if  the  supply  of  excess  air  is  such  as 
to  give  C02  by  volume  between  10  per 
cent  and  15  per  cent,  the  furnace  will 
be  operating  at  its  highest  efficiency, 
the  exact  best  percentage  varying 
with  different  conditions.  A  value 
below  10  per  cent  nearly  always  in- 
dicates too  great  an  amount  of  air 
and  a  value  above  15  per  cent  is 
generally  indicative  of  too  small  an 
amount,  as  it  is  usually  accompanied 
by  the  formation  of  prohibitive  quan- 
tities of  CO.  In  Fig.  321  the  region 
for  the  best  results  is  that  shown  by 
the  portion  of  the  curve  lying  between  (a)  and  (6) ;  in  Fig.  320 
it  falls  between  the  points  bearing  similar  letters;  and  it  ap- 
proximately corresponds  with  excess  coefficient  (X)  between  1.3 
and  2.0,  given  in  (b)  of  this  section. 

(d)  In  order  that  the  boiler  attendant  may  obtain  an  indica- 
tion of  the  amount  of  air  being  supplied,  various  devices  known 
as  COi  Recorders,  Econometers,  Combustion  Recorders,  Com- 
posimeters,  etc.f  are  used  to  indicate  the  COz  content  of  the  flue 
gases.  Some  of  these  appliances  operate,  or  indicate,  intermit- 
tently, some  continuously,  and  some  give  a  continuous  graph- 
ical record  so  that  the  owner  or  manager  of  the  plant  can  check 
the  operation  over  any  desired  period  of  time.  In  the  use  of  all 
these  instruments  it  is,  of  course,  necessary  to  obtain  samples  of 
gas  truly  representative  of  the  average  and  to  guard  against  the 
infiltration  of  air  through  the  boiler  setting  or  the  flues  between 
the  furnace  and  the  sampling  point. 

*  Although  the  percentage  of  C02  is  somewhat  less  because  of  the  other  combus- 
tible and  noncombustible  constituents  present  in  the  flue  gas  in  the  actual  case. 

t  For  description  and  method  of  using  such  apparatus  see  Carpenter  and  Diede- 
richs,  "  Experimental  Engineering,"  published  by  John  Wiley  &  Sons. 


506  HEAT-POWER  ENGINEERING  ' 

251.   Conditions  for  Complete  and   Smokeless  Combustion. 

(a)  If  air  is  passed  upward  through  a  deep  bed  of  ignited  carbon 
devoid  of  volatile  matter,  there  is  a  tendency  for  any  C02  that 
is  formed  in  lower  layers  to  be  reduced  to  CO  when  coming  into 
contact  with  the  carbon  above.  If  this  CO  is  not  subsequently 
supplied  with  a  proper  amount  of  air  while  still  at  a  high  tempera- 
ture it  will  pass  off  unoxidized  and  this  will  result  in  a  loss  of  heat 
which  would  otherwise  be  made  available.  It  is,  therefore, 
important  that  an  adequate  air  supply  and  a  suitable  tempera- 
ture be  maintained  in  the  upper  part  of,  and  just  above,  the  bed 
of  fuel.  This  air  may  either  pass  through  the  bed  or  be  supplied 
from  above. 

The  foregoing  applies  of  course  to  the  combustion  of  coke 
and  charcoal  as  well  as  to  carbon.  Anthracite  coal,  which  is 
mostly  fixed  carbon,  behaves  similarly,  but  in  this  case  there  is 
also  a  small  amount  of  volatile  matter  which  must  be  properly 
burned.  These  fuels,  which  have  little  or  no  volatile  matter, 
give  short  flames  above  the  fuel  bed,  the  flames  being  due  to  the 
combustion  of  CO  and  the  small  quantity  of  volatile  matter 
present. 

(b)  When  coal  possessing  a  considerable  amount  of  volatile 
matter  is  placed  on  a  hot  bed  of  fuel,  the  greater  part  of  the  vola- 
tile portion  distills  off  as  the  temperature  rises,  and  the  residue, 
which  is  coke,  burns  in  the  manner  just  described.  The  more 
serious  problem  that  confronts  the  engineer  in  this  case  is  the 
complete  oxidation  of  the  combustible  part  of  this  volatile  mat- 
ter. Evidently  in  the  ordinary  up-draft  furnaces  that  are  fired 
from  above  the  combustion  of  this  part  of  the  fuel  must  occur 
above  the  fuel  bed,  just  as  is  the  case  with  CO;  and  in  order  that 
the  combustible  gases  may  be  completely  burned,  the  following 
four  conditions  must  exist : 

(i)  There  must  be  sufficient  air  just  above  the  fuel  bed,  supplied 
either  from  above  or  through  the  fuel  bed  itself;  (2)  this  air 
must  be  properly  distributed  and  intimately  mixed  with  the  com- 
bustible gases;  (3)  the  mixture  must  have  a  temperature  suffi- 
ciently high  to  cause  ignition  (some  of  the  combustible  gases, 
when  mixed  with  the  burned  gases  present  above  the  fuel,  have 
an  ignition  temperature  of  approximately  1450°  F.);  and  (4) 
there  must  be  sufficient  time  for  the  completion  of  combustion, 
that  is,  the  combustion  must  be  complete  before  the  gases 


ACTUAL  COMBUSTION  OF  FUELS  507 

become  cooled  by  contact  with  the  relatively  cold  walls  of  the 
boiler  (which  are  at  a  temperature  of  about  350  degrees)  or  with 
other  cooling  surface. 

(c)  To  prevent  the  stratification  of  the  air  and  gases,  special 
means  are  sometimes  adopted/ such  as  employing  ateam  jets 
above  the  fire  and  using  baffle  walls,  arches,  and  piers  in  the 
passage  of  the  flame,  to  bring  about  an  intimate  mixture. 

(d)  In  order  that  the  air  used  above  the  fuel  bed  shall  not 
chill  and  extinguish  the  flame,  it  should  be  heated  either  by 
passing  it  through  the  fuel  bed,  or  through  passages  in  the  hotter 
parts  of  the  furnace  setting,  or  in  some  other  way  before  mingling 
with  the  gases;    or  else  the  mixture  of  gases  and  air  should  be 
made  to  pass  over  or  through  hot  portions  of  the  fuel  bed,  or 
should  be  brought  into  contact  with  furnace  walls,  or  other  brick- 
work, which  is  at  a  temperature  sufficiently  high  to  support  the 
combustion. 

(e)  In  order  that  the  flame  shall  not  be  chilled  and  extinguished 
by  coming  in  contact  with  cold  objects,  it  should  be  protected 
by  the  hot  furnace  walls  until  combustion  is  complete.     The 
furnace  should  have  proper  volume  to  accommodate  the  burning 
gases,  and,  when  the  conditions  are  such  that  the  flame  is  long, 
the  distance  from  the  fuel  bed  to  the  relatively  cold  boiler  sur- 
faces with  which  the  gases  first  come  in  contact,  should  be  at 
least  as  great  as  the  length  that  the  flame  attains  when  the  fire 
is  being  forced.     The  length  of  flame  depends  on  the  amount  and 
character  of  the  volatile  matter  in  the  fuel,  on  the  rapidity  of 
combustion  and  on  strength  of  draft.     It  varies  from  a  few 
inches,  with  coke  and  anthracite  coal,  to  8  feet  or  even  more 
with  highly  volatile  coals  —  even  20  feet  has  been  reached  with 
some  western  coals. 

(f)  In  order  to  have  complete  combustion  of  all  the  fuel  in  a 
furnace  it  is  necessary  that  uniform  conditions  prevail  through- 
out the  fuel  bed ;  and  to  bring  this  about  it  is  essential  that  the 
fuel  itself  be  uniform  in  character.     Therefore,  the  best  results 
are  obtained  with  coal  that  has  been  graded  as  to  size.     Espe- 
cially is  this  true  with  anthracite  coal  which  ignites  slowly  and 
is  more  difficult  to  keep  burning  than  volatile  coals.     This  coal 
requires  a  rather  strong  draft  and  unless  the  bed  is  uniform  the 
rush  of  air  through  the  less  dense  portions  tends  to  deaden  the 
fire  in  those  regions,  hence  good  results  can  be  obtained  with  this 


5oS  HEAT-POWER  ENGINEERING 

coal  only  when  it  is  uniform  in  size  and  evenly  distributed.  The 
more  common  sizes  of  coal  are  given  in  Tables  XVI  and  XVII, 
on  pages  465  and  466. 

(g)  Smoke  may  be  composed  of  unconsumed,  condensible 
tarry  vapors,  of  unburned  carbon  freed  by  the  splitting  of  hydro- 
carbons, of  fine  noncombustible  matter  (dust),  or  of  a  combina- 
tion of  these.  It  is  an  indication  of  incomplete  combustion,  and 
hence  of  waste,  and  in  certain  communities  is  prohibited  by 
ordinance  as  a  public  nuisance.  Smoke  can  be  avoided  by  using 
a  smokeless  fuel,  such  as  coke  or  anthracite  coal;  or,  when  the 
more  volatile  coals  are  used,  by  bringing  about  complete  com- 
bustion of  the  volatile  matter.  In  general,  the  greater  the  pro- 
portion of  the  volatile  content  of  the  coal  the  more  difficult  it  is 
to  avoid  smoke,  though  much  depends  on  the  character  of  the 
volatile  matter.  Coals  which  smoke  badly  may  give  from  3  to 
5  per  cent  lower  efficiencies  than  smokeless  varieties. 

For  each  kind  of  coal  and  each  furnace  there  is  usually  a  range 
in  the  rate  of  combustion  within  which  it  is  comparatively  easy 
to  avoid  smoke.  At  higher  rates,  owing  to  the  lack  of  furnace 
capacity,  it  becomes  increasingly  difficult  to  supply  the  air,  mix 
it  and  bring  about  complete  combustion.  Hence  when  there  is 
both  a  high  volatile  content  in  the  coal  and  a  rapid  rate  of  com- 
bustion it  is  doubly  difficult  to  obtain  complete  and  smokeless 
combustion. 

However,  although  smoke  is  an  indication  of  incomplete  and 
hence  inefficient  combustion,  it  may  sometimes  be  more  profitable, 
because  of  lower  price  or  for  other  reason,  to  use  a  coal  with 
which  it  is  difficult  to  avoid  smoke,  provided  the  latter  is  not  a 
nuisance  or  is  not  prohibited  by  statute. 

252.  Value  of  Coal  as  Furnace  Fuel,  (a)  The  principal 
factors  which  determine  the  commercial  value  of  coal  used  in 
furnaces  are:  (i)  price  per  ton,  (2)  calorific  value,  (3)  moisture, 
(4)  volatile  matter,  (5)  ash,  (6)  clinkering  tendency,  (7)  sulphur 
content,  (8)  skill  and  attention  required  in  firing,  (9)  suitability 
for  the  furnace  and  grate  in  which  it  is  to  be  used,  (10)  size  of 
coal  and  (11)  available  draft.  These  will  be  briefly  discussed 
in  this  section. 

(b)  As  exposure  to  weather  (sun  and  rain,  humidity,  etc.), 
during  transportation  and  storage,  may  affect  the  amount  of 


ACTUAL  COMBUSTION  OF  FUELS  509 

moisture  and  may  also  alter  the  chemical  composition  and  heat 
value  of  the  fuel,  especially  if  rich  in  volatile  matter,  the  various 
analyses  to  which  the  coal  may  be  subjected  should  be  made 
after  the  coal  is  received,  or  as  received,  if  it  is  desired  to  deter- 
mine its  value  to  the  consumer.  The  calorific  value  is  preferably 
determined  by  using  a  fuel  calorimeter  (see  Sect.  244)!  it  may, 
however,  be  approximated  by  any  of  the  methods  given  in  Sect. 
22 7 (a)  to  (d).  The  moisture,  fixed  carbon,  volatile  matter,  and 
ash  per  pound  of  material  may  be  found  by  making  a  proximate 
analysis  (Sect.  226(0)). 

(c)  If  payment  is  made  on  the  basis  of  weight  of  coal  "  as 
received,"  and  if  the  heat  value  is  stated  per  pound  of  "dry 
coal,"   part  of  the  expenditure  is  for  an  unknown  weight  of 
moisture  and  the  true  value  of  the  coal  is  unknown.     Evidently, 
from   the   consumer's    standpoint,    the    purchase   price   should 
depend  directly  on  the  calorific  value  per  pound  of  the  moist  coal 
as  received.     In  any  case  the  ultimate  test  of  the  commercial 
value  is  the  cost  per  B.t.u.  delivered,  or  the  number  of  B.t.u. 
received  for  a  unit  of  money  expended,  other  things  being  equal. 

(d)  The  moisture  in  the  coal  is  undesirable  as  it  not  only  (i) 
reduces  the  heat  value  per  pound  of  material  fired,  but  (2)  adds 
to  the  transportation  expense  per  B.t.u.  delivered,  and  this  in 
direct  proportion  to  its  weight,  and  (3)  decreases  the  furnace 
and  boiler  efficiency  since  it  becomes  superheated  steam,  thereby 
absorbing  heat  (latent  and  sensible),  which  is  carried  up  the 
chimney  with  the  flue  gases.     The  heat  thus  carried  away  per 
pound  of  moisture  is  the  same  as  that  per  pound  of  water  vapor 
formed  from  the  combustion  of  hydrogen  and  is  given  approxi- 
mately by  Eqs.  (364)  or  (365).     Roughly,,  the  loss  of  the  total 
heat  value  of  dry  fuel  is  about  TV  per  cent  for  each  per  cent  of 
moisture    present.     In    eastern    coals    the    moisture    normally 
ranges  from  I  to  5  per  cent,  and  in  western  coals  from  3  to  15 
per  cent. 

(e)  Coals  in  which  the  volatile  matter  is  proportionately  very 
high  usually  give  very  long  flames,  and  cannot  be  burned  com- 
pletely or  smokelessly  unless  used  with  furnaces  of  proper  type, 
size,  and  proportions  and  unless  special  means  are  provided  for 
regulating  the  air  supply  above  the  grate.     Even  with  the  most 
careful  management  it  is  usually  difficult,  and  in  some  cases 
impossible,  to  obtain  complete  combustion  with  such  coals  even 


HEAT-POWER  ENGINEERING 


n 

I85 

—•  ^ 

^-^ 

^>s 

X 

\ 

fift 

\ 

10        20         80        40         60         60 

jf  Volatile  Matter  .in  Dry  Cgmbuatible 


Fig.  322. 


though  an  extreme  amount  of  air  is  used;  hence,  the  calori- 
metric  test  is  not  a  true  measure  of  the  commercial  value  of  such 
fuels  in  furnaces.  Fig.  322  shows  in  a  very  general  way  how  the 

efficiency  of  combustion  varies  with 
the  percentage  of  volatile  matter  in 
the  dry  combustible.* 

Coals  moderately  rich  in  volatile 
matter,  such  as  semibituminous  and 
the  less  volatile  bituminous  coals, 
not  only  have  the  highest  calorific 
values  (as  shown  by  the  Mahler  curve 
in  Fig.  315),  but,  when  properly 
fired,  generally  produce  the  highest  efficiencies  of  any  of  the 
coals  used,  and  with  suitable  conditions  and  reasonable  atten- 
tion can  be  burned  smokelessly,  or  practically  so. 

(f)  The  ash  detracts  from  the  value  of  coal  in  a  number  of 
ways.  The  greater  its  percentage  the 
more  difficult  it  is  to  obtain  complete 
combustion  because  of  its  tendency  to 
pack  and  obstruct  the  passage  of  air; 
also  the  greater  may  be  the  proportion 
of  coal  lost  through  the  grates  with  the 
ash,  and  the  less  is  the  capacity  of  a 
given  furnace  because  of  the  reduction 
of  combustible  per  square  foot  of  grate 
area.  The  way  in  which  the  value  of 


!360 
^50 


11) 


10     15     20     25     30     35    40 
Per  Cent  Ash  iii  Dry  Coal; 


Fig.  323- 


the  fuel  decreases  as  the  percentage  of  ash  increases  is  shown  in 
Fig.  323,  which  in  a  general  way  applies  to  any  kind  or  grade  of 
coal.  When  the  ash  constitutes  40  per  cent  of  coal,  the  fuel  is 
practically  valueless  in  ordinary  furnaces. 

The  expense  of  generating  a  given  amount  of  heat  is  increased 
(i)  by  the  cost  of  transporting  the  inert  matter  in  the  coal,  (2) 
by  the  transportation  and  disposal  of  the  ash,  (3)  by  the  extra 
labor  involved  in  handling  the  larger  weight  of  material,  (4)  by 
the  unconsumed  coal  carried  through  the  grates  with  the  ash 
(which  may  be  from  10  per  cent  to  60  per  cent  of  the  latter),  and 
(5)  by  the  heat  absorbed  by  the  ash  (specific  heat  =  0.2  to  0.24) 
and  carried  with  it  to  the  ash  pit.  In  commercial  coals  the  ash 


*  "  Steaming  Tests  of  Coals,"  Bull.  23,  U.  S.  Bureau  of  Mines.     Page  233. 


ACTUAL  COMBUSTION  OF  FUELS 


1000 


Size.ofCoal(Inchej) 

Fig.  324. 


generally  ranges  from  4  per  cent  to  25  per  cent  of  the  total 
weight. 

The  smaller  the  size  of  coal  the  more  difficult  is  it  to  remove 
the  inert  portion,  hence  the  greater  is  the  proportion  of  ash 
present,  as  is  shown  by  curve  I  in  Fig.  324  for  one  particular 
kind  of  coal. 

(g)    If  the  ash  is  fusible  at  a  comparatively  low  temperature,  it 
will  form  clinkers  when  a  hot  fire  is  maintained,  as  when  the 
capacity  of  the  furnace  is  being  forced.     This  clinker,  of  course, 
detracts  from   the  value  of  the  coal. 
Steam,  or  water  vapor,  passed  through 
the  fire  with  the  air,  is  supposed  to 
decrease  the  tendency  to  clinker  be- 
cause of  absorption  of  heat  and  the 
consequent  lowering  of   the  tempera- 
ture of  the  ash.     For  this  reason  steam- 
blasts  are  sometimes   used  under  the 
grate  with  clinkering  coals  and  often 
water  is  kept  in  the  ash  pit  to  furnish 
vapor.     If  clinker  is  formed,  the  fused 
mass  must  be  frequently  broken  up  to 

permit  the  free  passage  of  air  through  the  fuel  bed  to  support 
the  combustion. 

(h)  Sulphur  in  coal  is  objectionable  not  only  because  of  its 
relatively  low  heat  value,  but  because  of  the  deleterious  effect  on 
the  boiler  materials,  and  because  it  is  thought  that  in  some 
instances  it  indicates  the  presence  of  clinker-forming  matter, 
although  clinker  also  occurs  when  it  is  absent.  The  sulphur 
should  not  exceed  3  J  per  cent. 

(i)  In  general,  in  using  the  same  coal  with  a  given  furnace  and 
draft,  the  efficiency  and  capacity  of  a  grate  will  vary  with  the 
size  of  the  coal,  as  is  shown  by  curves  2  and  3  in  Fig.  324,  for  one 
particular  kind  of  coal  tested  under  a  certain  boiler.*  The  best 
size  for  given  conditions  can  be  determined  from  experiment  or 
from  a  study  of  data  relating  to  similar  coals  burned  under  like 
circumstances.  If  for  some  reason  it  is  necessary  to  burn  a  given 
size  of  a  particular  coal,  there  is  usually  some  design  of  furnace 
and  some  set  conditions  which  will  give  best  results ;  these  can  be 

*  Abbott,  "  Characteristics  of  Coals,"  Jour.  Western  Soc.  of  Eng'rs.,  Oct.  16, 
1906,  p.  528. 


HEAT-POWER  ENGINEERING' 

determined  experimentally  if  no  information  on  the  subject  is 
already  available. 

In  general,  the  smaller  the  coal  the  harder  is  it  to  burn  com- 
pletely and  the  greater  is  the  percentage  of  unburned  coal  lost 
through  the  grates  with  the  ash.  In  consequence  there  is  less 
general  demand  for  the  smaller  sizes,  hence  they  cost  less  per  ton 
than  the  larger  grades  and  therefore  are  widely  used  in  boiler 
furnaces  even  though  their  heat  value  per  pound  is  low  because 
of  the  large  percentage  of  ash  present.  Very  fine  coal  and  dust 
are  difficult  to  burn  on  ordinary  grates  as  they  tend  to  pack  and 
check  the  flow  of  air  through  the  fuel  bed,  or  else,  with  strong 
draft,  are  carried  along  with  the  air  to  be  deposited  within  the 
boiler  setting  or  to  be  carried  up  the  stack  to  become  a  nuisance 
to  the  surrounding  neighborhood.  They  may,  however,  be 
burned  successfully  by  the  methods  which  will  be  given  in  Sect. 

253. 

(j)  Caking  of  the  coal,  if  excessive,  is  in  general  undesirable 
because  of  its  tendency  to  prevent  the  passage  of  air ;  but  where 
provision  is  made  to  break  up  the  bed,  continuously  or  inter- 
mittently, a  certain  amount  of  caking  may  be  advantageous. 

(k)  The  different  kinds  of  coal,  and  the  various  sizes,  do 
not  generally  burn  at  the  same  rates  under  equal  drafts.  With 
a  given  grate  and  draft,  it  is  of  course  necessary  to  use  a  coal 
which  will  develop  the  amount  of  heat  that  is  needed  for  the 
particular  purpose  for  which  the  furnace  is  used,  for  example, 
if  used  under  a  boiler,  it  must  be  possible  to  burn  enough  coal 
to  evaporate  the  maximum  amount  of  steam  required  of  the 
apparatus.  Hence  under  certain  conditions  the  possible  rate  of 
combustion  may  have  an  influence  in  the  selection  of  a  coal. 
Sometimes  when  there  is  uncertainty  as  to  the  kind  of  coal  which 
will  eventually  be  used,  —  the  grate  is  made  of  such  size  that  the 
heat  output  will  be  sufficient  even  though  the  slowest  burning 
coal  is  used,  —  then  it  will  be  ample  for  freer  burning  kinds  — 
and,  subsequently,  if  desirable,  portions  of  the  grate  can  be 
blocked  off  to  reduce  its  area  when  the  latter  are  used. 

Further,  there  is  some  rate  of  combustion  (pounds  of  coal 
burned  per  square  foot  of  grate  surface  per  hour)  which  will  give 
the  best  combined  boiler  and  furnace  efficiency  for  each  kind  and 
size  of  coal.  Fig.  325  shows  the  variation  in  the  case  of  one 
particular  kind  and  size.  In  general,  the  rate  and  heat  develop- 


ACTUAL  COMBUSTION  OF  FUELS 


513 


Lbs.of  Coal  per  Sq.Ft.  of  Grate  Area 

Fig.  325- 


ing  capacity  of  the  furnace  is  least  with  coals  low  in  volatile 
matter,  rich  in  ash,  and  small  in  size,  and  is,  of  course,  directly 
dependent  on  the  rate  of  air  supply,  that  is,  on  the  draft. 
The  best  rate  to  adopt  in  each  particular  instance  can  be  deter- 
mined experimentally,  or  from  a  study  of  similar  cases,  when 
data  are  available. 

(1)    As  the  volatile  matter  is  mostly  burned  beyond  the  fuel 
bed,  the  rate  at  which  coal  can  be  burned  on  a  given  grate  area  is 
largely  dependent  on  the  proportion  of  fixed  carbon  it  contains. 
The  best  economies  are  usually  ob- 
tained when  from  12   to   16   pounds 
of  fixed  carbon  are  burned  per  square 
foot  of  grate  surface  per  hour.     The 
ordinary  rates   of  combustion    (under 
normal  conditions)  are  about  as  fol- 
lows:    Anthracite,     from    15    to    20 
pounds;  Semi-bituminous,  from  18  to 
22  pounds;  and  Bituminous,  from  24 
to  32  pounds.     Dividing  the  estimated 

total  weight  of  coal  which  is  normally  to  be  burned  per  hour, 
by  the  proper  normal  rate,  as  here  given,  results  in  the  necessary 
grate  area  and  allows  for  an  overload  capacity  of  from  50  per 
cent  to  100  per  cent,  depending  on  the  intensity  of  draft  that  is 
available.  Evidently  with  anthracite  coal  there  must  be  a  larger 
grate  area  for  a  given  total  capacity  than  with  bituminous  coal. 

Greater  rates  of  combustion  are  possible;  for  example,  in 
torpedo  boats  under  forced  draft  (4!  inches  to  6  inches  of  water) 
the  rate  is  from  55  to  65  pounds  per  square  foot;  and  from  80 
to  1 20  pounds,  and  even  more,  have  been  burned  (with  air 
pressure  of  from  4 inches  to  8  inches  of  water).  Rates  as  high  as 
90  pounds  per  square  foot  per  hour  are  commonly  used  in  loco- 
motive practice  where  exhaust  steam  nozzles  are  employed  for 
inducing  strong  drafts. 

(m)  The  maximum  capacity  obtainable  with  a  given  furnace 
and  with  a  certain  intensity  of  draft  available  varies  not  only 
with  the  kind  of  coal  but  also  with  the  size.  Curve  3,  in  Fig. 
324,  shows  how  it  varied  with  the  size  of  one  kind  of  coal  tested 
under  a  certain  boiler.  It  is  to  be  noted  that  the  maximum 
efficiency  is  not  necessarily  obtained  with  the  size  that  gives  the 
greatest  capacity. 


5!4  HEAT-POWER  ENGINEERING" 

The  capacity  per  square  foot  of  grate  area  with  anthracite  coal 
is  limited  largely  by  the  fact  that  if  this  fuel  is  burned  rapidly, 
it  has  a  tendency  to  break  up  into  small  pieces  which  pack  and 
clog  the  passage  of  air  through  the  fuel  bed.  This  action  also 
increases  the  amount  of  unconsumed  coal  lost  through  the  grates 
with  the  ash  and  this  lowers  the  efficiency. 

253.  Burning  Powdered  Coal,  (a)  Powdered  coal  can  be 
burned  in  much  the  same  way  as  a  liquid  fuel  (see  Sect.  (258))  if 
it  is  finely  pulverized  and  properly  injected  into  a  furnace. 
When  used  in  this  way  it  has  many  of  the  advantages  incident 
to  the  use  of  liquid  fuel. 

However,  the  cost  of  crushing  and  the  difficulty  of  uniform 
feeding,  combined  with  the  complicated  apparatus  necessary, 
have  thus  far  prevented  any  wide  use  of  powdered  coal  as  a 
boiler  fuel  although  it  has  been  very  successfully  and  widely 
used  for  firing  cement  kilns  in  regions  in  which  the  price  of  oil 
is  high. 

(b)  Coal  too  fine  to  use  on  ordinary  grates  may  be  briquetted 
by  using  a  suitable  binder,  as  has  already  been  mentioned,  and 
can  then  be  used  conveniently  and  efficiently  on  ordinary  grates. 

(c)  Where  special  dumping  grates  are  used  with  air  supplied 
from  below,  under  pressure  that  can  be  readily  regulated,  very 
small  anthracite  coal  has  been  successfully  burned  in  the  following 
manner:    The  fuel  bed  is  not  disturbed  for  cleaning  for  several 
hours,  the  ash  being  allowed  to  accumulate ;   the  intensity  of  air 
pressure  in  the  ash  pit  is  increased  as  the  fuel  bed  becomes 
thicker,  but  is  always  such  that  it  becomes  atmospheric  at  the 
surface  of  the  bed;    the  products  of  combustion  are  carried  off 
by  draft  induced  by  a  stack  or  other  device  above  the  fuel  bed ; 
and  the  fuel  is  distributed  as  evenly  as  possible  in  firing.     Owing 
to  the  fineness  of  the  coal,  there  is  a  strong  tendency  for  it  to 
burn  out  in  spots,  to  prevent  which  the  surface  of  the  fuel  bed 
must  be  smoothed  very  frequently  by  using  a  distributing  bar 
with  a  T-head.     As  the  pressure  just  above  the  fuel  bed  is 
atmospheric  there  is  no  objection  to  the  frequent  opening  of  the 
doors  which  is  necessary  for  thus  working  the  fire.      Culm  and 
other  low  grade  coal,  which  is  ordinarily  considered  to  be  waste 
material,  may  in  some  instances  be  burned  with  satisfactory 
results  by  this  method. 


ACTUAL  COMBUSTION  OF  FUELS 


515 


254.  Selection  and  Purchase  of  Coal,  (a)  The  price  per  ton 
of  the  coal  delivered  is  the  sum  of  the  cost  at  the  mines  and  the 
transportation  charges;  hence  the  distance  from  the  mines  may 
have  an  important  bearing  on  the  cost  to  the  consumer.  The 
cost  at  the  mine  depends  on  the  difficulty  in  mining  —  hence 
for  hard  anthracite  it  is  greater  than  for  the  softer  bituminous 
coals.  Also  the  price  is,  of  course,  dependent  on  the  supply  and 
demand.  Thus  the  smaller  sizes,  being  in  the  least  general 
demand,  are  the  cheapest  per  ton  at  the  mine.  Grades  that  are 
generally  considered  worthless  cost  least,  hence  much  attention 
is  being  devoted  to  devising  methods  tor  utilizing  these  grades. 

(b)  In  selecting  coal  for  boilers  the  problem  is  to  find  that 
kind  and  size  which  will  give  the  greatest  number  of  useful  heat 
units,  or  which  will  evaporate  the  largest  weight  of  water,  per 
dollar  expended  for  the  fuel  and  its  firing.     In  default  of  avail- 
able information  on  the  subject,  a  series  of  tests  under  varying 
conditions  may  be  conducted  to  determine  the  coal  best  suited 
to  a  given  furnace  and  to  find  the  size  of  that  coal,  thickness  of 
fire,  strength  of  draft,  method  of  firing,  etc.,  which  will  give  the 
best  results  under  the  prevailing  conditions.     But  such  tests 
may  be  as  much  a  determination  of  the  skill  of  the  fireman  as  of 
the  quality  of  the  coal,  and,  therefore,  may  not  give  the  true  value 
that  the  coal  would  have  when  properly  used.     Although  many 
such  tests  have  been  made,  the  published  data  of  this  kind  at 
present  available  are  rather  meager. 

(c)  The  principal  sources  of  data  are  reports  of  the  U.  S. 
Bureau  of  Mines,  of  State  Geological  Surveys,  Engineering  Ex- 
periment Stations,  engineering  "pocket  books,"  special  treatises 
on   fuels,   combustion,   and   boilers,    catalogs   of   boiler   manu- 
facturers, etc.     Nearly  all  of  these  reference  books  give  tables 
of  the  chemical  and  proximate  analyses  of  the  fuels  from  the 
more  important  coal  fields  and  while  the  coals  from  a  given  field, 
and  even  from  the  same  mine,  vary  considerably  in  character, 
such  data  may  be  used  in  default  of  tests  of  samples  of  the  coal 
actually  under  consideration. 

(d)  Some  large  consumers  have  adopted  the  following  plan 
for  the  selection  and  purchase  of  coal:    By  actual  test  in  their 
furnaces  they  determine  what  kind  is  cheapest  and  most  desir- 
able to  use  under  the  prevailing  conditions  and  thus  a  standard 
specification  as  to  heat  value,  size,  ash,  volatile  matter,  mois- 


516  HEAT-POWER  ENGINEERING' 

ture,  sulphur,  etc.,  is  drawn  up.  Then  a  "standard  price"  for 
such  coal  is  agreed  upon  with  the  dealer,  with  adjustments 
by  premiums  and  penalties  for  variations  from  the  specification. 
The  adjustment  is  directly,  or  almost  directly,  according  to  the 
variation  in  the  heat  value  per  pound  of  the  moist  coal  (or  coal 
"as  received"),  and  is  dependent  on,  but  not  directly  propor- 
tional to,  the  variation  in  the  percentage  of  ash,  volatile  matter, 
and  sulphur  from  the  standard. 

For  example,  the  Interborough  Rapid  Transit  Company  (New 
York  City)  accepts  a  run  of  mine  bituminous  coal  without 
penalty  or  premium  if  it  contains  20  per  cent  or  less  of  volatile 
matter,  9  per  cent  or  less  of  ash,  and  ij  per  cent  or  less  of  sulphur. 
The  standard  heat  value  per  pound  is  14,250  B.t.u.  with  penalty 
and  premium  averaging  about  one  cent  per  ton  per  50  B.t.u. 
variation  from  standard.  Penalties  per  ton  range  up  to  18 
cents  for  4  per  cent  excess  in  volatile  matter,  and  to  23  cents 
for  4i  per  cent  additional  ash,  and  to  12  cents  for  I  per  cent 
excess  sulphur.* 

Some  concerns  specify  as  standard  a  run  of  mine,  semibitumi- 
nous  coal  with  I  per  cent  moisture,  20  per  cent  volatile  carbon, 
7  per  cent  ash,  and  not  over  I  per  cent  of  sulphur.  If  x  is  the 
per  cent  of  variation  from  standard,  the  adjustment  in  the  price 
is  inversely  proportional  to  x  for  moisture,  to  2  x  for  volatile 
carbon,  and  to  3  x  for  ash. 

The  government  awards  contracts  on  competitive  bids  which 
are  accompanied  by  specifications  of  the  kind  and  composition 
of  the  coal  (ash,  B.t.u.,  and  size),  which  the  bidders  propose  to 
furnish.  The  analyses  are  made  on  the  coal  "as  received," 
which  takes  care  of  the  effect  of  moisture.  The  coal  is  rejected 
if  it  clinkers  or  produces  smoke  excessively  and  if  it  exceeds 
certain  limits  in  the  amount  of  ash,  volatile  matter,  sulphur, 
fine  coal,  and  dust.  A  small  variation  from  the  specified  stand- 
ard is  tolerated  without  penalty  or  premium;  but  if  there  is 
much  difference,  the  price  is  varied  directly  with  the  heat  value 
of  the  coal  "as  received"  (including  moisture)  and  is  adjusted 
according  to  a  sliding  scale  for  variations  in  ash  and  sulphur. f 

*  Am.  El.  Ry.  Eng'g.  Assoc.,  Report,  1911. 

t  U.  S.  Bureau  of  Mines,  Bulletin  n,  "Purchase  of  Coal,  etc.;"  Bull.  41, 
"  Results  of  Purchasing  Coal  under  Government  Specifications;"  and  Technical 
Paper,  No.  15,  "  Sampling  Coal,  with  Specifications." 


ACTUAL  COMBUSTION  OF  FUELS  517 

255.  Furnace  Operation,  (a)  The  efficiency  and  capacity 
obtained  with  a  given  coal  and  furnace  depend  much  on  the 
knowledge,  skill,  and  attention  of  the  furnace  attendant  and 
especially  is  this  the  case  if  the  furnace  is  hand  fired. 

(b)  In  addition  to  the  considerations  already  discussed  it  is 
important  with  many  kinds  of  coal  to  have  the  right  combination 
of  thickness  of  fuel  bed  and  draft.     For,  in  general,  with  each 
quality  and  size  of  fuel,  and  with  each  method  of  firing  and  rate 
of  combustion,  there  is  some  combination  of  thickness  and  draft 
which  will   give   best  results  —  although   there  is  considerable 
latitude  with  some  coals.     Thin  beds  tend  to  let  an  excessive 
amount  of  air  pass  through  and  require  frequent  and  careful 
firing  and  close  regulation  of  draft.     Very  thick  beds  require  less 
attention  and  give  quicker  response  to  sudden  increase  in  de- 
mand, but  necessitate  stronger  drafts  and  are  conducive  to  the 
formation  of  CO.     With  a  given  draft  and  coal  the  maximum  rate 
of  combustion  is  largely  dependent  on  the  thickness  of  bed.     In 
general,  the  coarser  the  coal  and  the  stronger  the  draft,  the 
thicker  should  be  the  bed.     But  here,  again,  it  seems  impossible 
to  give  any  rule  that  would  be  at  all  general  in  application;  for 
with  anthracite  coal,  the  thicknesses  used  vary  from  4  inches  to 
12  inches  and,  with  bituminous,  from  6  inches  to   16  inches, 
depending  on  the  quality  and  size  of  coal,  the  draft,  method  of 
firing,   etc.     Hence   the   best  combination   must  ordinarily   be 
found  by  experience  in  each  instance. 

(c)  With  anthracite  coal  not  only  must  the  bed  be  kept  uni- 
form but  it  must  be  disturbed  as  little  as  possible  in  cleaning 
the  fire.     Hence  shaking  grates,  which  cut  off  the  lower  part  of 
the  bed  with  minimum  disturbance  of  the  upper  part,  can  be 
used  to  special  advantage  with  this  coal. 

(d)  The  intensity  of  draft  pressure  needed  is  directly  dependent 
on  the  resistance  offered  to  the  passage  of  air  through  the  fuel 
bed.    Its  pressure  is  usually  stated  in  terms  of  "inches  of  water." 
For  the  usual  kinds  and  sizes  of  coal  and  for  ordinary  conditions 
the  drops  in  air  pressure  through  the  fuel  bed  are  shown  by  the 
ordinates  of  the  curves  in  Fig.  326,*  in  which  the  abscissas  are 
rates  of  combustion  expressed  as  pounds  burned  per  square  foot 
of  grate  surface  per  hour. 

*  Modified  from  curves  given  in  "Stirling,"  published  by  the  Stirling  Co.  (1905). 


HEAT-POWER  ENGINEERING    ' 


(e)  In  an  up-draft  furnace,  fired  from  above,  the  air  ordinarily 
enters  through  the  ash  doors  below  the  grates,  the  draft  being 
induced  by  the  stack,  which  in  some  instances  is  assisted  by 
steam  blowers,  or  by  fans.  The  amount  of  air  and  the  rapidity 
of  combustion  can  be  regulated  by  adjusting  the  dampers  in  the 
flues  leading  to  the  stack,  by  regulating  blowers  or  fans,  and  by 
varying  the  openings  in  the  ash  doors.  If  coal  is  fired  inter- 
mittently, as  in  hand  firing,  the  layer  of  fresh  coal  temporarily 


10          15         20          25          30          35          40          45         50 
p  Pounds  of  Coal  per  Sq.Ft.  of  Grate  Surface  per  Hour 

Fig.  326. 

chokes  the  air  supply  received  through  the  bed  and  this  occurs 
at  the  time  when  the  most  rapid  distillation  of  volatile  matter 
is  in  progress.  Hence,  immediately  after  firing  a  fresh  quantity 
of  coal,  particularly  if  it  is  rich  in  volatile  matter,  an  adequate 
supply  of  air  should  be  introduced  above  the  fuel  bed  and  this 
amount  should  be  diminished  gradually  as  the  rate  of  distillation 
decreases.  This  air  may  be  furnished  through  the  fire  doors, 
which  may  be  gradually  closed  by  hand  or  by  some  automatic 
device  so  arranged  that  the  rapidity  of  its  action  can  be  adjusted 
to  suit  the  fuel,  or  it  may  enter  through  inlets  in  the  boiler  front 
or  in  furnace  walls,  or  through  passages  in  the  bridge  wall  at 
the  back  of  the  grate. 

In  hand  firing  there  is  also  a  loss  due  to  the  relatively  long 
period  of  time  during  which  the  doors  are  open  while  firing, 


ACTUAL  COMBUSTION  OF  FUELS  519 

which  permits  large  quantities  of  cold  air  to  enter  and  pass  over 
the  boiler  heating  surfaces.  As  the  conditions  in  the  furnace 
vary  widely  and  quite  rapidly  with  the  method  of  firing,  the  best 
results  can  only  be  obtained  by  close  attention  on  the  part  of  the 
attendants  and  especially  is  this  the  case  when  the  fire  is  being 
forced  —  a  time  when  it  is  the  most  difficult  to  give  such  at- 
tention. 

(f)  The  way  the   coal  is  distributed  on  the  fuel  bed  is  of 
importance.     In  general,  there  are  three  methods  of  hand  firing 
commonly  used : 

(1)  In  one,  called  spread  firing,  the  fresh  coal  is  each  time 
spread  evenly  over  the  entire  surface  of  the  bed.     This  is  the 
method  commonly  adopted  with  anthracite  coal. 

(2)  In  the  second,  known  as  alternate  firing,  fresh  coal  is 
placed  on  but  one-half  of  the  grate  at  a  time,  which  permits 
excess  air  to  pass  through  the  other,  thinner  and  brighter  half 
for  the  combustion  of  freshly  evolved  volatile  matter.     Spot,  or 
checker,  firing  is  similar ;  alternate  spots  on  an  imaginary  checker- 
board are  fired  simultaneously,  and,  as  before,  the  volatile  matter 
from  the  fresh  coal  is  supplied  with  heated  air  by  the  excess 
amount  that  passes  through  the  remaining  portions  of  the  bed. 
In  these  methods  of  firing,  the  coal  is  placed  each  time  on  the 
brighter  portions  of  the  fuel  bed. 

(3)  In  coking  firing,  which  is  used  only  with  caking  coals,  the 
fuel  is  placed  on  the  front  edge  of  the  fuel  bed  and  allowed  to 
coke,  the  volatile  matter  passing  back  over  the  bed  and  mixing 
with  the  hot  air  passing  through  this  portion.     After  distillation 
is  complete  the  coke  is  pushed  back  and  distributed  over  the  bed. 
This  method,  while  effective,  does  not  permit  of  high  rates  of 
combustion. 

(g)  Evidently  the  best  results  can  be  obtained  only  when  the 
conditions  are   maintained  uniform,   that  is,  when  the  coal  is 
fired  continuously  and  uniformly  and  there  is  no  variation  in 
the  air  supply.     Thus,  with  hand  or  intermittent  firing,  the  coal 
should  be  fired  frequently,  in  small  amounts,  and  it  should  be 
distributed  with  skill,  while,  in  addition,  the  draft  should  be 
carefully  adjusted.     However,  such  close  attention  is  opposite 
to  the  natural  tendencies  of  furnace  attendants,  and  even  with 
it,  it  is  impossible  with  some  coals  to  obtain  complete  and  smoke- 
less combustion  with  hand  firing. 


520 


HEAT-POWER  ENGINEERING 


(h)  By  the  use  of  automatic  mechanical  stokers,  however,  the 
coal-feeding  operation  is  made  continuous  and  the  conditions  are 
kept  uniform.  They  involve  but  little  labor  or  attention  and 
with  them  it  is  possible  to  obtain  practically  smokeless  combus- 
tion with  nearly  all  kinds  of  coal  provided  that  (i)  the  grates  and 
the  furnace  setting  are  properly  proportioned  to  suit  the  fuel, 

(2)  proper  attention  is  given  to  the  firing  and  air  supply,  and 

(3)  a  suitable  rate  of  combustion  is  used  per  square  foot  of  grate 
surface.     Mechanical  stokers  will  be  described  in  Sect.  257. 

256.  Grates  and  Furnaces,  (a)  The  number  of  square  feet 
of  grate  surface  may  be  determined  in  the  manner  described  in 
Sect.  252  (1).  The  width  of  grate  is  commonly  made  equal  to  the 
distance  between  the  walls  of  the  boiler  setting,  and  the  length 
of  grate  is  ordinarily  found  by  dividing  the  desired  area  by  this 
width.  With  hand  firing,  grate  lengths  up  to  10  feet  have  been 
used  with  dumping  grates,  while  with  ordinary  grates  the  limit 
of  length  is  usually  6  feet  because  of  difficulty  in  cleaning  the  fire. 


Fig.  327. 

(b)  To  prevent  the  grate  bars  from  burning  away  they  should 
be  of  suitable  material  (white  C.  I.  is  generally  used),  and  should 
be  of  such  shape  as  to  present  relatively  small  surface  to  the  fuel 
bed  and  expose  large  radiating  surface  to  the  current  of  air. 
They  must  be  in  short  lengths  (not  over  3  feet  ordinarily),  set 
so  as  to  allow  for  expansion  and  contraction  and  also  for  warping. 
They  must  provide  sufficient  passage  for  air,  and  must  permit 
the  ash,  but  not  the  coal  to  pass  through.     In  addition  they  must 
be  readily  cleaned  of  clinker. 

(c)  Of  the  great  many  kinds  of  grate  bars  in  use  four  of  the 
most  common  forms  are  shown  in  Fig.  327.     In  this  figure,  (c) 


ACTUAL  COMBUSTION  OF  FUELS 


521 


is  for  sawdust  and  the  rest  are  for  coal.  For  fine  coal  flat  plates 
like  (d)  with  small  perforations  are  sometimes  used;  and  these 
may  have  the  exposed  surface  recessed  so  as  to  become  filled  with 
a  permanent  layer  of  fine 
ashes,  in  order  to  protect  the 
bar  from  the  heat  and  also 
to  prevent  the  adherence  of 
clinker  to  the  metal. 

(d)    Fig.    328    shows    one 
form  of  shaking  grate,  of  which 

there  are  a  great  many  dif-  Fig  328 

ferent    kinds    in  .use.     With 

such  grates  the  fire  is  not  only  more  easily  cleaned,  but  the  fire 
doors  do  not  have  to  be  opened  during  the  operation;  and  the 
bed  is  disturbed  but  little,  which  is  especially  valuable  when 
anthracite  and  noncaking  coals  are  burned.  Some  are  provided 
with  means  for  breaking  the  clinker,  or  the  caked  coal  bed,  and 
others  for  dumping.  Their  cost  is,  of  course,  greater  than  for 
ordinary  grates  but  they  often  give  from  I  per  cent  to  5  per 
cent  better  efficiency  than  flat  grates. 


Fig.  329. 

(e)  Fig.  329  shows  a  typical  furnace  with  fittings.  The 
arrangement  shown  in  Fig.  330  is  the  roofless  furnace  suitable  for 
coals  low  in  volatile  matter,  say  with  less  than  20  per  cent. 
Fig.  331  shows  the  tile  roof  arrangement  in  which  the  flame  is 
protected  by  a  roof  of  refractory  material  supported  by  the 


522 


HEAT-POWER  ENGINEERING 


lowest  row  of  boiler  tubes.  This  arrangement  is  suitable  for 
long  flame  coals,  for  ordinarily  there  is  little  difficulty  in  making 
the  roof  at  least  as  long  as  the  flame. 

(f)    Fig.  332  shows  a  Dutch  oven  which  can  be  built  in  front  of 
any  type  of  boiler.     It  offers  an  incandescent  roof  and  walls  to 


Fig.  330. 


Fig.  331- 


reflect  the  heat  and  makes  possible  the  complete  combustion  of 
volatile  matter,  but  it  adds  to  the  radiation  losses  because  of  the 
increased  surface  exposed.  When  possible  it  should  be  confined 
within  the  regular  boiler  setting,  so  as  to  reduce  this  external 
surface.  In  the  Dutch  oven  the  roof  and  walls  are  sometimes 
made  double  with  passages  between  for  the  circulation  of  air 

which  is  supplied  to  the  furnace. 
This  arrangement  serves  the 
double  purpose  of  furnishing  hot- 
ter air  and  of  reducing  the  radia- 
tion loss  by  lowering  the  temper- 
ature of  the  outer  walls. 

(g)    In  all  these  figures  of  fur- 
naces the  distance  A  should  at 

least  equal  the  flame  length,  and  the  external  radiating  surface  of 
the  setting  should  be  made  as  small  as  is  expedient.  The  fur- 
naces and  passages  for  the  hot  gases  must  be  lined  with  fire  brick, 
using  only  the  best  grades  in  furnaces  in  which  the  firing  is 
forced.  Baffle  arches,  piers,  wing  walls,  etc.,  are  sometimes 
introduced  in  the  passageway  of  the  gases  to  mix  them  and 
perfect  the  combustion. 

(h)  Fig.  333  shows  a  down-draft  furnace.  In  this  form  of 
furnace  the  upper  grate  bars  are  cooled,  and  are  rather  widely 
spaced.  The  coal  is  fired  on  the  upper  grate  and  the  volatile 
matter  is  carried  downward  by  the  draft  so  as  to  pass  over  the 
hot,  partly  burned  coals  which  have  fallen  to  the  lower  grate. 


Fig.  332. 


ACTUAL  COMBUSTION  OF  FUELS  523 

(i)  The  efficiency  of  a  grate  is,  of  course,  lowered  by  the  loss 
of  unburned  coal  with  the  ashes,  while  that  of  the  furnace  is  de- 
pendent on  the  completeness  of  combustion  and  on  the  radiation 
from  the  external  walls.  As  these  efficiencies  have  an  intimate 
bearing  on  the  performance  of 
the  boiler,  they  will  be  con- 
sidered in  connection  with  the 
general  discussion  of  boiler  ef- 
ficiencies in  Sect.  259. 

257.  Automatic  Mechanical 
Stokers,  (a)  The  principal  ad-  Fi 

vantages  derived  from  the  use 

of  mechanical  stokers  are:  (i)  Continuous  firing  and  uniform 
conditions;  (2)  progressive  distillation  of  volatile  matter  and 
proper  provision  for  burning  it;  (3)  a  saving  of  from  30  to  40 
per  cent  labor  cost  in  large  plants  (in  small  plants  there  may  be 
no  saving  because  a  certain  number  of  firemen  are  always  neces- 
sary and  the  introduction  of  stokers  may  not  reduce  the  number) ; 
(4)  relief  of  men  from  strenuous  duties  and  from  exposure  to 
heat;  (5)  greater  ease  in  obtaining  good  economy;  (6)  the  elimi- 
nation to  a  large  extent  of  the  personal  element  in  firing;  (7)  the 
greater  possibility  of  smoke  prevention  with  the  poorer  grades 
of  coal;  and  (8)  greater  rates  of  combustion  than  are  possible 
without  smoke. 

(b)  The  main  disadvantages  (which  may,  or  may  not,  be  pres- 
ent in  any  given  make  of  stoker)  are:  (i)  Greater  first  cost  (and 
interest  on  same);    (2)  possible  lack  of  durability  and  greater 
cost  of  repairs;    (3)  cost  of  power  to  operate;  (4)  greater  compli- 
cation ;  (5)  inability  to  meet  sudden  changes  in  load ;  (6)  failure 
to  distribute  coal  evenly;  (7)  loss  of  unburned  coal  with  ashes; 
and  (8)  loss  due  to  use  of  steam  in  the  air-blast.     What  was 
said  about  the  design  and  arrangement  of  grate  bars  and  furnaces 
in  general  in  the  preceding  sections  also  applies  to  automatic 
stokers. 

(c)  At  the  lower  rates  of  combustion  it  is  possible  to  obtain 
about  as  good  results  with  hand  firing  as  with  automatic  stokers, 
but  this  involves  the  employment  of  painstaking  men  of  great 
skill   who   command   higher   wages   than   the   ordinary.     With 
automatic  stokers  and  furnaces  designed  to  suit  the  coal  and 


524  HEAT-POWER  ENGINEERING' 

draft,  the  best  results  are  obtainable  with  very  little  effort  or 
skill  on  the  part  of  the  attendants.  Most  plants  using  auto- 
matic stokers  are  also  equipped  with  automatic  coal  conveying 
machinery  and  means  for  delivering  the  coal  by  gravity  to  the 
hoppers  of  the  stokers,  and  in  such  cases  the  labor  is,  of  course, 
rsduced  to  a  minimum.  •*?,;••• 

(d)  No  one  type  of  mechanical  stoker  is  equally  valuable  for 
all  kinds  of  coal,  but  practically  any  kind  of  coal  can  be  burned 
efficiently  and  smokelessly  with  a  suitable  stoker,  provided  the 
rate  of  combustion  does  not  exceed  a  certain  value  which  is 
dependent  on  the  kind  of  coal.* 

(e)  In  hand  firing  one  man  can  effectively  attend  to  from  200 
to  500  boiler  horsepower,  and  at  the  same  time  wheel  the  coal 
and  ashes,  and  regulate  the  feed  water  pumps,  draft,  etc.     In 
such  case  from  1000  to  2500  pounds  of  coal  are  handled  per  hour. 

When  merely  firing,  with  coal  delivered  by  others,  one  man  can 
hand  fire  about  1000  boiler  horsepower,  i.e.,  handle  from  4000 
"o  5000  pounds  of  coal  per  hour. 

With  automatic  stokers  provided  with  coal  fed  by  gravity 
from  overhead  bunkers,  one  attendant 
can  ordinarily  care  for  from  2000  to 
4000  boiler  horsepower,  using  from 
8000  to  20,000  pounds  of  coal  per  hour, 
(f)  Mechanical  stokers  may  in  gen- 
eral be  classified  as : 

(a)  Over  feed  (including  (i)  front 
feed,  (2)  side  feed,  and  (3)  chain  grate) 
and  (b)  underfeed. 

These  will  now  be  discussed  in  a  very 
general  way. 

(g)  In  most  over-feed  stokers  (see  Fig.  334)  the  coal  is  deposited 
in  a  hopper  from  which  it  is  automatically  and  continuously  fed 
to  the  grate  and  made  to  pass  under  a  more  or  less  extensive 
coking  arch,  which  is  maintained  at  a  high  temperature  and  serves 
the  same  purpose  as  the  roof  of  the  Dutch  oven.  Air,  heated  or 
otherwise,  is  usually  admitted  with  the  coal  under  the  coking 
arch.  The  grate  bars  are  moved  in  such  manner  as  to  carry  the 
bed  of  coal  constantly  in  one  direction  and  as  it  progresses  it 

*  Bull.  40,  U.  S.  Bureau  of  Mines,  "  Smokeless  Combustion,"  an  investigation 
.1  several  hundred  plants. 


ACTUAL  COMBUSTION  OF  FUELS  525 

gradually  burns  out.  As  the  coal  approaches  the  hotter  portion 
of  the  fuel  bed  a  progressive  distillation  of  the  volatile  matter 
occurs.  The  resulting  gas  mixes  with  the  air  above  and  the 
mixture  then  passes  under  the  coking  arch  which,  being  heated 
to  incandescence,  reflects  the  heat  from  the  bright  portions  of 
the  bed  and  deflects  the  gas  so  as  to  make  it  pass  over  the  rest 
of  the  bed.  Thus  the  conditions  are  excellent  for  the  complete 
combustion  of  the  volatile  content. 

The  rate  at  which  coal  is  fed  from  the  hopper  to  the  grates  and 
at  which  it  is  carried  along  the  latter  can  be  varied  and  should  be 
so  adjusted  that  combustion  of  the  coal  is  just  completed  when 
the  end  of  the  grate  is  reached.  If  completed  before  this  point 
cold  air  will  force  its  way  through  the  thin  bed  of  ashes  at  the  end 
and  reduce  the  efficiency;  and  if  not  completed  unburned  coal 
will  be  lost  with  the  ashes. 

The  stokers  may  be  driven  in  various  ways,  such  as  by  small 
steam  engines,  by  electric  motors,  or  by  belting  from  conveniently 
located  line  shafting. 

(h)  Fig.  335  shows  diagrammatically  a  typical  arrangement 
of  a  front-feed  stoker  with  inclined  grate.  It  has  a  hopper,  coal- 
pusher  feeding-device,  dead  plate,  coking  arch,  and  air  inlet 
under  the  latter.  The  grate  bars  are  stepped  and  inclined,  and 
they  are  mechanically  oscillated,  or  reciprocated,  in  such  way 
as  to  cause  the  bed  of  coal  to  gradually  descend.  The  rapidity 
and  amplitude  of  motion  of  the  pushers  and  grates  can  be  so 
regulated  that  the  coal  is  just  burned  out  by  the  time  it  reaches 
the  bottom  of  the  grate.  The  ashes  and  clinker  become  de- 
posited on  the  ash  table,  which  is  dumped  by  hand  from  time  to 
time.  When  the  ash  table  is  tilted  a  guard  is  brought  into 
position  (as  is  shown  at  (a)  in  the  figure)  to  keep  the  fuel  bed 
from  sliding  down  and  being  dumped  at  the  same  time.  In  the 
figure,  the  upper  reciprocating  grate  bars  are  hollow  and  the  air, 
which  is  injected  into  their  interiors  by  steam  jets  S,  issues 
through  openings  in  the  risers  of  the  steps.  The  lower  grates 
rock  or.  oscillate  about  the  trunnions  shown  in  (b)  and  have 
replaceable  bars.  There  are,  of  course,  many  other  designs  and 
arrangements  of  front-feed  stokers. 

(i)  The  typical  arrangement  of  side-feed  stokers  is  shown 
diagrammatically  in  Fig.  336.  Coal  is  fed  into  the  magazine 
from  above  or  through  doors  (a)  in  the  front  and  is  pushed,  by 


HEAT-POWER  ENGINEERING  ' 


Adjustment 


Trunnion 


Fig.  336. 


ACTUAL  COMBUSTION  OF  FUELS 


527 


some  suitable  mechanism,  to  the  coking  plate  at  the  top  of  the 
inclined  grates.  The  whole  bed  of  fuel  is  covered  by  a  fire-brick 
arch,  and  air,  which  is  heated  by  passing  over  the  arch,  is  dis- 
charged into  the  furnace  just  above  the  entering  coal.  The  coal 
gradually  descends  on  the  inclined  grate  bars,  the  alternate  ones 
of  which  are  constantly  moving.  The  ash  and  clinkers  are 
crushed  by  rotating  (or  reciprocating)  grinders  located  at  the 
bottom  of  the  grates.  Some  grinders  are  made  hollow  and  are 
connected  to  the  draft  in  such  way  as  to  cause  cold  air  to  pass 
through  them  to  prevent  overheating.  When  clinkering  coal 
is  used,  steam  (from  the  stoker  engine,  if  there  is  one)  is  dis- 
charged through  the  bed  of  ashes  to  reduce  the  amount  of  clinker 
and  to  make  crushing  easier. 


Coal 


Fig.  337- 


The  advantageous  features  of  this  type  of  stoker  are  the  large 
coking  spaces,  the  ample  coking  arch,  and  the  voluminous  com- 
bustion chamber.  These  stokers  operate  successfully  with  both 
uniform  and  variable  loads  and  under  a  great  variety  of  condi- 
tions. With  some,  when  certain  types  of  coal  are  used,  there  is 
difficulty  in  getting  rid  of  the  ash  and  clinker.  The  types  differ 
principally  in  the  manner  of  feeding  the  coal  and  getting  rid  of 
the  residue. 

(j)  The  typical  arrangement  of  chain-grate  stokers  is  shown  in 
337-  This  has  the  hopper,  the  coking  arch  with  air  ducts 


5*8 


HEAT-POWER  ENGINEERING  ' 


and  the  feeding  device  common  with  the  other  forms  of  over-feed 
stokers  already  described.  The  grates  consist  of  a  series  of 
endless  chains  carried  on  sprocket  wheels  which  slowly  rotate 
and  thus  carry  the  coal  toward  the  back  of  the  grate.  The  whole 
mechanism  is  usually  mounted  on  wheels  on  a  track  and  can  be 
pulled  forward  for  inspection  or  repairs.  These  stokers  are 
particularly  adapted  to  the  smaller  and  poorer  grades  of  non- 
caking  coals.  To  operate  satisfactorily  the  thickness  of  fire, 
the  draft,  and  the  speed  of  the  grate  must  be  adjusted  to  suit  the 
load.  Combustion  should  be  complete  when  the  coal  has  just 
reached  the  back  of  the  grate. 

(k)    In  the  under-feed  stokers,  a  typical  arrangement  of  which 
is  shown  in  Fig.  338,  the  coal  is  fed  forward  from  the  hopper,  by  a 


Fig.  338. 

reciprocating  pusher,  as  shown  (or  by  a  screw  conveyer  or  other 
suitable  feeding  device),  into  a  retort,  around  the  upper  edges  of 
which  are  replaceable  tuyere  blocks,  through  which  air  is  supplied 
under  pressure.  The  combustion  takes  place  at  the  top  of  the  bed 
towards  which  the  fresh  coal  is  fed  from  below.  The  ashes  and 
clinkers  fall  to  the  sides  of  the  retort  on  dead  plates  from  which 
they  can  be  readily  removed  through  doors  in  the  furnace  front. 
The  volatile  matter  is  liberated  as  the  coal  becomes  heated  and 
this  must  pass  through  the  intensely  hot  coals  above,  where  it  is 
mixed  with  the  entering  air  and  is  completely  burned.  Even 
with  volatile  coals,  the  combustion  is  completed  within  a  very 
short  distance  from  the  surface  of  the  fuel  bed,  hence  only  a  very 
short  combustion  space  is  necessary.  Such  stokers  give  satis- 


ACTUAL  COMBUSTION  OF  FUELS  529 

factory  results  even  when  placed  in  corrugated  flues  as  small  as 
three  feet  in  diameter,  such  as  are  used  in  internally  fired  boilers. 

With  such  stokers  it  is  necessary  to  use  very  strong  draft 
(about  three  inches  of  water)  which  must  be  furnished  by  some 
forced  draft  system,  hence  the  operation  is  independent  of 
weather  conditions.  In  some  instances  the  rate  at^  which  air 
and  coal  are  supplied  is  controlled  automatically  by  the  steam 
pressure.  In  one  such  arrangement  the  speed  of  the  blower- 
engine  is  regulated  by  the  steam  pressure  (a  drop  in  pressure,  due 
to  a  sudden  demand  on  the  boiler,  causing  an  increased  speed  and 
hence  a  greater  delivery  of  air)  and  the  valves  for  the  steam- 
actuated  coal  feeder  are  operated  by  this  same  engine ;  hence  the 
rates  at  which  the  air  and  coal  are  supplied  are  changed 
simultaneously,  are  kept  properly  balanced,  and  the  boiler  pres- 
sure is  automatically  maintained  substantially  constant. 

With  these  stokers  it  is  possible  to  obtain  very  high  rates  of 
combustion  in  a  very  limited  space,  from  500  to  600  pounds  of 
coal  per  hour  being  consumed  in  each  retort.  They  operate 
best  with  bituminous  coals  which  are  low  in  ash  and  they  are  not 
ordinarily  satisfactory  with  fine  anthracite  coals.* 

There  are,  of  course,  numerous  possible  arrangements  of  such 
stokers.  In  some  the  retorts  are  inclined  and  have  two  hori- 
zontal pushers,  one  above  the  other. 

258.  Burning  Liquid  Fuel,  (a)  Both  crude  petroleum  and  the 
product  of  its  partial  refinement,  fuel  oil,  are  very  extensively 
used  as  fuel  in  boiler  plants.  The  fuel  oil  is  generally  preferable 
to  crude  petroleum  on  the  score  of  safety  as,  due  to  the  removal 
of  the  more  volatile  constituents  during  the  refining  process, 
its  flash  point  is  higher.  Most  fuel  oil  also  has  a  lower  water 
content  than  the  crude  material  and  for  this  reason  there  is  less 
danger  of  the  flame  being  extinguished  by  water  collecting  in 
the  fuel  pipes  and  then  passing  as  a  "slug"  through  the  burner. 

(b)  To  successfully  burn  fuel  oil  it  is  necessary  to  spray,  or 
"atomize,"  it  very  effectively  and  to  mix  this  in  the  furnace  with 
the  necessary  air.  The  furnace  should  be  well  lined  with  brick 
which,  becoming  incandescent  during  operation,  will  insure 
satisfactory  combustion  so  long  as  there  is  sufficient  air  well 
mixed  with  the  fuel.  It  is  also  essential  that  the  furnace  be  so 
large  and  so  shaped  that  the  burning  fuel  does  not  come  in  con- 
*  Bull.  40,  U.  S.  Bureau  of  Mines. 


530 


HEAT-POWER  ENGINEERING 


Steam  Valve 


Fig-  339- 


Fig.  34i. 


Fig.  342. 


Fig.  343- 


ACTUAL  COMBUSTION  OF  FUELS 


53* 


tact  with  boiler  heating  surface ;  failure  in  this  respect  will  result 
in  incomplete  combustion  of  the  fuel,  as  in  the  case  of  long 
flaming  bituminous  coal,  and  is  also  liable  to  result  in  the  over- 
heating and  ultimate  failure  of  the  exposed  heating  surface.  ^ 

(c)  The  oil  is  generally  atomized  or  sprayed  by  compressed 
air  or  by  steam,  the  latter  being  now  the  more  common  method. 
It  is  also  occasionally  atomized  mechanically.  In  most  cases  the 
oil  is  pumped  from  storage  tanks  to  burners  by  small  steam- 
driven  pumps.  On  the  way  to  the  burners  it  is  heated  by  means 
of  the  exhaust  steam  from  the  pumps,  after  which  it  enters  the 
nozzles  or  "burners,"  from  which  it  is  so  sprayed  as  to  give  a  long 
jet  of  finely  divided  fuel  which  can  thoroughly  mix  with  air 
admitted  to  the  furnace.  The  amount  of  steam  required  in 
handling  the  oil  varies  from  about  2.5  per  cent  to  5  per  cent  of 
the  total  amount  generated  —  usually  it  is  about  3  per  cent  and 
is  about  evenly  divided  between  the  pumps  and  the  burners. 


Fig-  344- 


Fig.  345- 


I. 


(d)    The  principal  advantages  of  burning  oil  under  boilers  are: 

Ease  of  handling  from  tank  car  to  furnace,  as  no  man- 
ual labor  is  required  even  in  the  smallest  plants. 

Small  weight  and  volume,  since  the  oil  has  30  per  cent 
higher  calorific  value  for  equal  weight,  as  compared 
with  coal. 

Lack  of  clinkers  and  ash. 

Higher  average  operating  efficiency  because  of  (a)  ease 
of  operation,  (b)  ability  to  properly  gauge  and  main- 
tain necessary  air  supply,  (c)  smaller  excess  of  air 
required  because  of  ease  of  forming  good  mixture,  and 


HEAT-POWER  ENGINEERING 

(d)  more  uniform  furnace  conditions  because  there  is 
no  necessity  to  open  doors  at  frequent  intervals. 

5.  Practical  elimination  of  soot  and  smoke. 

6.  Decreased  labor  bill  in  large  plants  because  of  ease  with 

which  one  man  can  handle  several   thousand  boiler 
horse  power. 

7.  Ease  with  which  boiler  can  be   made  to  follow  rapid 

fluctuations  of  load. 

(e)  To  offset  these  advantages  are  high  cost  of  oil  fuel  in 
comparison  with  coal  in  many  parts  of  the  country  and  the 
increased  danger  of  fire  due  to  the  more  inflammable  character. 

(f)  Figs.  339,  340,  and  341   show  several  burners,  of  which 
there  are  a  great  many  other  forms  in  use.     One  of  the  numerous 
possible   arrangements  of   the   oil-feeding  system   is   shown   in 
Fig.  342;  and  in  Figs.  343,  344,  and  345  are  illustrated  three  of 
the  many  arrangements  of  furnace  in  use. 

258A.  Burning  Gaseous  Fuels,  (a)  Low-priced,  blast-furnace, 
natural  and  coke  oven  gases  are  frequently  used  in  boilers. 
Air  for  combustion  is  generally  admitted  through  or  around  the 
burner,  and  with  gases  of  high  heat  value  a  number  of  small 
burners  is  preferable  to  a  single  large  one,  to  prevent  a  blow- 
pipe action.  The  gas  and  air  should  have  a  rotary  motion  or 
else  a  checker-work  wall  should  be  used  to  insure  proper  mixing. 
The  sizes  of  gas  and  air  openings  depend  on  the  heating  value 
and  pressure  of  the  gas.  The  furnace  arrangements  are  similar 
to  those  for  oil  fuels,  with  volume  from  f  to  i|  cu.  ft.  per  rated 
horse  power.  A  stack  130  ft.  high  is  ordinarily  sufficient. 

(b)  If  a  combustible  mixture  of  gas  and  air  is  passed  through 
a  mass  of  finely  broken  refractory  material  in  a  tube  at  such  rate 
that  the  flame  will  not  "strike  back,"  the  combustion  will  take 
place  at  a  fixed  point  in  the  refractory  mass  which  will  become 
incandescent  and  transmit  heat  at  rapid  rate,  by  radiation  and 
conduction,  to  the  water  surrounding  the  tube.  This  method 
of  burning  gas,  which  has  been  called  Surface  Combustion,  has 
been  used  in  experimental  boilers  by  Bone  and  others  with 
highly  efficient  results,  due  principally  to  the  small  amount  of 
excess  air,  the  perfect  combustion,  and  the  low  temperature  of 
flue  gas.  The  rapid  rate  of  heat  transfer  permits  the  use  of  less 
heating  surface  for  given  output.* 

*  London  Engr.,  Apr.  14  and  Nov.  14,  1911,  Jr.  A.S.M.E.,  1914,  Eng.  Survey. 


CHAPTER  XXX. 
BOILERS. 

259.  Losses  Connected  with  Steam  Generation,  (a)  Be- 
cause of  the  very  intimate  connection  between  the  boiler  proper  * 
and  the  other  parts  which  make  up  the  steam  generating  appara- 
tus, it  is  most  convenient  to  discuss  the  losses  and  efficiencies  of 
boiler,  furnace,  and  grate  at  the  same  time.  Reference  to  the 
energy  stream  in  Fig.  346  will  assist  in  following  the  discussion. 

(b)  It  should  first  be  observed  that  it  is  the  function  of  the 
furnace  to  receive  fuel,  with  its  supply  of  heat  in  latent  form, 
and  to  make  the  maximum  possible  amount  of  this  heat  avail- 
able for  use.  The  furnace  may  therefore  be  called  the  "  heat 
generator."  It  is  then  the  function  of  the  boiler  proper  to  serve 
as  a  "  heat  absorber  "  and  to  transmit  to  the  contained  water 
and  steam  as  large  a  part  of  this  heat  as  possible.  But  losses 
always  occur  in  making  the  heat  available  in  the  furnace  and 
similarly  there  are  some  that  are  unavoidable  in  utilizing  that 
heat. 

There  are  in  general  three  losses  in  the  furnace:  (i)  Some  of 
the  combustible  is  not  burned,  but  is  lost  with  the  ash;  (2) 
some,  which  is  not  so  lost,  is  incompletely  burned  and  passes  off 
with  the  products  of  combustion  in  fine  particles;  and  (3)  some 
of  the  heat  actually  made  available  in  the  furnace  is  lost  by 
radiation  and  cannot  therefore  be  utilized  by  the  boiler. 

Thus,  only  a  fraction  of  the  heat  originally  supplied  with  the 
fuel  is  really  brought  to  the  boiler  heating  surfaces  for  utilization 
and  part  of  this  must  always  be  unavailable  even  in  an  ideal 
boiler,  for  after  the  products  of  combustion  are  cooled  to  the 
boiler  (steam)  temperature  there  can  be  no  further  transfer  of 

*  The  term  "  boiler  "  is  ambiguous.  It  is  used  to  refer  to  the  boiler  proper  (or 
vessel  containing  the  water  and  steam)  and  also  to  this  element  in  combination 
with  the  furnace,  setting  and  other  parts,  which  collectively  comprise  the  whole 
steam  generating  apparatus.  However,  this  should  not  lead  to  confusion  as  the 
context  always  makes  clear  the  sense  in  which  the  term  is  used. 

533 


534 


HEAT-POWER  ENGINEERING 


heat  to  the  boiler.*  This  unpresentable  loss  is  equal  to  the  heat 
required  to  raise  the  temperature  of  the  flue  gases  from  atmos- 
pheric to  boiler  temperature. 

Including  this  one  there  are  three  losses  of  heat  associated 
with  the  boiler  proper  or  "  heat  absorber."  These  boiler  losses 
are:  (i)  The  unpreven table  loss  (in  the  ideal  case)  equal  to 
the  heat  utilized  in  raising  the  flue  gases  to  boiler  temperature; 
(2)  a  loss  resulting  from  the  fact  that  in  commercial  boilers 
the  temperature  of  the  flue  gases  is  never  reduced  to  that  of  the 
steam ;  and  (3)  a  loss  resulting  from  the  radiation  from  external 
surfaces  of  boiler  and  setting. 

&  *"* 

M          ri  Sz  -O-  |  S^ 

"PL  *     lr     l2-||g.         fi>. 

^O          ifiTw=l        *~i  1°.  eJk  ^ 


00 


£ 

O   aW 


A        g >?'_  .4.-.  .§."£>,,.-..*..,*-,,.-,..., ..-,-. ,- 


^-r'   I*  (5)  Stack  loss  above  }  *,  § 
Steam  Temp.        /  jp 
}*  (4)  Heat  used  in        hfj 
-«      raising  flue  gases    V  M^ 
A      to  temp.of  steam    )«.g 


Fig.  346. 

The  exact  values  of  the  total  radiation  loss  of  the  complete 
apparatus  and  the  proportions  chargeable  separately  to  furnace 
and  to  boiler  are  generally  indeterminate,  but  they  may  be 
approximated  more  or  less  closely  in  some  instances. 

(c)  During  a  boiler  test,  it  is  possible  to  obtain  data  which 
can  be  used  in  determining  the  distribution  or  destination  of  the 
known  heat  value  of  the  fuel  actually  fired.  The  tabulation  of 
such  information  is  called  a  heat  balance  and  accounts  for  all 
the  heat  utilized  and  lost.  It  is  usually  stated  both  in  terms 
of  B.t.u.'s  and  on  the  percentage  basis.  A  complete  heat  balance 
would  include  the  following  eleven  items:  (i)  The  heat  utilized 
(absorbed  by  the  water  heated  and  the  steam  generated);  the 

*  There  is  an  exception  to  this  statement  in  the  special  case  of  boilers  that 
operate  on  the  "counter  flow  principle."  This  will  be  discussed  later. 


BOILERS 


535 


losses  due  (2)  to  unconsumed  combustible  in  the  ash  and  (3) 
to  the  removal  of  ash  from  the  ash  pit  while  at  high  tempera- 
ture; the  stack  losses  (Sect.  248)  occasioned  by  (4)  moisture  in 
the  fuel,  (5)  humidity  in  the  air  supplying  the  oxygen,  and  (6) 
water  formed  by  the  combustion  of  hydrogen,  and  that  due  to 
(7)  the  sensible  heat  in  the  flue  gas;  the  losses  due  to  (8)  uncon- 
sumed CO,  (9)  unburnt  hydrogen  and  hydrocarbons  and  (10) 
to  the  solid  fuel  (such  as  fine  coal  dust  and  soot)  carried  off  by 
the  draft;  and  (n)  the  losses  not  otherwise  accounted  for  — 
principally  radiation.  The  sum  of  the  items  on  the  B.t.u.  basis 
must,  of  course,  equal  the  heat  in  the  coal  actually  fired,  and 
on  the  percentage  basis  it  must  total  100  per  cent. 

(d)  In  real  tests  it  is  seldom  practicable  to  make  any  such 
complete  balance  as  that  just  given.  It  is  common  practice  * 
to  limit  it  to  the  following  six  items:  —  (i)  Heat  absorbed  by  the 
boiler  proper  and  the  losses  due  to  (2)  moisture  in  the  coal, 
(3)  moisture  formed  by  the  burning  of  hydrogen,  (4)  sensible 
heat  in  flue  gases,  (5)  unconsumed  CO,  and  (6)  those  not  other- 
wise accounted  for  (including  that  due  to  unconsumed  H  and 
hydrocarbons,  moisture  in  air,  radiation  and  others  not  listed 
above) . 

A  complete  discussion  of  the  method  of  determining  the  vari- 
ous losses  is  outside  the  province  of  this  book.  For  further 
details  the  student  is  referred  to  books  devoted  to  Boilers  and 
Furnaces  and  to  Experimental  Engineering. 

260.  Efficiencies  Connected  with  Steam  Generation,  (a) 
After  the  preceding  discussion  of  the  losses  occurring  in  boilers 
and  after  a  study  of  the  energy  stream  in  Fig.  346,  it  is  evi- 
dent that  numerous  ratios  between  the  widths  of  the  stream  at 
various  points  will  give  efficiencies  of  the  different  elements  of 
the  steam  generating  apparatus  and  of  their  combinations.  The 
more  important  of  these  efficiences  will  now  be  given,  but  as 
they  are  clearly  shown  in  Fig.  346  the  discussion  will  be  very  brief. 

(b)  Of  the  combustible  placed  in  the  furnace,  a  part  may  be 
lost  through  the  grates  with  the  ash.  That  which  is  not  thus 
lost  must  ascend  from  the  grate  as  volatile  combustible,  as 
gaseous  products  of  combustion,  as  unburnt  solid  matter,  or  as 
a  mixture  of  these;  it  will  be  called  "combustible  ascending 

*  A.S.M.E.  Power  Test  Code,  page  54. 


536  HEAT-POWER  ENGINEERING' 

from,  the  grate  "  or  "  ascending  combustible."     Obviously,  the 
Grate  Efficiency  is 

Weight  (or  heat  value}  of  ascending  combustible 
Weight  (or  heat  value)  of  combustible  fired 

which  is  shown  in  Fig.  346  by  the  ratio  CD/CE. 

(c)  The   Efficiency   of  the    Combustion   Space    (including   the 
coking  arch,  gas  mixing  structures,  and  other  parts  of  the  furnace 
above  the  grate)  is 

Heat  made  available  for  absorption  by  boiler       ,       . 
Heat  in  ascending  combustible 

This  is  shown  in  Fig.  346  by  the  ratio  FG/FH. 

(d)  The  furnace,  or  "  heat  generator  "  includes  both  the  grates 
and  the  combustion  space.     Hence  the  Furnace  Efficiency  is 

.  _  Heat  made  available  for  absorption  by  boiler     ,       , 

Heat  value  of  combustible  fired 
=  GEfXCEf.    .     .     .    '..-.*   ..     .  ...    y  :.     (40ia) 

In  Fig.  346,  FEf  is  the  ratio  IJ/IK. 

The  numerator  in  Eq.  401  is  evidently  equal  to  the  sum  of  (i) 
the  heat  absorbed  by  water  and  steam,  (2)  the  heat  in  flue  gases 
leaving  boiler  and  (3)  the  radiation  from  the  boiler  and  its  walls. 
Items  (i)  and  (2)  can  .be  determined  without  difficulty,  but  the 
radiation  losses  can  in  general  only  be  approximated.  For  this 
reason  the  Furnace  Efficiency  is  often  omitted  from  reports  of 
tests. 

(e)  It  has  been  seen  that  the  heat  used  in  raising  the  flue  gas 
from  the  temperature  of  the  atmosphere  to  that  of  the  steam 
is  not  ordinarily  available  for  use  in  the  boiler  proper;  *  hence, 
if  the  products  of  combustion  are  at  a  temperature  equal  to,  or 
below,  that  of  ebullition  there  will  be  no  heat  used  by  the  boiler, 
even  though  the  furnace  itself  has  high  efficiency,  —  and  as  far 
as  the  boiler  proper  is  concerned,  all  of  the  heat  is  then  wasted. 
To  have  the  boiler  use  the  maximum  amount  of  heat  evolved, 
the  unavailable  portion  must  of  course  be  made  as  small  as 
possible.     This  useless  amount  is  not  only  dependent  on  the 
temperature  difference  between  the  air  and  steam,  but  also  on 
the  weight  of  the  gas  heated.     It  can,  therefore,  be  minimized 

*  See  footnote  on  page  534  for  exception. 


BOILERS  537 

by  decreasing  the  weight  of  excess  air  supplied  for  combustion. 
Furthermore,  the  benefit  of  such  reduction  is  twofold,  for  not 
only  does  it  decrease  the  amount  of  heat  unavailable,  but  it 
results  in  higher  temperature  of  the  products  of  combustion, 
which  makes  the  unavailable  portion  a  smaller  percentage  of  the 
total  heat  evolved,  which  in  turn  increases  the  efficiency  of  the 
steam  generating  apparatus  as  a  whole.* 

(f)  The  Apparent  Efficiency  of  Boiler  (alone)  may  be  defined 
as 


A  R  /?f  —  absorbed  by  water  and  steam 

Heat  developed  in  furnace 

and  in  Fig.  346  ABEf  =  LM/LN.  The  determination  of  this 
efficiency  involves  a  knowledge  of  the  furnace  losses,  —  hence, 
like  the  Furnace  Efficiency,  it  is  difficult  to  determine  accurately. 
(g)  But  some  of  the  heat  developed  in  the  furnace  has  been 
shown  to  be  unavailable  for  the  ordinary  boiler,*  and  it  is  hardly 
just  to  charge  against  such  a  boiler  the  non-utilization  of  this 
portion  ;  hence,  the  apparent  efficiency  is  not  a  true  measure  of 
the  performance  in  such  case.  Calling  the  heat  with  tempera- 
ture above  that  of  the  steam  "potential  heat,"  then,  what  may  be 
termed  the  True  Boiler  Efficiency  is,  evidently, 

_  _  _  .,       Heat  absorbed  by  water  and  steam  ,       . 

TBEf  =  Potential  heat  "'    '     (4°3) 

In  Fig.  346,  TBEf  =  OP/OQ,  the  unavailable  heat  being  shown 
byQR. 

(h)  What  is  called  "Efficiency  Based  on  Combustible"  in  the 
A.S.M.E.  Power  Test  Code  (1915)  applies  to  the  combined  effi- 
ciency of  boiler  proper  and  combustion  space  and  is  expressed  as 
follows: 

Heat  absorbed  by  water  and  steam  ,       . 

™  ~~  Heat  available  in  ascending  combustible' 

=  ABEfXCEf  .........    (4<>4a) 

*  It  has  been  suggested  (Bull.  23,  U.S.  Bureau  of  Mines)  that  the  numerators 
in  Eqs.  (400)  and  (401)  should  include  only  the  heat  above  the  steam  temperature. 
However,  while  this  limitation  would  be  satisfactory  for  comparison  between  boilers 
of  the  ordinary  type,  it  would  be  inapplicable  to  those  using  the  "counter  flow" 
principle.  Hence,  in  this  text,  the  numerator  will  be  taken  as  the  total  heat  evolved 
in  the  furnace,  regardless  of  its  temperature. 


538  HEAT-POWER  ENGINEERING 

In  Fig.  346  BCEf  =  ST/SU.  This  efficiency  measures  the 
perfection  of  operation  of  the  boiler  and  combustion  space  com- 
bined (not  including  the  grate)  and  as  it  can  be  readily  deter- 
mined it  is  generally  given  in  reports  of  boiler  tests. 

1 1  Efficiencies  Based  on  Combustible ' '  have  been  obtained  as  high 
as  85  per  cent  with  oil  fuel  in  short  tests  under  exceptional  con- 
ditions. In  continuous  running,  75  per  cent  efficiency  with  coal, 
and  80  per  cent  with  oil,  are  attainable  under  uniform  conditions. 
With  variable  loads  and  ordinary  conditions,  average  efficiencies 
of  60  to  65  per  cent  throughout  the  year  represent  good  perform- 
ance. 

(i)  The  Overall  Efficiency  (OEf  =  VW/  VX  in  Fig.  346)  includes 
the  Grate  Efficiency  and  the  "  Efficiency  Based  on  Combustible," 
and  in  the  A.S.M  .E.  Code  is  termed  "  Efficiency  of  Boiler,  Furnace 
and  Grate."  It  is  a  measure  of  the  perfection  of  the  combined  per- 
formance of  the  boiler,  furnace,  and  grate,  and  is  affected  by  the 
skill  of  the  firemen,  the  suitability  of  the  coal  and  draft,  the 
dropping  of  coal  through  grate  bars,  etc.  Hence 

^p.  _  Heat  absorbed  by  water  and  steam  .       , 

Heat  in  the  combustible  fired      '      *  /  ' '     '     (4°5 ' 

=  BCEf  X  GEf  =  GEf  X  CEf  X  ABEf.     .     .  (4O5a) 

The  OEf  can  be  readily  determined  and  hence  is  usually  incor- 
porated in  reports  of  boiler  tests.  With  solid  fuels  its  numerical 
value  is  slightly  less  than  the  BCEf. 

(j)  Except  in  the  case  of  "  Efficiency  Based  on  Combustible" 
(BCEf)  and  of  Overall  Efficiency  (OEf),  there  is  lack  of  agree- 
ment among  engineers  as  to  the  definitions  and  names  of  the 
efficiencies  of  the  various  elements  of  the  steam  generating 
apparatus.  Hence,  before  proceeding  with  the  discussions 
including  the  use  of  such  terms  it  is  always  important  to  first 
arrive  at  an  understanding  of  their  meanings.  The  terms  and 
definitions  used  in  the  foregoing  treatment  appear  to  the  authors 
to  be  the  most  satisfactory  ones. 

261.  Boiler  Heating  Surface  and  Heat  Transmission,  (a) 
The  water  heating  surface  (H.S.)  of  a  boiler  is  the  surface  of 
those  parts  of  the  shell  which  are  in  contact  with  water  on  one 
side  and  with  the  furnace  gases  on  the  other.  As  the  transmis- 
sion of  heat  from  the  flue  gases  to  the  boiler  shell  is  less  rapid 


BOILERS  539 

than  that  from  the  shell  to  the  water,  the  heating  surface  should 
theoretically  be  measured  on  the  gas  side  of  the  plates  or  tubes. 
In  the  case  of  tubes,  however,  it  is  common  practice  to  consider 
the  outer  (larger)  surface  as  heating  surface,  regardless  of 
whether  it  is  exposed  to  water  or  gases. 

(b)  With  a  given  amount  of  potential  heat  in  hot  gases,  the 
more  extensive  the  heating  surface  the  nearer  will  the  flue  gases  be 
cooled  to  boiler  temperature  and,  neglecting  radiation,  the  higher 
will  be  the  true  efficiency  of  the  boiler. 

This  is  shown  by  curve  E  in  Fig.  347 
where  ordinates  are  efficiencies,  or 
relative  performance,  and  abscissas 
are  extent  of  H.S.  With  infinite  sur- 
face all  the  potential  heat  would  be 
absorbed  and  thus  this  efficiency  |or'"  il*  M 

...  .   .  .Extent  of'H.S. 

would  be  100  per  cent  on  this  assump-  F-        _ 

tion.  However,  it  is,  of  course,  neces- 
sary to  include  the  effect  of  the  radiation  losses  which  evidently 
depend  directly  on  the  extent  of  the  radiating  surface  which  is 
proportional  to  the  heating  surface.  In  Fig.  347  the  percentage 
of  this  loss  is  represented  by  the  ordinates  of  the  line  R.  The 
net  result,  or  percentage  of  heat  usefully  utilized,  is  given  by  the 
difference  between  the  ordinates  of  the  two  curves  and  is  shown 
by  line  E—R.  Evidently  the  maximum  efficiency,  considering 
radiation,  occurs  when  the  boiler  heating  surface  has  an  extent 
represented  by  the  abscissa  OM. 

(c)  Since  the  cost  of  boiler,  together  with  that  of  its  floor 
space  and  housing,  increases  with  the  extent  of  heating  surface, 
and  since  the  interest  on  first  cost  plus  the  amount  set  aside 
yearly  for  depreciation,  insurance  and  taxes  also  increases  at 
the  same  rate,  there  is  also  a  commercial  reduction  in  value  with 
the  extent  of  surface,  which  may  be  shown  by  some  line  such  as 
C  in  the  figure.     Hence,  the  true  or  commercial  value  of  the  heat- 
ing surfaces  would  be  shown  by  some  such  curve  as  E-R-C, 
and  the  maximum  value  corresponds  to  a  heating  surface  shown 
by  OM ' .     Either  greater  or  smaller  amounts  of  heating  surface 
would  give  less  return  per  dollar  expended,  hence  the  extent  of 
heating  surface  should  correspond  to  this  abscissa. 

(d)  The  mean  rate  of  evaporation  per  square  foot  of  heating 
surface  per  hour  for  the  whole  boiler  is  obtained  by  dividing  the 


540 


HEA  T-POWER  ENGINEERING ' 


1 

1! 

-^W- 
HtT* 

=^ 

~-v 

^~* 

31 

~a 

/ 

x 

^ 

\ 

*J 

Xv 

^ 

1 

* 

JN 

5D 

^A 

9133458780 

U.E.  per  Sq.  Ft..  H.S.  per  Hr. 

Fig.  348. 


total  weight  of  equivalent  evaporation  per  hour  by  the  total 
heating  surface.  From  data  obtained  from  tests  of  many  boilers 
operated  at  different  rates,  points  may  be  plotted  with  abscissas 
representing  these  mean  rates  of  evaporation  and  with  ordinates 
representing  either  efficiencies  or  Units  of  Evaporation  per 
pound  of  combustible  per  hour.  Average  curves  drawn  with 
respect  to  such  points  resemble  those  shown  in  Fig.  348  *  and 

are  seen  to  be  similar  to  E-R  in 
Fig-  347-  They  indicate  that  the 
maximum  efficiency  occurs  when 
the  "equivalent"  mean  rate  of 
evaporation  for  the  whole  boiler  is 
between  2  and  4  pounds  per  square 
foot  per  hour,  corresponding  ap- 
proximately to  a  transmission  of 
from  1900  to  4000  B.t.u.  per 
square  foot  per  hour. 

(e)  But  all  parts  of  the  heating  surface  are  not  equally  effec- 
tive.    Evidently  those  parts  in  the  direct  path  of  the  gases  are 
of  greater  value  than  those  exposed  merely  to  stagnant  gases, 
and  those  nearest  the  source  of  heat  are  the  most  effective  of 
any.     Heating  surface  exposed  to  the  "radiant"  heat  of  the  fuel 
bed  and  burning  gases  is  very  much  more  effective  than  that  not 
so  exposed.     Thus,   in  some  cases,   the  small   heating  surface 
immediately  over  the  fire  may  transmit  as  much  as  two-thirds 
of  the  total  heat  absorbed  by  the  boiler,  and  at  this  point  from 
20  to  35  or  more  pounds  of  water  may  be  evaporated  per  square 
foot  of  heating  surface  per  hour,  whereas  the  average  for  the 
whole  boiler  may  not  be  more  than  one- tenth  as  much.     It 
follows  that  surfaces  farthest  away  from  the  furnace  must  neces- 
sarily transmit  very  much  less  than  the  average.     Hence  impor- 
tance should  be  placed  not  only  on  the  amount  of  heating  surface 
but  also  on  its  distribution  and  location. 

(f)  Without  going  into  a  detailed  discussion  of  Heat  Trans- 
mission at  this  point  (for  this  will  be  given  in  Chapter  XXXV)  it 
will  be  advantageous  to  mention  here  the  manner  in  which  the 
heat  generated  in  the  furnace  is  transmitted  to  the  steam. 

Briefly,  the  heat  from  the  fuel  bed  is  first  brought  to  the  heat- 

*  Such  curves  are  given  in  Kent's  "Steam  Boiler  Economy"  and  in  Donkin's 
"Steam  Boiler  Performance." 


BOILERS  541 

ing  surface  by  direct  radiation  from  the  glowing  coal  and  burn- 
ing gases  (i.e.,  as  "radiant"  heat),  and  by  convection  by  the 
gases  which  come  from  the  furnace;  it  is  then  passed  through 
the  metal  walls  by  conduction,  to  be  absorbed  by  the  water  which 
may  also  transport  it  by  convection  due  to  the  circulation  of 
this  liquid;  and  finally,  when  the  water  has  reached  the  tem- 
perature of  ebullition,  the  further  addition  of  this  heat  results 
in  the  formation  of  the  vapor. 

(g)  The  rate  of  transmission  *  per  unit  of  area  of  heating 
surface  depends,  among  other  things,  on  (a)  the  difference  in 
temperature  between  the  transmitting  and  the  receiving  media; 
(b)  the  rapidity  (velocity)  with  which  the  gases  are  brought  in 
contact  with  the  heating  surface,  and  (c)  the  rapidity  with 
which  the  heat  can  be  carried  away  by  the  water  (rapidity  of 
water  circulation);  (d)  the  amount  of  scale  and  grease  on  the 
water  side  of  the  plate,  and  (e)  the  amount  of  soot  on  the  surfaces 
exposed  to  the  flue  gases. 

(h)  The  effectiveness  of  each  part  of  the  heating  surface  is 
dependent,  among  other  things,  on  the  difference  between  the 
temperature  (tg)  of  the  gases  on  the  one  side  and  that  (tw)  of  the 
water  on  the  other,  i.e.,  on  (tg  —  tw).  In  the  case  of  the  ordinary 
boiler,  as  has  been  shown,  tw  is  constant  and  equal  to  the  tem- 
perature of  the  steam,  since  all  the  water  is  (approximately)  at 
that  temperature.  As  the  gases  progress  over 
the  heating  surface  this  temperature  differ- 
ence diminishes  and  the  heat  transmission  per 
square  foot  becomes  less  until  the  limit  of 
effectiveness  is  reached,  which  generally  occurs 
when  the  temperature  difference  has  been  re- 
duced to  around  100°  to  200°  F. 

(i)  There  is,  however,  one  way  of  obtaining 
a  value  of  tw  that  is  below  the  steam  tempera- 
ture and  therefore  of  making  it  possible  to 
absorb  more  of  the  heat  from  the  flue  gas 
than  can  be  accomplished  in  the  ordinary 
boiler ;  this  involves  the  use  of  counter  current  flow.  The  prin- 
ciple under  which  this  operates  can  be  explained  in  connection 
with  Fig.  349,  in  which  the  arrangement  is  such  that  the  pump 

*  Reference,  U.  S.  Bureau  of  Mines,  Bull.  18,  "The  Transmission  of  Heat  into 
Steam  Boilers." 


542  HEAT-POWER  ENGINEERING' 

forces  the  water  downward  through  the  heating  coils,  whereas 
the  hot  gases  pass  upward  —  that  is,  the  heat-conveying  and 
heat-absorbing  media  flow  in  opposite  directions.  With  such 
arrangement  it  is  obvious  that  the  addition  of  more  heat  absorb- 
ing coils  at  the  top  (as  shown  dotted)  will  result  in  lowering  the 
temperature  at  which  the  gases  leave,  and  that  by  adding  a  suffi- 
cient number  this  temperature  could  be  reduced  to  that  of  the 
entering  water.  Hence,  with  the  counter  current  principle,  tw  is 
not  limited  to  the  steam  temperature  and  more  heat  can  be 
absorbed  by  the  heating  surface  than  is  possible  in  the  ordinary 
arrangement  of  boiler.  Parenthetically  it  may  be  remarked  that 
without  considerable  modification  the  simple  arrangement  shown 
diagrammatically  in  Fig.  349  would  probably  not  be  satisfactory 
as  a  boiler  element. 

The  counter  current  arrangement  is  approximated  in  some 
instances  by  placing  an  "economizer"  (to  be  described  later) 
beyond  the  boiler  so  that  the  hot  gases  after  leaving  the  boiler 
surrender  some  of  their  heat  to  the  water  which  passes  through 
the  economizer  on  its  way  to  the  boiler.  So  far,  the  counter 
current  principle  has  been  ignored  in  the  design  of  most  boilers, 
but  it  is  approximated  in  a  few  types. 

(j)  The  rapidity  with  which  the  gases  flow  over  the  heating 
surfaces  has  a  twofold  influence  on  the  rate  of  heat  transmission : 
for  (i)  more  heat  is  conveyed  to  the  surface  in  a  unit  of  time, 
and  (2)  the  gases  are  brought  more  intimately  in  contact  with 
those  surfaces,  since  there  is  less  opportunity  for  a  stagnant 
nonconducting  film  to  adhere  to  the  surfaces. 

(k)  The  rapid  circulation  of  water  within  the  boiler  is  of  especial 
importance  when  it  is  necessary  to  have  high  rates  of  heat 
transmission,  for  it  brings  larger  amounts  of  water  in  contact 
with  the  heating  surfaces  in  a  given  time  and  also  prevents  the 
metal  from  becoming  overheated.  This  circulation  is  brought 
about  by  providing  a  free  and  unrestricted  path  for  the  current  of 
water  and  by  applying  the  more  intensa  heat  at  the  proper  point 
in  this  path.  In  Fig.  350,  (a)  and  (b)  show  elements  of  common 
forms  of  boilers  and  the  arrows  indicate  the  direction  of  circu- 
lation. The  water  just  above  the  furnace  is  less  dense  than 
that  in  the  other  portions  of  the  boiler,  since  it  has  absorbed  more 
heat  and  is  charged  with  bubbles  of  steam,  and  it  therefore  rises, 
being  replaced  by  an  equal  amount  of  water  which  descends  at 


BOILERS 


543 


points  in  the  boiler  where  it  is  colder  and  denser.  This  is  the 
manner  in  which  the  current  is  established  and  maintained  in 
nearly  all  the  standard  types  of  boilers,  as  will  be  seen  in  study- 
ing the  figures  in  the  subsequent  sections. 

(1)  In  some  cases  this  circulation  can  be  made  so  powerful 
that  the  water  in  the  ascending  column  can  be  discharged  at  an 


elevation  even  considerably  above  that  of  the  surface  of  the 
body  of  water  from  which  the  descending  column  receives  its 
supply.  This  can  be  accomplished  with  the  arrangement  shown 
in  Fig.  351,  in  which  the  arrows  indicate  the  direction  of  flow. 
The  circulation  is  due  to  the  fact  that  material  in  riser  A  is 
sufficiently  charged  with  vapor  to  make  it  weigh  less  than  that 
in  the  down-comer  B,  although  the  altitude 
H  is  greater  than  h.  As  the  liberation  of 
the  steam  from  the  water  is  supposedly 
more  effective  when  the  ascending  column 
discharges  in  this  manner,  some  boilers  have 
arrangements  somewhat  like  that  shown  in 
the  diagram.  Sometimes  a  nonreturn  valve 
like  V  is  inserted  to  insure  the  proper  direction 
of  flow.  After  the  circulation  is  once  estab- 
lished, however,  this  valve  is  no  longer  neces- 
sary, as  the  current  is  then  very  positive. 

(m)  The  effectiveness  of  the  heat  transmission  depends  on 
the  cleanliness  of  the  heating  surface.  It  is  diminished  by  any 
deposit  of  soot  and  dust  on  the  exterior  surfaces  as  well  as  by  any 
interior  coating  of  soft  scale  (mud) ,  of  hard  scale,  or  of  grease. 

Water  in  its  natural  state  contains  more  or  less  foreign  matter 
in  suspension  or  in  solution.  Some  of  the  latter  precipitates 
when  the  temperature  reaches  about  200°  F.,  still  more  when 
300°  is  approached,  and  the  remainder,  which  is  left  when  the 
water  becomes  steam,  gradually  becomes  concentrated  until  it 


544 


HEAT-POWER  ENGINEERING' 


reaches  the  stage  where  deposition  occurs.  Deposits  on  the 
water  side  of  the  walls  of  the  boiler  reduce  the  heat  transmitting 
ability  of  the  plates  from  o  to  20  per  cent,  depending  on  the 
thickness  of  the  scale  and  on  the  chemical  and  physical  proper- 
ties of  the  material. 

The  formation  of  scale  should  be  prevented  as  far  as  possible 
by  purifying  the  water  before  feeding  it  to  the  boiler;  but  even 
then  there  will  be  some  deposit  formed  which  must  be  removed 
from  time  to  time.  Boilers  are  therefore  always  so  arranged 
that  they  can  be  readily  cleaned  internally,  and  so  that  the 
deposit  shall,  as  far  as  possible,  occur  at  points  where  the  heat  is 
the  least  intense  and  where  the  blow-off  pipe  can  be  connected 
(as  in  Fig.  350)  so  that  the  softer  material  can  be  removed  by 
blowing  off  some  of  the  water  from  time  to  time.  The  exterior 
of  the  heating  surfaces  should  also  be  accessible  for  removing 
the  soot  and  dust. 

262.  Boiler  Explosions.  It  has  been  seen  that,  by  expanding 
steam,  heat-energy  can  be  made  available  which  can  be  utilized 
in  forcing  water  and  steam  through  the  orifice  of  a  nozzle  at  very 
high  velocity.  As  a  result  of  such  discharge  there  is,  of  course, 
a  force  of  reaction  which  will  move  the  nozzle  and  attached 
parts  unless  prevented  in  some  manner.  The  size  of  this  force 
depends,  among  other  things,  directly  on  the  area  of  the  orifice. 

A  similar  process  occurs  when  a  boiler  shell  is  ruptured,  for, 
in  passing  through  the  rent  in-  the  boiler  shell,  the  steam  and 
boiling  water  are  subject  to  a  decrease  from  the  original  pressure 
to  atmospheric,  and  surrender  heat  which  is  converted  into  the 
kinetic  energy  of  the  issuing  mass.  The  reactive  force  acting 
on  the  boiler  shell  is  dependent  in  amount  on  the  area  of  the  rent, 
and  may  be  sufficiently  great,  compared  to  the  weight  of  the 
boiler,  to  propel  the  vessel  to  a  considerable  distance.  In  addi- 
tion to  the  probable  destruction  of  property  and  possible  en- 
dangerment  of  lives  which  may  result,  the  escaping  steam  and 
water  may  itself  cause  considerable  damage,  —  in  fact  persons 
near  by  may  be  seriously,  and  perhaps  fatally,  scalded,  even 
though  the  reaction  is  not  sufficient  to  displace  the  boiler. 

With  boilers  containing  little  water  and  having  elements 
which  are  of  small  size  and  so  designed  as  to  have  small  rents 
when  ruptured,  the  effect  of  an  explosion  is  less  disastrous  than 


BOILERS  545 

in  the  case  where  a  large  opening  can  occur  and  thus  instan- 
taneously release  a  large  mass  of  water  and  steam. 

263.  Selection  of  Boilers,  (a)  There  are  a  great  many  items 
to  be  considered  in  the  selection  of  a  boiler  for  a  given  service; 
only  some  of  the  more  important  ones  can  be  discussed  here. 
Between  the  various  kinds  of  boilers  which  have  become  well 
established  there  is  little  choice  as  regards  the  efficiency,  as  their 
performances  are  substantially  equal,  hence  the  selection  among 
such  standardized  types  depends  largely  on  general  suitability 
for  the  conditions  of  operation  and  space  available,  on  personal 
prejudice  and  familiarity,  on  convenience  in  transportation  and 
ease  of  erection,  and  on  the  first  cost  together  with  the  various 
other  items  of  expense. 

In  considering  an  unfamiliar  or  untried  design  the  following 
are  some  of  the  items  to  be  checked : 

(b)  Suitability.     It   should   be   decided   whether   or   not   the 
boiler  is  suitable  for  the  coal  that  is  available,  and  for  the  kind 
of  grates  (or  stoker)  and  furnace  best  adapted  to  that  fuel.     In 
special  cases  where  the  water  is  bad  and  the  draft  poor  these 
items  must  also  be  considered.     It  is  not  only  important  that 
the  boiler  should  have  sufficient  size  to  meet  the  normal  demands, 
but  it  should  have  overload  capacity  sufficient  for  all  emergencies. 

(c)  Safety  and  Durability.     These  depend  on  the  design   for 
structural   strength,    on   the   character   of   the    materials   used 
(castings  under  pressure  being  avoided)  and  on  the  character  of 
the  workmanship.     The  arrangement  should  be  such  as  to  avoid 
stresses  due  to  the  unequal  expansion  and  contraction  of  the 
different  parts  of  the  boiler;   and  the  method  of  support  should 
be  such  that  the  structure,  as  a  whole,  is  free  to  adjust  itself  with 
change  of  temperature.     There  should   be  no  thick  plates  or 
other  parts  (such  as  boiler  joints)  and  no  projecting  portions, 
or  plate  edges.,  exposed  to  the  current  of  the  hotter  gases;   nor 
should  the  blow-off  pipe  be  exposed  to  these  gases. 

(d)  Accessibility.     The  ability  to  easily  reach  all  parts  of  the 
boiler  for  inspection,  cleaning  and  making  repairs,  must  be  in- 
vestigated.    Doors  in  the  boiler  setting  must  be  provided  for 
access  to  all  exterior  parts;    manholes,  or  handholes,  must  be 
so  located  as  to  render  accessible  all  internal  parts. 

In  connection   with   internal   cleaning  cognizance   must   not 


546  HEAT-POWER  ENGINEERING' 

only  be  taken  of  the  number  of  manhole  and  handhole  joints 
to  be  broken  and  subsequently  made  tight,  but  also  of  the  time 
required  for  doing  this,  for  cooling  the  boiler  and  its  setting 
sufficiently  to  permit  of  starting  such  work,  and  for  bringing 
the  boiler  into  commission  again.  In  some  water  tube  boilers 
the  dust  and  soot  can  be  blown  from  the  tubes  by  means  of  a 
blast  of  steam  or  air  issuing  from  a  small  pipe  which  is  passed 
through  openings  in  the  front  and  rear  of  the  boiler  or  its 
setting.  Other  boilers  are  provided  with  openings  in  the  side 
walls  for  this  purpose. 

The  design  of  the  boiler  should  be  such  as  to  permit  of  making 
repairs  without  difficulty.  In  most  types  of  boilers  the  principal 
difficulty  is  with  the  tubes.  The  arrangement  should  be  such 
as  to  permit  readily  of  the  removal  and  replacement  of  any  one 
of  the  tubes  without  disturbing  the  other  tubes  or  other  parts. 
If  the  tubes  are  straight  but  few  need  be  carried  in  stock,  whereas 
if  they  differ  widely  in  curvature  it  may  be  necessary  to  have  on 
hand  a  large  collection  to  meet  any  emergency  that  may  arise. 

(e)  Circulation  of  Water.      It   is   necessary  to    see   that  the 
arrangement  is  such  as  to  allow  a  free  and  unrestricted  circulation 
of  the  water  and  that  the  heat  is  applied  at  such  a  point  as  to 
establish  and  maintain  the  current.     The  rapidity  of  circulation 
is  of  course  limited  by  the  smallest  cross-section  of  the  circuit. 
The  arrangement  of  the  structure  should  be  such  that  there  are  no 
pockets  where  steam  can  form  rapidly  and  keep  the  water  away 
from  the  heating  surfaces  subject  to  high  temperature,  for  under 
such  conditions  the  boiler  shell  will  burn  away  at  such  points. 

(f)  Circulation  of  the  Furnace  Gases.     It  is  desirable  to  main- 
tain a  uniform  velocity  of  the  furnace  gases  and  to  avoid  sudden 
contraction  and  expansion  as  they  proceed  through  the  boiler. 
Within  limits,  the  greater  the  velocity  the  more  rapidly  will  the 
heat  be  conveyed  to  the  heating  surface  and  the  greater  will  be 
the  amount  of  evaporation  from  a  given  surface.     There  should 
be  no  pockets  where  the  gas  can  remain  stagnant  and  it  is  de- 
sirable to  have  the  gas  baffled  in  such  a  way  as  to  constantly 
bring  the  fresher  portions  into  contact  with  the  heating  surface 
as  the  gas  proceeds. 

(g)  Dryness  of  Steam.     To  prevent  priming,  or  the  entrainment 
of  a  considerable  portion  of  moisture  in  the  steam,  the  liberating 
surface  of  the  water  from  which  steam  arises  should  be  ample. 


BOILERS  547 

When  the  water  contains  certain  impurities  foaming  may  occur, 
and  this  always  increases  the  amount  of  entrained  moisture.  By 
providing  a  large  steam  space  the  life  of  the  particles  of  steam  within 
the  boiler  may  be  made  sufficiently  long  to  allow  a  more  or  less 
complete  precipitation  of  the  moisture  to  occur.  Provision  is  often 
made  within  the  boiler  for  the  separation  of  moisture  by  means  of 
"  dry  pipes,"  baffles,  or  other  steam  separating  devices. 

(h)  Quantity  of  Water.  If  the  boiler  contains  a  large  volume  of 
water  there  is  less  attention  required  in  maintaining  the  water 
level,  and  the  boiler  has  a  greater  reserve  to  meet  sudden  demands 
than  is  the  case  in  boilers  having  a  small  volume;  but  greater 
damage  would  ordinarity  result  in  case  of  explosion.  In  marine 
and  similar  service  the  greater  weight  involved  is  of  course 
objectionable. 

(i)  Feed  Water.  The  boiler  feed  should  be  introduced  in  such 
manner  as  not  to  retard  the  circulation  of  the  water,  and,  if  cold, 
should  not  come  in  contact  with  the  boiler  shell.  Certain  of 
the  impurities  in  solution  in  the  entering  water  precipitate  when 
the  higher  temperatures  are  reached  and  are  deposited  as  mud. 
The  water  should  be  introduced  at  such  a  point  that  this  precipi- 
tate will  be  deposited  where  it  will  do  no  damage  and  from  which 
it  can  be  readily  removed,  see  Fig.  350  (a)  and  (b).  Sometimes 
a  "  mud  drum  "  is  provided  as  in  the  latter  figure,  or  a  "  settling 
chamber,"  as  in  Figs.  362  and  363,  from  which  the  mud  may  be 
blown  off  from  time  to  time. 

(j)  Space  Occupied.  In  addition  to  the  floor  space  and  height 
occupied  by  the  boiler  and  furnace,  there  must  be  charged  against 
the  apparatus  the  amount  of  space  that  must  be  provided  for 
the  replacement  of  tubes  and  for  cleaning.  In  some  horizontal 
boilers  there  must  be  space  in  front  (or  rear)  at  least  equal  to  the 
length  of  the  tubes  (see  Fig.  361).  This  fixes  the  minimum 
distance  between  parallel  rows  of  boilers  or  between  the  boiler 
end  and  the  wall  of  the  building.  In  some  types  of  vertical 
boilers  sufficient  room  must  be  provided  overhead  for  the 
replacement  of  tubes. 

When  the  exterior  of  the  heating  surface  is  accessible  for 
cleaning  from  the  front  or  rear  of  the  setting,  the  boilers  may  be 
arranged  in  a  continuous  "  battery "  (with  adjacent  walls  in 
common),  in  which  case  the  walls  between  boilers  are  thickened 
slightly.  When  the  cleaning  is  done  from  the  side,  the  boilers 


548  HEAT-POWER  ENGINEERING 

are  arranged  in  a  series  of  batteries  of  two  each,  with  sufficient 
space  between  the  pairs  to  permit  of  access  to  the  openings  in  one 
side  of  each  boiler  setting. 

(k)  Cost.  This,  of  course,  is  one  of  the  items  of  fundamental 
importance.  Besides  the  first  cost  of  the  boiler,  with  its  setting 
and  trimmings,  and  the  expense  of  transportation  and  erection, 
it  is  necessary  to  consider  charges  for  up-keep  and  depreciation. 
The  size  of  the  boiler  and  furnace  and  the  space  necessary  for  the 
removal  of  tubes  and  for  cleaning  must  also  be  considered  in  con- 
nection with  their  influence  on  the  cost  of  the  ground  and  building. 

264.  Classification  of  Boilers.  Boilers  may  be  classified  in 
many  different  ways,  only  a  few  of  which  need  be  given  here. 

(a)  In  Internally  fired  boilers  the  furnace  is  located  within  the 
structure  of  the  boiler  and  is  usually  made  integral  with  it,  while  in 
externally  fired  boilers  the  furnace  is  placed  below  the  boiler  proper 
and  is  surrounded  by  a  "  setting  "  which  is  generally  of  brickwork. 

(b)  In  fire  tube  boilers  (commonly  called  "  Tubular  Boilers  ") 
the  furnace  gases  pass  through  the  tubes  which  are  surrounded 
by  the  water  from  which  the  steam  is  generated;    whereas  in 
water  tube  boilers  (sometimes  called  "  Tubulous  Boilers  ")  the 
water  circulates  through  the  tubes  while  the  hot  gases  pass  over 
their  exteriors.     Fire  tube  boilers  are  shown  in  Figs.  352  to  359; 
and  water  tube  boilers  are  illustrated  in  Figs.  360  to  366.    These 
will  be  discussed  later. 

(c)  Sectional  boilers  are  composed  of   small  elements  so  ar- 
ranged that  any  rupture  which  may  occur  will  produce  only  a 
relatively  small  opening  and  will  result  in  but  little  damage  to 
the  boiler  itself  and  to  its  surroundings.     Such  boilers  may  be 
shipped  in  small  parts  which  are  assembled  when  being  installed. 
Examples  of  this  type  of  boilers  are  shown  in  Figs.  360  and  365. 

(d)  In  vertical  boilers  the  tubes  are  arranged  perpendicularly, 
or  approximately  so.     In  general,  such  boilers  demand  less  floor 
space  than  horizontal  ones  but  their  height  is  greater. 

(e}  In  straight  tube  boilers  it  is  comparatively  easy  to  clean 
and  inspect  the  tubes.  The  use  of  curved  tubes  is  inherent  in 
the  design  of  some  boilers  and  they  give  a  certain  degree  of 
flexibility  to  the  structure.  (See  Fig.  363.) 

(f)  Boilers  are  also  sometimes  classed  according  to  their  use; 
for  example,  there  are  locomotive  boilers,  marine  boilers,  portable 


BOILERS 


549 


boilers,   stationary   boilers,  etc.     The    descriptions  which   will 
follow,  will  be  limited  in  most  cases  to  the  stationary  types. 

(g)  There  are  innumerable  arrangements  of  boilers  and  their 
settings;  only  a  few  of  the  more  typical  ones  will  be  considered 
in  the  following  sections. 

265.  Internally  Fired,  Tubular  Boilers,  (a)  Such  boilers  are 
generally  compact  and  self  contained;  they  are  shipped  corn- 


steam 

Gauge 


Fig.  352.  — Tubular  Boiler. 
Submerged  Tube  Type. 


Fig.  353- — Tubular  Boiler. 
Exposed  Tube  Type. 


plete,  and  immediately  upon  arrival  are  ready  to  connect  to  the 
flues  and  steam  system.  While  they  cost  more  than  ordinary 
boilers,  they  avoid  the  expense  of  special  brickwork  "  setting  " 
and  eliminate  the  possibility  of  leakage  of  air  through  cracks 
which  may  develop  in  such  brickwork.  Sometimes  there  is 
difficulty  in  transporting  the  larger  sizes. 

(b)  Fig.  352  shows  a  small  vertical  boiler  of  this  kind  with 


550 


HEAT-POWER  ENGINEERING 


water  level  above  the  tubes.  Such  boilers  are  of  the  submerged 
tube  type.  In  Fig.  353  is  a  somewhat  similar  boiler  in  which  the 
tubes  extend  above  the  water  level  —  the  exposed  portions  pre- 
senting surface  to  the  steam.  Boilers  of  this  kind  are  called  ex- 
posed tube  boilers.  The  one  shown  in  this  figure  is  of  such  large 


Hand  Holes 

Fig.  354-  — Locomotive  Type  of  Boiler. 


size  that  the  space  at  a  can  be  occupied  by  a  man  while  cleaning 
the  tubes,  the  crown  sheet  and  the  plates  around  the  furnace. 

(c)  Fig.  354  shows  a  Locomotive  type  of  boiler  with  a  steam 
dome  which  provides  additional  steam  space.     Such  boilers  are 


Fig-  355-  —Continental  Type  of  Boiler. 

not  only  used  for  locomotives  and  for  traction  engines,  but  also 
for  stationary  service. 

(d)  In  Fig.  355  is  a  longitudinal  section  of  a  boiler  of  the 
Continental  type,  the  exterior  of  which  resembles  Fig.  356. 
The  furnace  wall  is  a  cylindrical  flue  with  strengthening  cor- 


BOILERS 


551 


rugations.  The  combustion  chamber  is  lined  with  fire  brick  or 
other  refractory  material  and  is  located  in  a  casing  of  thin  metal 
extending  from  the  main  shell  of  the  boiler.  These  boilers  have 
large  liberating  surface,  voluminous  steam  space  and  large 
volume  of  water.  They  usually  have  either  one  or  two  furnace 
flues,  and  because  they  are  compact  and  have  short  tubes,  they 
can  be  used  in  places  where  the  space  is  limited. 

(e)    The  Scotch  Marine  type  of  boiler  is  shown  in  Fig.  356  and 
is  similar  to  the  Continental  except  that  its  combustion  chamber 


Uptake 


Fig.  356.  —  Scotch  Marine  Type  of  Boiler. 

(see  Fig.  357)  has  metal  walls  and  is  entirely  surrounded  by 
water.  As  these  walls  tend  to  collapse  under  the  external 
pressure  to  which  they  are  subjected,  they  are  carefully  stayed. 
Such  boilers  have  from  one  to  four  corrugated  furnace  flues,  and 
their  outer  shells  range  from  5!  feet  to  16  feet  in  diameter.  Be- 
cause of  the  very  short  tubes,  large  steaming  capacity  for  space 
occupied,  absence  of  brick  setting,  and  accessibility,  they  are 
particularly  adapted  to  marine  service. 

266.  Externally  Fired  Tubular  Boilers,  (a)  Boilers  of  this 
type  generally  require  a  separately  constructed  "  setting " 
(usually  of  brickwork  with  lining  of  firebrick)  to  surround  the 


552 


HEAT-POWER  ENGINEERING 


furnace  and  boiler.  This  is  so  arranged  as  to  properly  confine 
the  flue  gases  and  guide  them  to  and  from  the  boiler.  It  takes 
considerable  time  to  construct  and  dry  out  the  brickwork  setting 


Fig.  357.  — Submerged  Combustion  Chamber. 

and  the  expense  involved  must  be  added  to  the  cost  of  the  boiler 
itself.  Such  boilers  usually  occupy  more  space  than  internally 
fired  boilers  and  the  setting  should  be  kept  in  repair  so  as  to 


w£&r- 

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£- :y  r^^r^jw5SJS^!y5fii  '0>^->^r^^7rvr-j^>*-^ 

Fig.  358.  —Horizontal  Return  Tubular  Boiler  with  "  Half  Front." 

avoid  air  leakages,  which  have  a  detrimental  effect  on  the  draft 
and  boiler  performance. 

(b)  An  externally  fired  boiler  classified  as  of  Horizontal  Return 
Tubular  type  ("  H.R.T.  boiler  ")  is  shown  in  Fig.  358.      In  this 


BOILERS 


553 


boiler  the  smoke  box  is  formed  in  an  extension  of  the  boiler 
shell  which  projects  beyond  the  brick  front  wall.  The  cast  iron 
"  boiler  front  "  covers  only  the  portion  of  this  wall  located 
below  the  smoke  box,  and  is  therefore  commonly  called  a  "  half- 
front."  The  boiler  shown  in  this  figure  is  suspended  from  cross 
beams  or  "  Gallows  frames." 

(c)  In  Fig.  359  is  shown  a  H.R.T.  boiler  with  "full  flush 
front"  the  smoke  chamber  being  formed  in  the  brickwork  of 
the  front  wall.  The  boiler  is  shown  to  be  supported  by  brackets, 


Manhole 


Fig.  359.  —Horizontal  Return  Tubular  Boiler  with  "  Full  Flush  Front." 

the  rear  pair  of  which  is  mounted  on  rollers  to  allow  free  ex- 
pansion. The  brick  setting  is  braced  by  "  buck  staves." 

As  most  of  the  scale  is  deposited  at  the  rear  of  the  boiler,  as 
in  Fig.  350  (a),  the  blow  off  is  located  at  this  point.  The  back 
end  of  the  boiler  is  lowered  slightly  to  aid  in  draining  the  shell. 

As  the  boiler  shell  is  exposed  to  the  direct  heat  of  the  furnace, 
the  thickness  of  metal  must  not  be  so  great  as  to  make  it  liable 
to  burn  thinner,  and  as  the  shell  thickness  must  increase  with 
the  diameter  of  the  boiler,  these  boilers  cannot  be  constructed 
beyond  a  certain  size.  They  are  not  ordinarily  built  larger  than 
200  boiler  horse  power  and  are  seldom  used  with  pressures  above 
150  pounds.  The  H.R.T.  boilers  are  about  the  cheapest  made, 
hence  are  quite  widely  used  for  low  pressures. 


554 


HEAT-POWER  ENGINEERING'' 


267.  Water  Tube  Boilers,  (a)  Figs.  360  and  361  illustrate 
sectional  water  tube  boilers  known  as  the  Babcock  and  Wilcox 
type  (or  "  B.  and  W."  type).  The  tubes  are  expanded  into 
pressed  steel  front  and  rear  "  headers  "  to  form  tube  "  sections." 
The  sections,  the  drums,  connecting  nipples  and  other  parts  are 
shipped  "  knocked  down,"  and  are  assembled  at  the  power  house. 
The  parts  to  be  transported  and  handled  are  therefore  relatively 
small.  Being  of  the  sectional  type  with  small  elements,  the 
danger  of  disastrous  explosions  is  slight,  as  ruptures  seldom  occur 


Header 


Fig.  360.  —  B.  and  W.  Type  of  Boiler. 


elsewhere  than  in  the  tubes.  Opposite  each  tube  is  a  hand-hole 
cover  which  can  be  removed  for  cleaning  and  replacing  tubes. 
Doors  for  external  cleaning  are  provided  in  the  side  walls,  hence 
these  boilers  cannot  be  arranged  in  continuous  batteries,  but 
they  may  be  grouped  in  batteries  of  two  each.  The  boiler  has 
elements  similar  to  (b)  in  Fig.  350,  with  mud  drum  located  at  the 
bottom  of  the  rear  headers.  It  is  hung  from  above,  hence  is 
free  to  expand  or  contract. 

As  shown  in  the  figure  the  furnace  has  an  exposed  roof  and  the 
gases  are  baffled  so  as  to  make  three  "  passes  "  across  the  tubes. 


BOILERS 


555 


Other  arrangements  of  baffles  and  furnace  can  of  course  be  used. 
The  tubes  are  not  arranged  in  vertical  rows,  but  are  "  staggered," 


Dam  aer 


Fig.  361.  —  B.  and  W.  Type  of  Boiler. 

as  shown  by  the  header  at  (a)  in  Fig.  360,  so  as  to  further  baffle 
the  gases. 

(b)   In  Fig.  362  is  shown  the  Heine  type  of  water  tube  boiler 
having  the  front  and  rear  "  water  legs  "  made  of  steel  plates  and 


Stop  Valve 


Feed 
Pipe 


'JlancLHole 


Fig.  362.  —Heine  Type  of  Boiler. 

riveted  to  the  drum.  The  front  and  back  plates  of  each  water 
leg  are  held  together  by  hollow  stay  bolts  having  holes  large 
enough  to  permit  the  insertion  of  a  steam  or  air  pipe  for  blow- 
ing the  soot  and  dust  from  the  exterior  of  the  tubes;  and  opposite 


556 


HEAT-POWER  ENGINEERING 


each  tube  in  each  water  leg  is  a  hand  hole  giving  access  to  the 
interior  of  tubes. 

The  feed  water  enters  a  "  mud  drum,"  where  it  remains 
quiescent  for  a  considerable  time  before  it  mixes  with  the  water 
which  is  circulating  through  the  tubes.  As  this  feed  water  be- 
comes heated  certain  of  the  impurities  are  precipitated  in  the 
mud  drum,  from  which  they  can  be  blown  off  at  intervals. 

The  water  legs  of  the  boiler  shown  in  the  figure  rest  on  the 
brickwork  and  have  rollers  under  the  rear  one.  The  boiler  may,  of 

course,  be  supported 
in  other  ways.  This 
boiler  is  shipped  com- 
pletely assembled, 
ready  to  have  the  set- 
ting constructed  im- 
mediately upon  its 
arrival.  As  no  clean- 
ing doors  are  located 
in  the  side  walls,  such 
boilers  can  be  arranged 
in  continuous  batter- 
ies. 

As  shown,  the  fur- 
nace has  a  tile  roof 
supported  by  the  lower 
row  of  tubes  and  the 
furnace  gases  are  baf- 
fled so  as  to  pass  along 

the  tubes.     The  same  type  of  boiler  is  often  used  with  baffles 
arranged  similar  to  those  in  Fig.  361. 

(c)  Fig.  363  shows  the  Stirling  type  of  water  tube  boiler  which 
may  be  classed  as  a  vertical  one.  It  is  composed  of  drums  and 
tubes  which  are  not  assembled  until  they  reach  their  destination. 
Since  the  elements  are  simple  and  easy  to  make,  the  cost  of  such 
boilers  is  less  than  that  of  those  having  more  complicated  parts. 
The  feed  water  enters  a  precipitation  pocket  in  drum  D  and  is 
heated  as  it  descends  to  drum  C.  The  circulation  of  water  is 
through  tubes  joining  drums  A,  B  and  C.  All  the  upper  drums 
are  connected  by  steam  pipes. 

The  rows  of  tubes  running  circumferentially  around  the  drums 


Fig-  363-  —Stirling  Type  of  Boiler. 


BOILERS 


557 


are  arranged  in  pairs,  between  which  is  sufficient  space  for  the 
removal  or  insertion  of  tubes  located  in  the  interior  of  the  nests. 
The  tubes  are  curved  and  the  mud  drum  is  suspended  by  the 
tubes  —  an  arrangement  which  gives  flexibility  and  permits  of 
expansion  and  contraction  accompanying  temperature  changes. 
All  drums  have  man  holes  which  give  access  to  their  interiors 
and  to  the  tubes.  The  side  walls  of  the  setting  are  provided 
with  cleaning  doors  exposing  the  exteriors  of  the  tubes,  hence 


Fig.  364.  —  Wickes  Type  of  Boiler. 

these  boilers  cannot  be  arranged  in  continuous  batteries  — 
they  may,  however,  be  arranged  in  pairs.  The  arrangement 
provides  for  large  combustion  space  and  for  an  ample  coking 
arch,  or  Dutch  oven  roof. 

(d)  There  are  many  other  arrangements  of  boilers  composed 
of  simple  horizontal  drums  and  vertical  tubes.  In  some  the 
vertical  tubes  enter  a  single  upper  drum  and  a  single  lower  one, 
and  the  gases  are  baffled  so  as  to  make  two  or  three  passes. 

In  other  boilers  there  are  two  drums  above,  with  steam  and 
water  connections  between,  and  two  lower  drums,  with  water 


558 


HEAT-POWER  ENGINEERING'' 


connections,  and  between  these  pairs  are  vertical  tubes.  The 
furnace  gases  pass  up  along  the  tubes  joining  the  front  drums 
and  down  along  the  rear  tubes,  to  a  flue  connection  near  the  bot- 
tom of  the  setting.  There  are  still  other  arrangements,  but  those 
given  will  suffice  to  show  the  possibilities  of  this  construction. 

(e)  Fig.  364  shows  the  Wickes  type  of  vertical  water  tube 
boiler  having  single  upper  and  lower  drums  with  vertical  axes. 
The  tubes  are  removed  and  inserted  through  hand  holes  located 
in  the  dome  of  the  steam  space;  hence,  it  is  necessary  to  provide 
overhead  room,  or  sky-lights,  immediately  over  the  boilers. 


,  Steam  Nozzle- 


Fig.  365.  — Parker  Type  of  Boiler. 

(f)  In  Fig.  365  is  shown  the  Parker  type  of  boiler,  which  differs 
radically  in  several  respects  from  the  ordinary  types,  since  it 
makes  use  of  the  counter- flow  principle  (Sect.  261  (i))  and  de- 
livers the  steam  and  water  at  points  above  the  water  level 
(Sect.  261  (/)).  Under  the  best  conditions  of  operation,  the 
feed  water  enters  the  system  at  A  (check  valve  E  being  closed), 
passes  downward  through  the  zig-zag  tubes  in  a  general  direction 
opposite  to  that  of  the  ascending  flue  gases  (just  as  in  Fig.  349) 
and  is  finally  delivered  at  B  into  the  drum,  with  a  temperature 
high  enough  to  cause  the  precipitation  of  most  of  the  impurities. 
The  water  from  the  drum  enters  another  set  of  zig-zag  pipes  at 
C,  constituting  the  vaporizing  element,  is  further  heated  as  it 
descends  and  is  finally  discharged  as  steam  into  the  drum  at  D. 


BOILERS  559 

Owing  to  the  countercurrent  flow  it  is  possible,  by  providing 
sufficient  heating  surface,  to  cool  the  flue  gases  below  the  temper- 
ature of  the  steam.  Hence,  sometimes  a  third  nest  of  tubes  is 
added,  in  which  case  the  upper  is  called  an  "  economizer  element." 

Should  the  feed  valve  be  shut  off  the  circulation  will  still  con- 
tinue, for  water  will  then  pass  through  check  valve  E  into  the 
upper  element  of  tubes,  but  the  operation  will  be  somewhat  less 
efficient  than  before. 

The  "  junction  boxes  "  joining  the  ends  of  the  tubes  have 
hand  holes  and  some  have  non-return  valves  which  ensure  the 
circulation  of  the  water  in  the  proper  direction.  Besides  the 
scale  pocket  F  there  is  a  blow  off  (not  shown)  located  under  the 
diaphragm  in  the  bottom  of  the  drum. 

(g)  In  boilers  of  the  porcupine  type,  the  tubes,  with  closed 
outer  ends,  project  from  a  water  drum,  or  header,  into  the  path 
of  the  flue  gases.  Fig.  366  shows  an  arrangement  having  a 
double  header  and  concentric  tubes.  With  such  arrangement  the 
cold  water  descends  through  the  left  water  leg,  passes  through 
the  inner  tube  to  the  end,  then  returns  through  the  annular 
passage  between  the  two  tubes  and  ascends  in  the  riser  to  the 
steam  drum  above.  But  little  use  is  made  of  this  arrangement, 
^owever,  because  of  the  expense  of  construction. 


t 


Fig.  366.  —  Niclausse  Tubes. 

(h)  Fig.  367  shows  a  double-furnace  boiler  arranged  to  be  fired 
from  both  front  and  "  rear  ";  thus  it  has  about  double  the  grate 
area  and  generate*  steam  nearly  twice  as  rapidly  as  in  the  ordi- 
nary case.  However,  as  the  rate  of  evaporation  is  high  the 
efficiency  is  slightly  less  than  is  obtained  under  less  intensive 
conditions.  Such  arrangements  are  frequently  adopted  when 
floor  space  is  limited  or  when  the  cost  of  real  estate  is  great,  as 
is  the  case  in  powpr  plants  located  in  congested  districts  of  large 
cities.  The  sam^  «cheme  can,  of  course,  be  used  with  boilers  of 
other  types  than  that  shown, 


560  HEAT-POWER  ENGINEERING 

268.  Boiler  Accessories.  In  addition  to  the  fittings  already 
described,  boilers  are  always  fitted  with  steam,  gauges,  glass 
water  gauges,  try  cocks,  safety  valves,  feed  valves,  blow-off 
valves  and  steam  stop  valves.  In  addition  they  frequently  have 
"  water  columns  "  with  floats  to  operate  sentinel  whistles  when 


Fig.  367. — Double-furnace  Boiler. 

the  water  level  becomes  too  high  or  too  low ;  and  they  may  have 
"  fusible  plugs  "  which,  when  the  water  level  becomes  danger- 
ously low,  become  uncovered  and  melt,  and  thus  allow  steam  to 
escape  and  attract  attention  before  the  plates  become  over- 
heated. Automatic  feed -water  regulators  are  sometimes  used, 
and  in  plants  where  the  load  fluctuates  rapidly  damper  regula- 


TOILERS  561 

tors,  controlled  by  the  steam  pressure,  are  also  provided  to 
automatically  adjust  the  draft.  When  water  tube  boilers  are 
used,  the  boiler  room  equipment  generally  includes  mechanical 
tube  cleaners,  of  which  there  are  many  varieties. 

269.  Boiler  Performance,  (a)  In  stating  the  evaporative 
performance  of  boilers  and  similar  apparatus,  it  is  customary  to 
use  the  latent  heat  of  vaporization  of  one  pound  of  steam  at 
atmospheric  pressure  as  the  "  Unit  of  Evaporation  "  (U.E.). 
The  value  of  this  unit  is,  therefore,  970.4  B.t.u.  (old  value  965.7); 
and,  as  this  is  the  heat  absorbed  by  one  pound  of  steam  in  being 
converted  from  water  with  temperature  of  212°  F.,  to  steam  at 
the  same  temperature,  the  performance  may  also  be  stated  in 
terms  of  the  "  Equivalent  Evaporation  "  or  "  number  of  pounds 
of  water  from  and  at  212°  F."  that  would  be  evaporated  by  the 
same  amount  of  heat.  Evidently  there  would  always  be  the 
same  number  of  pounds  of  Equivalent  Evaporation  as  there  are 
Units  of  Evaporation. 

When  boilers  are  tested,  the  temperature  of  the  feed  water,  the 
actual  weight  of  steam  generated  per  hour,  and  the  quality  (or 
superheat)  are  all  determined.  With  these  quantities  known,  the 
equivalent  evaporation  from  and  at  212°  F.  can  be  determined  by 
dividing  the  heat  given  to  water  and  steam  by  970.4  (965.7). 

(b)  This  same  unit  can  also  be  used  for  expressing  the  value 
of  fuels  when  used  for  generating  steam;    thus,  the  Theoretical 
Equivalent  Evaporation  (T.U.E.)  per  pound  of  fuel  is  found  by 
dividing  the  calorific  value  per  pound  by  970.4. 

Based  on  the  usual  calorific  values,  the  T.U.E. 's  per  pound  of 
combustible,  are  about  as  follows  for  the  different  kinds  of  fuel :  - 
Carbon,  15  pounds;   good  anthracite,  15.4  pounds;   semi-bitumi- 
nous,  16.3  pounds;    bituminous,   14  to  15.8  pounds;    and  oils, 
18.5  to  22  pounds. 

Obviously  the  Theoretical  Equivalent  Evaporation  per  pound 
of  fuel  can  be  obtained  by  multiplying  the  foregoing  figures  by 
the  percentage  of  combustible  present. 

(c)  The  steam  generating  apparatus  as  a  whole  delivers  with 
the  steam  only  a  portion  of  the  calorific  value  of  the  fuel,  the 
percentage  depending  on  the  overall  efficiency  of  the  apparatus. 
These  efficiencies  were  given  in  Sect.  260  (h)  and   (i).     With 
good  coal  the  Actual  Equivalent  Evaporation  should  be  at  least 


562  HEAT-POWER  ENGINEERING'' 

9  pounds  per  pound  of  combustible,  and  in  the  best  instances 
\2\  pounds  have  been  reached.  With  oil  this  evaporation  is 
from  14.4  to  16.9  per  pound  of  fuel. 

When  the  rate  of  evaporation  is  under  consideration,  the  unit 
of  time  generally  adopted  is  the  hour  —  hence  the  terms  "Equiv- 
alent Evaporation  per  hour  "  and  "  Units  of  Evaporation  per 
hour  "  are  in  common  use.  If  no  unit  of  time  is  specified  the 
hour  is  implied. 

(d)  In  boiler  computations  it  is  sometimes  convenient  to  make 
use  of  a  quantity  called  the  "  Factor  of  Evaporation  "  (F.E.). 
This  quantity  is  the  ratio  of  the  heat  absorbed  per  pound  of 
steam  generated  to  970.4  (or  965.7  as  the  case  may  be).  Hence 

Factor  of  Evaporation  -  &+  »  ~  ^      -     (406) 


in  which  q,  x,  r,  D  and  Cp  are  respectively  the  sensible  heat, 
quality,  latent  heat,  degrees  of  superheat  and  specific  heat 
of  the  steam  leaving  the  boiler,  and  t  is  the  temperature  of  the 
feed  water.  Evidently  the  Factor  of  Evaporation  is  the  ratio 
)f  the  equivalent  evaporation  to  the  actual  weight,  and  as  this 
;atio  is  frequently  used  its  values  are  generally  tabulated  in 
reference  books  for  different  pressures  of  dry  saturated  steam 
with  various  temperatures  of  feed  water. 

(e)  The  rated  size  and  the  maximum  capacity  of  boilers  are 
usually  stated  in  terms  of  a  unit  miscalled  a  "  Boiler  Horse 
Power"  (B.P.).  It  has  been  suggested  that  this  be  changed 
to  "  Boiler  Power''  as  the  term  "  horse  power  "  is  inapplicable 
to  boilers.  The  Boiler  Horse  Power  is  defined  as  the  equivalent 
°f  34-5  pounds  of  steam  evaporated  "  from  and  at  "  212°  F. 
per  hour;  (i.e.,  34^  U.E.  per  hr.).  It  is,  therefore,  merely  a 
measure  of  the  heat  given  to  the  water  and  steam  and  is  equiva- 
lent to  the  transfer  of  33,479  B.t.u.  per  hour  (with  U.E.  =  970.4 
B.t.u.). 

The  "  horse  power  "  of  a  boiler  which  is  evaporating  a  given 
weight  of  steam  per  hour  at  a  certain  pressure,  with  a  certain 
quality,  and  from  feed  water  at  a  certain  temperature,  can  there- 
fore be  found  in  two  ways:  —  First,  by  dividing  the  equivalent 
evaporation  by  34^;  second,  by  dividing  the  total  heat  supplied 

*  The  expression  in  this  parenthesis  is  written  so  as  to  apply  to  both  super- 
heated and  saturated  steam,  as  was  first  done  on  page  173. 


BOILERS 

to  the  water  and  steam  per  hour  by  the  number  33,479  given 
above. 

(f)  In  this  connection,  however,  it  is  important  to  note  that 
there  is  no  definite  relation  between  engine  horse  power  and  the 
so-called  boiler  horse  power;  the  ratio  of  the  engine  h.p.  to  the 
"  boiler  h.p."  in  any  plant  depends  entirely  upon  the  "economic 
performance  of  the  engine,  hence  it  is  not  necessarily  the  same  in 
different  plants. 

270.  Proportioning  the  Boiler  for  Power  Output,     (a)  The 

American  Society  of  Mechanical  Engineers  has  made  the  follow- 
ing recommendation  regarding  boiler  ratings.  "  A  boiler  rated 
at  any  stated  capacity  should  develop  that  capacity  when  using 
the  best  coal  ordinarily  sold  in  the  market  where  the  boiler  is 
located,  when  fired  by  an  ordinary  fireman,  without  forcing  the 
fires,  while  exhibiting  good  economy.  And  further,  the  boiler 
should  develop  at  least  one-third  more  than  the  stated  capacity 
when  using  the  same  fuel  and  operated  by  the  same  fireman, 
the  full  draft  being  employed  and  the  fires  being  crowded,  the 
available  draft  at  damper,  unless  otherwise  understood,  being 
not  less  than  one-half  inch  water  column."*  Boilers  of  the 
commercial  types  generally  have  overload  capacity  considerably 
in  excess  of  the  33^  per  cent  here  specified.  Some  boilers  are 
being  operated  continuously  under  loads  double  those  for  which 
they  were  originally  intended,  and  triple  outputs  have  been 
obtained  in  a  few  instances. 

(b)  The  total  amount  of  heating  surface  needed  by  boilers 
can   be   determined   either   by   multiplying   the   boiler   "  horse 
power  "  by  the  number  of  square  feet  needed  for  developing 
one  horse  power,  or  by  dividing  the  total  equivalent  evaporation 
per  hour  by  the  allowable  rate  of  evaporation  per  square  foot. 

(c)  Most  stationary  boilers  of  the  "water  tube"  type  have 
10  square  feet  of  heating  surface  per  boiler  horse  power  under 
normal  load,  the  corresponding  rate  of  equivalent  evaporation 
per  square  foot  per  hour  being  about  3^  ( =  34.5  -*-  IO)  J   while 
the  more  common  types  of  stationary  "  fire  tube  "  boilers  usually 
have  12  or  more  square  feet  per  boiler  horse  power,  the  equivalent 
evaporation  being  3  pounds  per  square  foot  or  less.     However 
values  both  larger  and  smaller  than  these  are  sometimes  used. 

*  Trans.  A.  S.  M.  E.    1899. 


564  HEAT-POWER  ENGINEERING.- 

When  there  are  limitations  as  to  space  or  weight,  less  heating 
surface  and  higher  rates  of  evaporation  are  used.  For  example, 
in  marine  boilers  from  4  to  8  square  feet  of  heating  surface  are 
provided,  the  corresponding  evaporation  being  from  8  to  4 
pounds  per  square  foot  per  hour,  and  in  some  instances  marine 
boilers  of  the  water  tube  type  have  been  operated  continuously 
with  average  rates  as  high  as  16  pounds.* 

(d)  The  fuel  needed  per  boiler  horse  power  hour  can  be 
readily  determined  by  dividing  34^  by  the  equivalent  evapora- 
tion per  pound  —  or  by  dividing  33,476  by  the  actual  calorific 
value  per  pound  corrected  for  boiler  and  grate  efficiencies. 
Thus  the  combustible  required  per  boiler  horse  power  ordinarily 
ranges  from  3  to  4  pounds  per  hour,  depending  on  the  kind  of 
coal,  and  the  weight  of  coal  is  roughly  from  3.5  to  5  pounds. 

*  Melville,  Engineering  Magazine,  January,  1912. 


CHAPTER  XXXI. 
SUPERHEATERS. 

271.  Advantages  of  Superheating,  (a)  It  has  already  been 
shown  (Sect.  128  and  i8oj)  that  the  water  rates  of  steam  engines 
and  turbines  may  be  materially  improved  by  the  use  of  super- 
heat, but  that  the  improvement  in  steam  consumption  is  not  a 
correct  measure  of  the  gain  effected,  since  one  pound  of  super- 
heated steam  contains  more  heat  than  an  equal  weight  of  satu- 
rated steam  at  the  same  pressure.  Leaving  out  of  consideration, 
for  the  time  being,  certain  incidental  advantages  of  superheating, 
the  true  measure  of  gain  is  on  the  basis  of  the  heat  economy 
resulting  from  its  use  and  this  is  given  by  the  ratio  of  the  number 
of  heat  units  supplied  to  the  superheated  steam,  per  horse  power 
delivered  by  the  engine  or  other  prime  mover,  to  that  used  when 
saturated  steam  is  the  working  substance. 

(b)  In  addition  to  such  gains  as  may  be  effected  in  the  prime 
movers  themselves  by  the  use  of  superheat,  there  may  be  a  two- 
fold reduction  in  the  heat  lost  in  the  connecting  pipe  lines,  be- 
cause (i)  superheated  steam  loses  heat  much  less  rapidly  than 
does  wet  steam  and  because  (2)  the  radiating  surfaces  of  the 
pipes  may  be  made  less  —  for  smaller  pipes  can  be  used,  as  super- 
heated steam  may  be  allowed  to  flow  at  higher  velocities  than 
are  permissible  with  saturated  vapor. 

(c)  But    the   ultimate  test  of   the  advisability  of   installing 
additional  apparatus,  such  as  superheaters,  is  always  on  the 
basis  of  the  financial  economy  effected.     In  the  case  in  question 
the  addition   of  the  superheaters  may  not  increase  the  total 
expense  for  the  power  plant  equipment,  for  the  improvement 
in  heat  economy  may  permit  a  reduction  in  the  size  and  cost  of 
the  boilers,  and  the  diminution  of  the  water  rates  may  make 
possible  a  decrease  in  the  size  and  cost  of  the  condensers  and 
other  auxiliary  apparatus.     Then,  the  operating  expenses  may 
be  reduced  not  only  by  the  saving  in  the  expenditure  for  fuel  but 
also  by  the  reduction  in  the  outlay  for  purchasing  and  pumping 

565 


566  HEAT-POWER  ENGINEERING 

the  water  used  for  feed  and  for  condensation.  To  offset  the  gains 
is  the  additional  expense  involved  in  the  operation  and  mainte- 
nance of  the  superheaters.  The  use  of  the  smaller  pipe  lines,  which 
are  permissible  with  superheated  steam,  may  not  effect  a  saving 
in  their  cost,  as  the  materials,  construction  and  fittings  must  be 
of  better  quality  than  is  required  when  saturated  steam  is  used. 

272.  Types  of  Superheaters,  (a)  There  are  two  general 
types  of  superheaters — (i)  separately  fired  superheaters,  and 
(2)  built  in,  or  boiler  draft  superheaters. 

The  first  class  is  installed  in  a  separate  setting  of  its  own  and 
receives  hot  gases  from  its  own  furnace.  The  second  class  is 
located  inside  of  the  boiler  setting  and  in  line  with  one  of  the 
•"  passes  "  of  the  products  of  combustion. 

(b)  In  each  type  the  saturated  steam,  generally  containing 
from  2  to  4  per  cent  of  moisture,  is  led  from  the  steam  nozzle  on 
the  drum  of  the  boiler,  through  the  superheating  apparatus  on 
its  way  to  the  steam  consumer. 

(c)  Superheaters  of  both  types  generally  consist  of  a  multi- 
plicity of  elements  containing  a  small  volume  but  exposing  a 
relatively   great   surface.      There  are,  however,  several    super- 
heaters in  which  a  few  very  large  elements  are  so  constructed 
that,   by  means  of  baffles  or  equivalents,   the  steam   flowing 
through  them  is  divided  up  into  thin  streams  in  contact  with 
extended  wall  areas. 

(d)  Generally  the  metal  used  is  mild  steel,  and  the  elements 
are  composed  of  seamless  tubes  which  are  of  small  diameter 
(i   inch  to   ij  inch   bore)   with  thick  walls   (0.15  to  0.2   inch 
thick)  and  which  are  connected  with  built-up,  forged,  or  cast  steel 
headers  or  their  equivalents.     In  a  few  instances  cast-iron  ele- 
ments with  comparatively  thick 
walls  are  still  used,  but  there  is 
a  growing  tendency  to  look  with 
suspicion  on  the  use  of  this  ma- 
terial in  cases  where  temperatures 
and  pressures  are  high  and  where 

Fig.  368.  temperature  changes  are  great. 

Figs.  368  and  369  show  the  two 

elements  most  commonly  used  in  this  country.     Instead  of  hav- 
ing the  tube  ends  enter  separate  headers,  they  are  sometimes 


SUPERHEATERS  567 

connected  with  a  single  one  arranged  with  suitable  partition 
plates  or  baffles.  The  element  shown  in  Fig.  369  has  a  thin 
annular  steam  passage  between  a  sealed  inner  tube  and  an  outer 
one  which  is  surrounded  by  flanges.  The  flanges,  which  are  of 
cast  iron,  present  large  heat-absorbing  surfaces  to  the  hot  gas, 
protect  the  steel  tubes  and  store  heat,  but  add  to  the -expense  of 
construction.  The  steam  is  brought  intimately  into  contact  with 
the  walls  of  the  larger  tube,  since  it  can  flow  through  the  thin 
annular  passage  only. 

(e)  Experience  has  shown  that  the  ideals  to  be  attained  in 
superheater  construction  and  arrangement  are:  (i)  perfect  free- 
dom of  expansion;  (2)  ability  to  withstand  high  temperature, 
high  pressure,  and  violent  changes  in  temperature;  (3)  avoid- 


Fig.  369- 

ance  of  screwed  joints;  (4)  the  protection  of  all  joints  from  ex- 
posure to  the  hot  gases;  (5)  provision  for  cleaning  externally 
and  internally;  (6)  means  for  adjusting  the  superheat  to  any 
desired  temperature;  (7)  natural,  or  automatic,  regulation  to 
maintain  that  temperature;  (8)  means  of  bypassing  the  steam 
around  the  superheater  when  the  latter  is  out  of  commission; 
(9)  provision  for  flooding  the  elements  (in  some  cases)  with  water 
and  for  draining  them;  (10)  small  space  requirements;  (n)  low 
first  cost;  and  (12)  small  expense  of  operation  and  maintenance. 

273.  Separately  Fired  Superheaters,  (a)  Two  examples  of 
separately  fired  superheaters  are  illustrated  in  Figs.  370  and  371. 
In  all  such  apparatus  it  is  nearly  always  necessary  to  prevent  the 
flame  and  very  hot  gases  from  impinging  directly  on  the  super- 
heating surface,  it  being  generally  considered  that  temperatures 
of  from  1300  to  1500°  are  the  highest  allowable  for  the  gases 
which  are  in -contact  with  such  surfaces;  hence,  the  use  of  inter- 
cepting brick  arches  and  walls  through  which  the  hot  gases  must 


568 


HEAT-POWER  ENGINEERING 


pass,  as  shown  in  Fig.  370,  though  a  greater  degree  of  security 
is  attained  by  combining  a  water  element  with  these  walls,  as 
shown  in  Fig.  371- 

(b)  The  temperature  of  superheat  may  be  controlled  directly 
by  varying  the  rate  of  combustion,  by  means  of  a  damper,  as  in 
Fig-  37 J I  by  bypassing  the  gases,  or  by  .both  of  these  methods, 
as  in  Fig.  370.  But  even  if  the  dampers  be  made  to  normally 
follow  the  delivery  temperature  exactly,  as  can  be  done  by 
means  of  thermostatic  control,  the  heat  stored  in  the  walls  of 
the  setting  will  cause  an  abnormal  rise  of  temperature  when  the 


Fig.  370. 

demand  for  steam  suddenly  decreases  to  any  considerable  extent. 
Then  there  may  also  be  sudden  drops  in  the  temperature  due 
to  the  inflow  of  cold  air  when  the  furnace  doors  are  opened  for 
firing. 

(c)  Compared  with  the  built-in  type,  the  separately  fired 
superheater  has  many  disadvantages,  of  which  the  principal  ones 
are:  (i)  Greater  first  cost  because  of  the  separate  setting  and 
grate;  (2)  larger  maintenance  cost  because  of  separate  setting; 
(3)  greater  cost  of  operation  because  of  separate  furnace  to  be 
fired;  (4)  greater  floor  space  occupied;  (5)  grate  losses,  which 
in  this  case  are  added  to  those  of  the  boiler;  (6)  lower  efficiency 
because  the  flue  gas  enters  the  stack  at  a  temperature  which 
must  be  higher  than  with  built-in  type,  where  superheater  is 
followed  by  water  heating  surface;  (7)  greater  radiation  loss 


SUPERHEATERS  569 

because  of  individual  setting;  and  (8)  difficulty  of  controlling 
temperature  of  steam,  as  explained  in  (b)  above.  The  separately 
fired  superheater  has  the  advantage  that  the  boilers  can  still  be 
used  to  supply  saturated  steam  even  when  the  superheater  is  out 
of  commission;  that  it  permits. the  variation  in  the  degree  of 
superheat  to  be  made  independently  of  the  operation  of  the 
boiler,  and  one  superheater  can  be  used  for  several  boilers. 

(d)  Although  it  has  many  disadvantages,  the  separately 
fired  apparatus  may  be  of  value  in  many  instances.  In  some 
plants,  steel  mills  for  instance,  there  are  often  large  quantities 
of  hot  gases  which,  by  such  apparatus,  can  be  used  to  superheat 
the  steam  coming  from  the  boilers,  but  which  would  otherwise 


Fig.  371. 

be  wasted.  Then,  there  are  also  many  industries  in  which  steam 
exhausted  from  engines  is  used  in  some  manufacturing  process, 
and  in  many  such  cases  it  is  desirable  to  superheat  this  steam  in 
separately  fired  superheaters.  Again,  either  as  a  means  of  im- 
proving the  economy  or  of  increasing  the  capacity  of  a  boiler 
plant  already  installed,  it  may  be  desirable  to  superheat  the 
steam  generated,  and  in  such  cases  it  will  generally  appear  upon 
investigation  that  the  separately  fired  unit  is  the  better  invest- 
ment, as  it  will  involve  least  changes  in  piping  and  settings. 

274.  Boiler  Draft  Superheaters,  (a)  Examples  of  this  type 
are  illustrated  in  Figs.  372  to  374.  In  nearly  all  cases 
built-in  superheaters  are  installed  at  such  a  point  in  the  flues,  or 
gas  passes,  that  the  temperature  of  the  gas  reaching  them  can 
never  greatly  exceed  about  1500°  F,  There  are  a  few  instances, 


570 


HEAT-POWER  ENGINEERING 


however,  as  in  Fig.  372,  in  which  the  superheaters  are  installed 
in  a  separate  brick  chamber  within  the  boiler  setting  and  are 
supplied  with  hot  gases  directly  from  the  furnace,  by  means  of  a 

passage  in  the  brick  walls 
of  the  boiler  setting,  the 
flow  of  gas  being  controlled 
by  a  damper  in  the  passage, 
(b)  Two  distinctly  dif- 
ferent methods  of  main- 
taining an  approximately 
constant  temperature  of 
superheat  are  in  use.  In 
one,  the  superheating  ele- 
ments are  located  at  such 
a  point  (as  in  Fig.  373)  that 
the  gases  reaching  them 
vary  in  temperature  and  quantity  as  nearly  as  possible  in  propor- 
tion to  the  amount  of  steam  flowing.  The  attainment  of  such 
conditions  is  generally  more  ideal  than  real,  but  is  fairly  well 
approximated  in  a  few  instances,  since  the  amount  of  steam  gen- 

Safety  V'al 


Fig.  372. 


Drain 

Valve 


Gases 
from  Furnaces 


Fig.  373- 


erated  depends  directly  on  the  quantity  and  temperature  of  the 
gases  coming  from  the  furnace. 

In  the  other  method  the  superheating  elements  are  installed 
within  a  separate  chamber,  as  in  Figs.  372  and  374,  and  a  damper, 
which  regulates  the  supply  of  hot  gases,  is  put  under  some  sort 
of  control,  which  may  be  thermostatic.  These  superheaters 
have  a  certain  temperature  lag,  as  do  the  separately  fired  variety, 


SUPERHEATERS 


571 


but  it  is  not  as  great  as  in  that  case  because  of  the  smaller  amount 
of  brickwork  surrounding  them. 

275.  Protection  of  Superheater,  (a)  No  superheater,  no 
matter  what  its  construction,  will  last  for  any  considerable 
length  of  time  if  exposed  to  the  hot  furnace  gases  when  steam 
is  not  flowing  through  it.  To  prevent  damage  in  this  way, 
during  the  period  of  firing  up  and  when  cooling  down  or  standing 
idle,  some  protective  device  is  essential. 

(b)  With  separately  fired  superheaters  the  hot  gases  may  be 
deflected,  as  in  Figs.  370,  372,  and  374,  so  that  they  bypass  the 
superheater  and  flow  directly  from  the 

furnace  to  the  stack,  or  protecting  rings 
like  those  in  Fig.  369  may  be  used,  or 
provision  may  be  made  for  "  flooding  " 
the  superheater  —  that  is,  filling  it  with 
water  whenever  the  flow  of  steam 
ceases.  The  latter  method  is  open 
to  the  objection  that  scale-forming 
material  may  be  deposited  in  the 
superheater,  thus  decreasing  its  ability 
to  transfer  heat  from  gases  to  steam, 
which  would  ultimately  result  in  main- 
taining the  metal  of  the  superheater  at 
too  high  a  temperature"  when  in  opera- 
tion and  thereby  shortening  its  life. 

(c)  When  boiler  draft  superheaters 

are  located  in  a  separate  chamber  within  the  boiler  setting,  either 
of  the  above  methods  may  be  used,  but  the  objection  to  the  last 
holds  equally  well  for  this  case. 

(d)  When  boiler  draft  superheaters  are  located  directly  in  one 
of  the  passes  the  most  customary  method  of  protecting  is  by 
flooding.     They  are  generally  so  arranged  (as  in  Fig.  373)  that 
when  flooded  they  form  part  of  the  boiler  evaporating  or  heating 
surface,  practically  being  connected  in  parallel  with  it,  but  so 
that  they  can  be  drained  and  connected  in  series  with  the  boiler 
when  superheat  is  desired. 

(e)  In  connection  with  this  latter  arrangement,  an  auxiliary 
safety  valve  is  sometimes  placed  between  the  superheater  and 
the  main  stop  valve,  so  that  if  this  latter  valve  is  suddenly  closed, 


Fig.  374- 


572  HEAT-POWER  ENGINEERING 

or  if  the  demand  for  steam  suddenly  ceases,  before  the  fires  can 
be  deadened,  the  rising  pressure  of  steam  will  pop  this  safety 
valve  (before  the  main  safety  valve  opens),  and  allow  steam  to 
pass  through  the  superheater,  thus  protecting  it  temporarily 
and  warning  the  attendant  of  the  necessity  for  checking  the  fire 
and,  possibly,  for  flooding  the  apparatus. 

276.  Superheater  Surface,  (a)  The  determination  of  the 
amount  of  surface  required  by  a  superheater  to  give  a  definite 
degree  of  superheat,  when  fired  in  a  certain  way,  or  located  in  a 
given  position,  is  largely  a  matter  of  experience  with  each  manu- 
facturer of  each  different  type  of  boiler.  There  are  several 
distinct  methods  of  approximating  the  amount  of  super-heating 
surface  required ;  the  three  most  common  are  given  below. 

(b)  The  superheating  surface  may  be  taken  as  a  multiple  of 
the  grate  surface.     Thus  for  water  tube  boilers,  the  heating  sur- 
face of  built-in  superheaters  is  generally  taken  at  from  8  to  12 
times  the  grate  area,  depending  upon  location  within  the  setting, 
average  rate  of  firing,  superheat  desired,  character  of  coal,  etc. 
With  long  flaming  coals  the  gases  often  arrive  at  the  superheater 
at  a  higher  temperature  than  with  short  flaming  fuels  and  a 
smaller  surface  may  therefore  be  used. 

For  internally  fired  boilers,  values  between  25  and  35  times 
the  grate  area  are  used. 

(c)  The  superheating  surface  may  be  taken  as  a  fraction  of  the 
boiler  heating  surface.     For  water  tube  boilers  it  varies  between 
10  and  40  per  cent  of  the  boiler  heating  surface,  though  it  rarely 
exceeds  20  to  30  per  cent.     For  internally  fired  boilers  a  greater 
ratio  is  required,  reaching  in  some  cases  to  values  almost  equal  to 
the  boiler  heating  surface,  and  seldom  dropping  below  50  per 
cent  of  that  surface. 

(d)  The  number  of  square  feet  of  superheating  surface   (S) 
required  may  be  determined  by  calculations,  taking  account  of 
rate  of  heat  transmission  per  square  foot  per  hour,  which  depends 
both   on   the  coefficient   (K)   of    heat   transmission   and   mean 
temperature  difference  (0OT)  between  steam  and  gases.     In  this 
case,  the  heating  surface  required  to  transmit  per  hour  an  amount 
of  heat  equal  to  AQ  is 


SUPERHEATERS 


573 


The  coefficient  (K)  is  the  heat  (B.t.u.)  transmitted  per  square 
foot  of  surface,  per  degree  difference  of  temperature,  per  hour. 
Its  value  varies  widely  with  conditions  and  is  found  by  experi- 
ment or  experience.  High  velocity,  thin  streams  of  steam  or 
gas,  violent  agitation,  and  high  temperature  and  pressure,  in- 
crease its  value.  The  condition  of  the  superheater  also  has 
considerable  effect;  when  scaled  internally  and  covered  with 
ash  and  soot  externally,  the  rate  of  transmission  is  very  low. 

In  general,  values  of  K  vary  from  I  to  as  high  as  10,  and  con- 
siderable experience  is  required  in  choosing  a  proper  value. 


CHAPTER  XXXII. 
DRAFT  AND  DRAFT  APPARATUS. 

277.  General  Principles,  (a)  The  flow  of  air  and  products 
of  combustion  through  the  steam-generating  apparatus  is  re- 
tarded by  the  resistances  encountered  in  the  various  portions  of 
the  passage.  The  total  resistance  (R),  from  the  point  where  the 
air  enters  the  boiler  setting  to  the  base  of  the  stack,  is  the  sum- 
mation of  the  resistances  of  the  fuel  bed  (Rf),  of  the  boiler  passages 
(Rp),  of  the  flues  or  breeching  (Rb)  and  of  any  other  passages  (Rx) 
(such  as  that  through  an  "economizer")  which  are  traversed. 
Thus  R  =  Rf  +  RP  +  Rb  +  RX-  It  is  of  course  desirable  to  have 
the  total  resistance  as  small  as  possible,  hence  each  component 
resistance  should  be  reduced  to  the  fullest  extent  allowable. 

(b)  As  the  gases  flow  only  from  places  of  higher  pressure  to 
those  of  lower  (through  a  process  of  expansion)  the  gas  pressures 
must  decrease  progressively  from  the  point  of  entrance  to  the 
point  of  exit,  the  pressure  drops  through  the  different  portions 
depending  on  the  respective  resistances  of  the  parts. 

The  way  in  which  the  pressure  varies,  as  the  particles  of  gas 
advance  through  the  steam-generating  apparatus,  is  shown  in  a 
general  way  in  Fig.  375  by  the  curve  abed,  in  which  the  abscissas 
represent  the  decrease  of  pressure  below  that  at  the  point  of 
admission  and  the  ordinates  are  distances  along  the  passage, 
measured  from  the  same  point. 

Evidently,  the  same  curve  would  apply  (in  this  particular 
case)  regardless  of  whether  the  inlet  pressure  is  atmospheric,  or 
greater  or  less  than  that,  for  the  same  pressure  drops  and  the 
same  gradients  to  the  curve  would  still  be  required.  The  differ- 
ence between  the  abscissas  of  any  two  points  on  this  curve  gives 
the  pressure  drop  required  to  overcome  the  resistance  between 
the  corresponding  points  in  the  apparatus.  The  final  abscissa 
represents  the  pressure  drop  developed  through  the  whole  ap- 
paratus, and  is  evidently  equal  to  the  summation  of  all  the 
oressure  drops,  i.e.,  AP=  AP/  +  APP  +  AP6  +  APX,  in  whicl 

574 


DRAFT  AND  DRAFT  APPARATUS 


575 


Manometer 


Fig-  375- 


the  subscripts  refer  to  the  same  parts  as  before.  It  is  the  func- 
tion of  the  stack,  or  other  draft-producing  device,  to  develop  this 
difference  in  pressure. 

(c)  As  the  pressure  variations  of  the  flue  gas,  measured  from 
atmospheric  pressure,  are  very  low,  they  are  ordinarily  deter- 
mined by  means  of  water  manom- 

eters, as  shown  in  Fig.  375,  and  are 
therefore  commonly  expressed  in 
terms  of  inches  of  water  column 
("  hydraulic  inches  ")  as  compared 
with  atmospheric  pressure.* 

The  total  pressure  drop  from  air 
inlet  to  base  of  stack  is  generally 
between  0.4  and  1  .2  inches  of  water 
when  determined  in  this  way. 

The  velocity  of  flow  is  generally 
so  small  that  the  velocity  head  can  «J 
be  neglected  in  the  ordinary  prob- 
lems that  arise  in  connection  with 
the  subject  under  discussion. 

(d)  According  to  Bernoulli's  theorem  (which  can  be  applied  to 
the  steady  and  continuous  flow  of  gases  in  long  pipes  when  there 
are  small  pressure  drops)  ,  the  total  head  is  the  same  at  all  points 
in  the  passage.     At  the  point  (o)  of  entrance  it  is  the  sum  of  the 

©tP\ 
,  the  pressure  head  (  —    ,  and  the  potential 
o  Wo 

head  z0;    and  at  any  subsequent  point  (x)  it  is  the  sum  of  the 

similar  heads  for  that  point  together  with  friction  head  F  of  the 
intervening  passage.  Thus 

,     .    .    (408) 

in  which  v  =  velocity  of  flow  in  feet  per  second, 
P  =  pressure  in  pounds  per  square  foot, 
d  =  specific  density  =  weight  per  cubic  foot  of  gas,  and 
z  =  elevation  in  feet. 
The  friction  head  (ft.)  is 

F=ffgLxj  ......  (4°9) 


*  One  inch  of  water  column  corresponds  to 


5.2  pounds  per  square  foot; 


or  one  pound  per  square  foot  corresponds  to  .192  inches  of  water  column, 


576  HEAT-POWER  ENGINEERING 

in  which  L  =  length  of  flue  in  feet, 
/  =  coefficient  of  friction, 

5  =  length  of  perimeter  of  the  cross-section  in  feet, 
A  =  area  of  passage  in  square  feet, 

and  the  ratio  A/S  is  called  the  "  mean  hydraulic  radius.11 

In  the  passages  through  the  boiler  the  variation  in  velocity  and 

in  elevation  can  ordinarily  be  neglected,  hence  the  quantities  v 

and  z  disappear  from  Eq.  (408)  in  this  case. 

Then  from  Eqs.  (408)  and  (409)  ,  using  a  mean  density  dm  and 

letting  AP  =  (P0  —  Px),  the  change  in  pressure  head  is 


which  shows  that  the  pressure  drop  is  dependent  solely  on  the 
frictional  resistance,  which  varies  directly  with  v2,  L  and  the 
character  of  the  surfaces  and  inversely  with  the  mean  hydraulic 
radius  (A/S). 

The  velocity  of  flow  is,  from  Eq.  (410), 

.     .     .'.     (411) 


and  for  any  given  passage 

v  =  const  VAP  .........     (412) 

Evidently  the  rate  of  combustion,  which  is  dependent  on  the 
velocity  (amount)  of  the  air  passing  through  the  fuel  bed,  can  be 
reduced  by  decreasing  A  in  Eq.  (411),  other  things  remaining 
the  same,  as  by  partly  closing  the  damper. 

(e)  But  in  the  actual  case  of  flow  of  gases  through  steam-gen- 
erating apparatus,  the  conditions  are  quite  different  from  the 
hypothetical  ones  assumed  in  connection  with  Bernoulli's  The- 
orem, —  for,  through  part  of  the  passage  there  is  air  of  a  certain 
density,  through  the  rest  is  a  complicated  mixture  of  gases 
varying  as  to  composition,  density  and  temperature  ;  the  passages 
are  circuitous,  have  sudden  changes  in  areas  and  in  direction 
and  have  eddy  pockets;  the  resistance  through  the  fuel  bed  is 
constantly  varying  and  the  flow  of  gas  is  neither  steady  nor 
necessarily  continuous,  —  hence,  the  analysis  of  the  laws  gov- 
erning the  actual  case  is  difficult  and  as  yet  these  laws  are  not 
well  established. 

There  are,  however,  a  few  general  statements  which  can  be 
made  and  which  are  more  or  less  applicable  to  most  cases;  they 


DRAFT  AND  DRAFT  APPARATUS  577 

may  serve  as  rough  guides  in  approximating  the  solution  of 
problems  connected  with  boiler  draft.*  These  are  given  in  the 
following  paragraphs. 

(f)  Other  conditions  remaining  the  same  (temperatures,  re- 
sistances, etc.),  the  weight  (w)  of  air  entering  the  furnace  in  a 
unit  of  time  is  dependent  on  the  velocity  of  flow,  arid  appears 
to  vary  about  as  the  square  root  of  the  pressure  drop  (AP) 
through  the  passages,  f     As  the  rate  of  combustion  (R)  is  directly 
dependent  on  the  air  supply  it  varies  approximately  in  like  man- 
ner, i.e.,  R  =  const.  VAP,  where  the  constant  varies  with  the 
size  and  kind  of  coal,  method  of  firing  and  other  conditions. 
Thus,  doubling  the  pressure  drop  increases  the  rate  to  about 
1.4  (=V2)  its  former  value;   and  to  burn  fuel  twice  as  rapidly 
as  before  involves  nearly  quadrupling  the  draft  pressure. 

(g)  It  is  also  approximately  true  that  if  the  resistances  remain 
unchanged,  the  pressure  drop  through  any  portion  of  the  passage 
will  remain  the  same  fraction  of  the  total,  regardless  of  the  vari- 
ation in  the  over-all  drop,  that  is,  the  pressure  gradients  would 
vary    proportionally.     For    example,   for    the    case    shown    in 
Fig.  375,  with  change  in  draft,  the  curve  would  merely  be  re- 
plotted  with  all   abscissas  changed  proportionally  to  the  varia- 
tion in  the  over-all  drop,  or  the  same  curve  could  be  used  with 
suitable  change  in  scale. 

(h)  The  resistances  encountered  vary  about  as  the  square  of 
the  velocity  (as  in  Eq.  409),  although  probably  the  exponent 
should  be  slightly  less  than  2,  say  1.8.  Hence,  doubling  the 
velocity,  to  obtain  a  twofold  rate  of  combustion,  necessitates 
about  four  times  as  intense  a  draft,  and  nearly  four  times  as  much 
work  will  be  done  in  moving  the  gases. 

(i)  As  the  power  is  the  product  of  resisting  force  by  the  velocity 
of  motion,  the  amount  required  for  removing  the  gases  varies 
about  as  the  cube  of  the  velocity  of  flow,  i.e.,  as  the  cube  of 
the  amount  of  air  supplied,  or  as  the  cube  of  the  rate  of  combus- 
tion. Thus,  in  order  to  double  the  rate  of  combustion,  or  boiler 
output,  the  draft-producing  apparatus  would  have  to  do  nearly 
eight  times  as  much  work.  Therefore,  while  from  the  stand- 
point of  space  occupied  by  the  boiler  it  may  be  desirable  to 

*  Bull.  21,  U.  S.  Bureau  of  Mines,  "Significance  of  Drafts,"  contains  discussions 
of  experiments  on  draft. 

t  Thus  it  follows  approximately  Eq.  (412). 


578 


HEAT-POWER  ENGINEERING 


force  the  rate  of  combustion  as  much  as  possible,  the  additional 
expense  for  power  and  apparatus  for  handling  the  gases  with 
greater  velocity  places  a  limit  beyond  which  it  is  financially 
unprofitable  to  go. 

278.  Amount  of  Pressure  Drop  Required,  (a)  The  pressure 
drops  (hf  inches  of  water)  generally  needed  for  overcoming  the 
resistance  through  the  fuel  bed  have  already  been  given  in  Fig. 
326  for  the  different  rates  of  combustion  of  several  sizes  of 
various  kinds  of  coal  when  burned  under  the  usual  conditions. 
But  much  variation  from  these  curves  exists,  since  the  intensity 
of  draft  depends  also  on  the  thickness  of  the  fuel  bed,  character 
of  the  ash  and  clinker,  method  of  firing  and  other  items. 

(b)  The  drop  in  pressure  (hp  inches  of  water)  through  the 
boiler  passages  depends  on  the  length  and  cross  sections  of  pas- 
sages, arrangement  of  baffles,  arrangement  of  tubes,  etc.  Under 
ordinary  rates  of  combustion  it  ranges  as  in  Table  XXIV  and 
varies  about  as  the  square  of  the  rate  of  combustion  (as  explained 
in  Sect.  277  (f))  when  operating  at  greater  or  lower  rates. 

TABLE  XXIV.  — PRESSURE  DROPS  THROUGH  BOILERS.* 


B.  and  W.  — double  deck 0.4  in. 

B.  and  W.  — standard 0.3  " 


Stirling  or  Heine .......      0.2  in. 

Return  Tubular. .  o.i  " 


(c)  To  overcome  the  resistance  of  the  breeching,  or  flues,  be- 
tween the  boiler  and  the  stack,  a  pressure  drop  (hb)  of  about  TV 
inch  of  water  is  generally  assumed  per  100  feet  of  length  of  smooth 
round  passage  when  the  boilers  are  being  forced,  and  half  as 
much  for  each  elbow,  though  much  depends  on  the  mean  hy 

draulic  radius  f -=J  of  the  passage,  on  the  curvature  of  the  bends, 

character  of  wall  surface,  etc. 

It  would  of  course  reduce  the  cost  of  the  breeching  if  small  cross 
sections  and  high  velocity  of  flow  were  used.  But  since  the  re- 
sistance varies  as  the  square  of  the  velocity,  greater  draft  would 
then  be  needed  to  overcome  it,  and  this  would,  in  general,  add 
to  the  expense  for  the  stack  (or  other  draft-producing  apparatus) 
an  amount  greater  than  the  saving  effected  in  outlay  for  the 
breeching.  Hence,  the  breeching  is  usually  given  a  liberal  cross 
sectional  area,  one  at  least  equal  to  that  of  the  stack  and  gener- 
*  Kingsley,  Eng.  Record,  Dec.  21,  1907. 


DRAFT  AND  DRAFT  APPARATUS          579 

ally  20  per  cent  greater,  the  velocity  of  flow  being  not  more  than 
that  in  the  stack,  and  generally  about  20  per  cent  less. 

(d)  The  total  pressure  drop  (hi)  inches  of  water  between  air 
inlet  and  base  of  stack  evidently  equals  the  sum  of  the  drops 
through   these   various   elements   of    the   passage   and   of    any 
others,  such  as  those  through  economizers,  which  mayt>e  located 
between  the  boiler  and  stack.     Thus   hi  =  h/  +  hp  +  hb  -f-  hx. 
The  draft-producing  apparatus  should  of  course  be  proportioned 
to  give  a  pressure  drop  at  least  sufficient  to  cause  the  greatest 
rate  of  combustion  that  will  ever  be  demanded  with  the  poorest 
fuel  which  is  likely  to  be  used ;  then,  smaller  rates  can  be  obtained 
by  reducing  the  amount  of  air  supplied,  which  can  be  done  by 
regulating  the  dampers  and  air  inlets  either  by  hand  or  by  some 
automatic  device,  the  latter  being  generally  operated  by  the 
slight  variations  in  steam  pressure  which  accompany  the  changes 
in  the  demand  for  steam. 

(e)  The  current  of  gases  through  the  boiler  can  be  caused 
either  by  "natural"  draft  of  a  chimney  (or  stack),  or  by  "arti- 
ficial "  draft  maintained  either  by  steam  jets  or  by  power-driven 
fans. 

The  duty  of  the  draft-producing  apparatus  is  twofold  — 
first,  it  must  produce  the  needed  intensity  of  draft  and,  second, 
it  must  provide  means  for  carrying  off  the  products  of  combustion. 

279.  Chimney  Draft,  (a)  When  one  pound  of  carbon  is  com- 
pletely burned  in  air  to  CO 2,  the  latter  gas  will  have  the  same 
volume  at  the  same  temperature  and  pressure  as  did  the  oxygen 
with  which  the  carbon  united  (in  accordance  with  Sect.  238  (a)) ; 
but  the  resulting  flue  gas  will  have  one  pound  more  material 
than  was  in  the  air  which  supplied  the  oxygen.  Thus,  for  ex- 
ample, if  the  excess  coefficient  is  two,  24  pounds  of  air  with 
specific  density  =  .0807  *  are  supplied  for  the  complete  combus- 
tion of  one  pound  of  carbon  and  there  will  result  25  pounds  of 
gas,  which  will  have  a  specific  density  *  of  (f|)  X  .0807  =  .084. 
Hence  the  weight  of  a  column  of  air  one  foot  high,  at  sea  level 
and  at  temperature  /a°F.,  is 

D  =  (.0807  X  492)  ^  (ta  +  460),    .     .     .     (413) 

*  Pounds  per  cubic  foot  at  32°  F.  (or  492°  Absolute)  and  under  14.7  pounds 
square-inch  pressure  (measured  at  sea  level). 


58o 


HEAT-POWER  ENGINEERING 


and  that  of  a  similar  column  of  flue  gas,  with  excess  coefficient 
equal  to  two  and  with  temperature  ta°  F.,  is 

d  =  (.084  X  492)  •*•  (ta  +  460).    ',     .     .     (414) 

(b)  In  Fig.  376  (a)  the  intensity  of  pressure  exerted  on  the 
side  of  the  partition  X  by  the  column  (^4)  of  cold  air  at  tempera- 
ture ta,  and  that  exerted  by  the  equal  column  (G)  of  hot  gas  at 
tg°  F.,  are  respectively,  in  inches  of  water,* 

ha   =    .192  HD    =   7.64  H/(ta  +  460),     .        .        .         (415) 

and  hg  =  .192  Hd  =  7.95  H/(ta  +  460),     .     .     .     (416) 

where  H  is  the  height  of  the  columns  in  feet,  and  D  and  d  have 
the  value?  given  in  Eqs.  (413)  and  (414).     This  is  of  course  on 


(a) 


(6) 


Fig.  376. 

the  assumption  that  equal  pressures  of  air  are  exerted  on  the 
tops  of  these  columns.  The  difference  between  these  pressure 
intensities  on  the  opposite  sides  of  the  partition  is  (at  sea  level) 

=  #/_Zi64  7-95 


=  (ha  - 


(417) 


and,  if  the  partition  is  removed,  this  will  be  the  draft  pressure 
tending  to  cause  the  flow  of  gases  upward  through  column  G. 

(c)  If  means  are  provided  for  maintaining  the  high  temper- 
ature (tg)  in  column  G,  there  will  be  a  constant  flow  of  gases, 
and  as  the  air  in  column  A  is  under  atmospheric  conditions  the 
enveloping  shell  around  that  column  can  be  omitted.  Under 
these  circumstances  the  conditions  are  those  existing  when  a 
*  See  footnote,  page  575. 


DRAFT  AND  DRAFT  APPARATUS  581 

furnace  and  chimney  (stack)  are  in  operation,  as  in  Fig.  376  (b)  ; 
hence  Eq.  (417)  can  be  used  for  obtaining  the  theoretical  draft 
pressure  ht  developed  by  a  stack  of  height  H  feet  when  the  re- 
sistances through  the  stack  are  neglected,  and  it  gives  the  draft 
pressure  that  would  occur  when  the  ash-pit  doors  are  closed  and 
no  gases  are  flowing. 

Then,  the  theoretical  height  (Ht)  of  stack  needed  for  producing 
a  draft  pressure  of  h  inches  of  water  at  its  base  is  (from  Eq.  417) 


at  sea  level  (14.7  Ibs.  per  sq.  in.).     Obviously  Ht  will  vary  with 
changes  in  the  atmospheric  pressure  (barometer). 

(d)  Under  normal  conditions  the  temperature  of  the  flue  gas 
at  the  base  of  the  stack  generally  lies  between  500  and  600°  F. 
in  different  types  of  boilers;  but  if  "economizers  "  are  used,  it 
will  be  less  and  in  some  instances  may  be  reduced  to  300°  F. 
When  the  boilers  are  being  forced  the  temperature  rises  above 
the  normal,  which  helps  to  augment  the  draft.  In  using  Eqs. 
(417)  and  (418)  for  the  draft  and  the  height  of  a  new  stack,  ta 
should  be  taken  as  the  lowest  flue  temperature  and  ta  as  the 
highest  atmospheric  temperature  that  are  liable  to  exist  simul- 
taneously. As  the  gases  become  cooled  in  passing  up  the  stack, 
ta  should  be  the  mean  temperature;  it  is  customary,  however, 
to  use  the  temperature  at  the  base  of  the  stack  and  then  to 
correct  for  the  error,  and  for  the  resistances  within  the  stack, 
by  making  the  actual  height  about  25  per  cent  greater  than  the 
theoretical  one.  The  effects  of  the  column  of  hot  gases  above 
the  stack  and  of  the  wind  are  generally  neglected.  Whether 
the  wind  assists  or  retards  the  draft  depends  on  the  arrange- 
ment of  the  chimney  top. 

In  practice  the  height  of  stack  is  from  80  feet,  with  free  burn- 
ing coals  and  little  resistance,  to  175  feet,  or  more,  with  fine 
anthracite  coal  and  with  considerable  resistance  in  the  passages. 
But  in  settled  districts  the  height  should  always  be  sufficient  to 
satisfactorily  dispose  of  the  obnoxious  gases. 

(e)  The  cross  sectional  area  of  the  stack  should,  of  course,  be 
made  ample  for  accommodating  the  gases  when  the  boilers  are 
forced  to  their  maximum  capacity,  and  in  fixing  the  size  allow- 
ance should  always  be  made  for  any  possible  growth. 


582  HEAT-POWER  ENGINEERING 

Having  found  the  actual  height  of  stack,  it  is  quite  common 
practice  to  compute  the  cross  sectional  area  by  using  Wm.  Kent's 
empirical  formula,  which  was  derived  as  follows:  — 

Assuming  that  the  volume  of  gas  formed  per  hour  is  dependent 
on  the  amount  of  coal  burned,  which  in  turn  is  proportional  to 
the  boiler  horse  power  (BP)  developed,  and  that  the  velocity  of 
flow  varies  as  the  square  root  of  the  height  H  (feet)  of  stack,  it 
follows  that  the  area  is  a  function  of  BP  -r-  \/ET.  Then,  from  an 
analysis  of  numerous  chimneys,  Kent  found  that  the  effective 
area  (E),  in  square  feet,  should  be  about 

VS.     ...   ".     .     (419) 


It  is  also  assumed  that  if  it  is  considered  that  the  chimney  has  a 
two-inch  lining  of  stagnant  gas,  the  flow  through  the  remainder 
of  the  cross  section  can  be  taken  as  being  without  resistance. 
Hence  the  actual  diameter  of  a  circular  chimney  and  the  length 
of  side  of  a  square  one  are  made  four  inches  greater  than  the 
corresponding  dimensions  determined  for  the  effective  area. 

Kent's  proportions  are  liberal  as  they  provide  for  the  com- 
bustion of  about  5  pounds  of  coal  per  B.  P.  -hour,  whereas  not  over 
4  pounds  are  ordinarily  used.  They  allow  for  velocities  of  gas 
through  the  stack  ranging  from  about  20  ft.  /sec.  with  100  feet  of 
height  to  about  30  ft.  /sec.  in  a  2OO-foot  stack. 

(f)  A  more  rational  method  of  determining  the  proportions  of 
a  stack  for  a  given  set  of  conditions  may  be  carried  through  in 
the  following  order: 

1st.  Assuming  from  250  to  300  cubic  feet  of  air  at  60°  F.  as 
the  amount  needed  to  support  the  combustion  of  one  pound  of 
coal,  and  knowing  the  maximum  weight  of  fuel  to  be  consumed 
per  unit  of  time,  compute  the  corresponding  total  volume  of  gas 
at  stack  temperature. 

2d.  Assuming  a  velocity  of  flow  of  from  20  ft.  /sec.,  for  short 
stacks,  to  30  ft.  /sec.,  or  more,  for  very  tall  ones,  compute  the 
effective  cross  sectional  area  needed  to  discharge  this  volume; 
and  then,  allowing  for  a  two-inch  lining  of  stagnant  gas,  deter- 
mine the  final  dimensions  of  the  cross  section. 

3d.  Find  the  loss  of  draft  (h2  inches  of  water)  arising  from  the 
stack  resistances,  which  are  due  to  (a)  change  of  direction  of  the 
gases  upon  entering  the  base  of  the  stack,  (b)  the  skin  friction 
and  (c)  the  displacement  of  the  atmosphere  by  the  issuing 


DRAFT  AND  DRAFT  APPARATUS          583 

stream.     From  Kingsley's  experiments  *  this  loss  for  a  velocity 
v  ft.  /sec.  was  found  to  be  given  approximately  by  the  equation 

h2  =  .00036  1>2  .......     (420) 

4th.    Determine  the  pressure  drop  hi  up  to  the  base  of  the 
stack  and  compute  the  theoretical  height  (Ht)  from  Eq.  (418). 
5th.   Then  find  the  actual  height  (H)  of  stack  from 


(421) 


(g)  By  using  the  higher  velocities,  the  stack  diameter  is  de- 
creased, which  would  result  in  a  reduction  in  the  cost  of  the 
stack  if  other  things  remained  the  same;  but  these  greater 
velocities  necessitate  an  increase  in  the  height  of  stack,  thus  en- 
tailing an  additional  expense  which  either  partly  or  wholly 
offsets  that  saving.  Evidently  for  a  given  set  of  conditions 
there  is  some  velocity  which  will  give  a  proportion  of  height  to 
diameter  requiring  a  minimum  amount  of  material  for  con- 
structing the  stack,  and  hence  involving  the  least  outlay  of 
money. 

(h)  For  rough  estimating  it  can  be  assumed  that  a  loo-foot 
stack  with  gases  at  500°  and  air  temperature  at  70°  will  exert  a 
theoretical  draft  pressure  of  .6  inches  of  water  at  its  base;  that 
the  draft  varies  directly  with  the  height;  and  that  the  effective 
cross  sectional  area  in  square  feet  is  equal  to  the  number  of 
pounds  of  coal  burned  per  minute.  For  ordinary  conditions 
with  bituminous  coal  the  stack  area  is  about  |th  the  grate  area 
and  with  anthracite  coal  about  £th. 

(i)  The  different  parts  of  a  chimney  and  its  foundation  must 
not  only  carry  the  weights  above  but  must  also  withstand  the 
wind  pressure.  Chimneys  are  made  of  (i)  common  brick,  (2) 
radial  brick,  (3)  reinforced  concrete  and  (4)  steel  plates. 

A  comparison  of  Figs.  377  to  380,  which  illustrate  stacks  of 
the  different  types  but  of  the  same  height  and  internal  diameter, 
will  show  roughly  the  relative  thickness,  weight,  extent  of  foun- 
dation and  space  occupied  with  the  various  constructions. 

(j)  If  made  of  ordinary  brick  (Fig.  377)  the  chimney  must  be 
lined  at  least  for  part  of  its  height  with  fire  brick  so  set  as  to 
have  perfect  freedom  to  expand  or  contract  with  temperature 

*  Engineering  Record,  Dec.  21,  1907. 


HEAT-POWER  ENGINEERING 


12' 


-24" 


BRICK  CHIMNEY 
8ft  x  180  ft. 

Fig-  377- 


RADIAL  BRICK 
CHIMNEY 
8  ft.  x  180  ft. 

Fig.  378. 


DRAFT  AND  DRAFT  APPARATUS          585 

changes.  By  using  special  radial  brick  (Fig.  378),  composed  of 
suitable  material,  and  commonly  made  perforated,  (i)  the  lining 
may  be  omitted,  (2)  the  shell  may  be  thinner  and  of  lighter 
weight,  and  (3)  the  foundation  may  be  smaller;  besides  which 
(4)  the  construction  is  better  and  (5)  can  be  more  rapidly  done 
than  with  ordinary  brick.  The  tallest  chimney  in  the  world  is  of 
this  type.  It  is  located  at  Great  Falls,  Mont.,  and  is  506  feet 
high  with  50  feet  diameter  at  the  top. 

(k)  Many  chimneys  are  now  made  of  reinforced  concrete  (Fig. 
379),  the  steel  reinforcing  bars  being  arranged  both  circum- 
ferentially  and  vertically,  the  latter  extending  into  the  founda- 
tion, which  is  similarly  strengthened.  Such  chimneys  are  (i) 
thinner  than  the  brick,  (2)  weigh  less,  (3)  occupy  less  space, 
(4)  require  but  small  foundations,  (5)  are  free  from  joints  and 
(6)  can  be  rapidly  constructed.  The  inner  shell  may  be  either 
of  brick  or  reinforced  concrete  and  in  some  cases  is  entirely 
omitted. 

(1)  In  order  to  withstand  the  wind,  steel  stacks  are  either 
guyed  with  wire  or  wire  rope,  or  else  have  flared  bases  bolted  to 
the  foundation,  in  which  case  they  are  said  to  be  self-supporting. 
They  are  preferably  lined  with  brick  to  protect  the  metal  from 
the  heat  and  corroding  action  of  the  gases.  The  lining  may 
either  be  self-supporting  or  else  be  constructed  in  independent 
sections  each  resting  on  a  bracket  extending  from  the  steel  shell. 
Such  chimneys  are  (i)  of  light  weight,  (2)  easily  and  rapidly 
constructed,  (3)  cost  little,  (4)  occupy  small  space  (except  when 
flared)  and  (5)  are  free  from  air  leakage  if  properly  calked. 
They  must  be  painted  frequently  to  protect  the  metal  from  the 
weather  and  from  the  gases. 

280.  Artificial  Draft,  (a)  In  a  new  power  plant  artificial  draft 
apparatus  is  frequently  employed  as  a  substitute  for  a  tall 
chimney,  or  to  assist  a  short  one,  under  the  following  conditions: 
(i)  when  the  temperature  of  the  stack  gases  is  low,  as  when 
an  economizer  is  used;  (2)  when  the  rates  of  combustion  are 
high;  (3)  when  fuels  requiring  intense  draft  are  to  be  burned; 
(4)  when  certain  stokers,  like  the  underfed,  are  used;  and  (5) 
in  certain  other  cases  where  in  the  long  run  it  may  be  more  de- 
sirable or  more  economical  to  purchase,  operate  and  maintain 
such  apparatus  rather  than  have  a  chimney  of  large  size. 


586 


HEAT-POWER  ENGINEERING 


5" 


Inner 
Shell 


REINFORCED-CONCRETE 
CHIMNEY 
8ft.  xl  180  ft. 

Fig-  379- 


STEEL  I  STACK 
8  ft.  i  180  ft. 

Fig.  380. 


Fig.  381.  —Forced  Draft. 


DRAFT  AND  DRAFT  APPARATUS  587 

In  an  old  plant  it  may  be  desirable  to  install  artificial  draft 
apparatus  (i)  to  assist  the  original  chimney  when  the  plant  has 
been  increased  beyond  the  capacity  of  the  natural  draft;  (2) 
when  it  is  desired  to  adopt  unusual  rates  of  combustion,  or  (3) 
to  burn  fuels  requiring  intense  draft;  (4)  when  there^may  be 
large  emergency  overloads  or  peak  loads  of  short  duration;  and 
(5)  when  there  are  large 
and  sudden  changes  in 
demand  on  the  fur- 
naces. 

(b)  In  addition  to 
its  advantages  in  the 
instances  already  dis- 
cussed, the  artificial 
draft  apparatus  is  (i) 
easily  installed;  (2)  is 
transportable  and  (3) 
occupies  but  little  space;  and  (4)  it  also  permits  of  careful  adjust- 
ment of  the  air  supply,  which  makes  possible  more  perfect  condi- 
tions of  combustion.  The  regulation  of  air  can  be  automatic,  the 
controlling  device  being  operated  by  the  slight  changes  in  steam 
pressure  accompanying  the  varying  demand  on  the  boiler. 

(c)  Artificial  draft  is 
produced  either  by  steam 
jets  or  by  power-driven 
fans,  and  when  developed 
by  the  latter  it  is  generally 
called  mechanical  draft. 

With  forced  draft  (Fig. 
381)  the  ash  pit  is  "  closed" 
(hermetically  sealed)  and 
the  apparatus  supplies  it 
with  air  at  a  pressure 
above  atmospheric  (at  a 
"  plenum  ") ;  with  induced 
draft  (Fig.  382)  the  appa- 
ratus draws  the  gases  from  the  boiler  outlet,  thus  decreasing 
the  pressure  at  that  point  below  atmospheric;  and  with  balanced 
draft  these  two  systems  are  used  in  combination  in  a  manner 
which  will  be  discussed  later, 


Fig.  382.  — Induced  Draft. 


588 


HEAT-POWER  ENGINEERING 


Fig.  383- 


(d)  Fig.  383  shows  one  of  the  many  forms  of  steam  jets  used 
for  forcing  the  draft.     Somewhat  similar  devices  can  be  placed 
in  the  base  of  the  stack  (as  is  universally  done  in  locomotives) 

to  produce  induced  draft.  Such  apparatus  is 
relatively  low  in  first  cost,  but  is  very  wasteful 
of  steam,  using  generally  not  less  than  5  to  8 
per  cent  of  the  total  steam  generated,  and  it 
increases  the  stack  loss  because  of  the  added 
moisture  in  the  flue  gas.  Steam  jets  are  conven- 
ient auxiliaries  for  meeting  sudden  or  abnormal 
demands  on  the  boilers,  and  the  presence  of  the 
steam  in  the  air  supporting  combustion  tends  to 

avoid  the  formation  of  clinkers.     Fig.  384  shows  a  disc  fan  which 

is  used  in  a  similar  manner. 

(e)  With  mechanical  draft,  the  fans  and  their  driving  appa- 
ratus must  be  so  designed  as  not  to  be  affected  by  the  dust,  and 
with  induced  draft  they  must  also  be  suitable  for  handling  the 
hot  gases  without  injury.     If  entire  dependence  is  placed  on  fans 
for  providing  the  draft,  there  should  be  duplicate  (or  auxiliary) 
apparatus  installed  to  avoid  plant  shutdowns 

from  failure  of  the  draft  apparatus.  With 
a  very  short  stack  the  fan  equipment  for 
forced  draft  costs  roughly  from  20  to  30  per 
cent  as  much  as  the  equivalent  brick  chim- 
ney; while  with  induced  draft  the  cost  is 
about  double  that  for  forced  draft  as  a  larger 
fan  ("exhauster")  must  be  used  because  the 
gases  are  at  high  temperature.  But  though 
low  in  first  cost,  such  apparatus  depreciates  rapidly,  involves 
considerable  expense  for  attention  and  maintenance,  and  uses  for 
power  from  ij  to  5  per  cent  of  the  steam  generated. 

(f )  With  forced  draft  the  gas  pressure  within  the  boiler  setting 
is  above  atmospheric,  hence  the  tendency  for  hot  gases  and 
flames  to  issue  through  cracks  in  the  walls  and  also  to  belch 
forth  upon  the  opening  of  the  fire  doors.     To  avoid  the  latter 
occurrence   the  blast  is  shut   off,  usually  automatically,  when 
the  doors  are  opened.*     The  air  should  always  be  introduced 
into  the  ash  pit  in  such  manner  as  to  subject  the  fuel  bed  to 

*  Some  steamships  using  forced  drafts  have  "  closed  firerooms  "  (stoke-holds) 
under  pressure,  and  in  such  cases  all  leakage  is  into  the  interiors  of  the  settings. 


Fig.  384- 


DRAFT  AND  DRAFT  APPARATUS  589 

static  pressure,  or  plenum,  rather  than  to  any  localized  blast 
action. 

With  induced  draft  (either  natural  or  artificial)  the  pressure 
within  the  boiler  setting  is  below  atmospheric,  hence  there  may 
be  detrimental  infiltration  of  cold  air  through  cracks  in  the  set- 
ting and  through  the  fire  doors  when  opened.  With  this  system, 
however,  the  fuel  bed  burns  more  evenly,  and  demands  less 
attention  than  in  the  other,  and  it  is  not  necessary  to  shut  off 
the  draft  before  opening  fire  and  ash  doors.  Usually  a  by-pass 
flue  is  provided  (as  in  Fig.  382)  so  that  natural  draft  alone  can 
be  used  for  light  loads,  or  in  case  of  accident  to  the  apparatus. 

With  balanced  draft  the  air  is  forced  into  the  ash  pit  at  suffi- 
cient pressure  to  become  just  atmospheric  upon  issuing  from  the 
surface  of  the  fuel  bed,  and  the  gases  are  carried  away  from  the 
combustion  chamber  by  induced  draft  (either  natural  or  arti- 
ficial) of  such  intensity  as  not  to  cause  a  decrease  of  furnace 
pressure  below  atmospheric.  The  proper  balance  between  the 
forced  and  induced  draft  is  usually  maintained  by  some  auto- 
matic device  which  regulates  the  two  systems  simultaneously. 
With  balanced  draft  (i)  there  is  no  tendency  for  leakage  either 
into  or  from  the  furnace;  (2)  the  fire  is  not  affected  by  opening 
the  furnace  doors  for  adding  coal  or  "working"  the  fire;  (3)  it 
is  possible  to  burn  the  smaller  sizes  of  fuel,  which  are  otherwise 
worthless,  and  which  must  be  burned  at  high  rates  of  combus- 
tion but  cannot  be  used  with  forced  draft  because  of  their  fine- 
ness; and  (4)  very  high  rates  of  combustion  can  be  used  with- 
out detriment  to  economy. 


CHAPTER  XXXIII. 
GAS  PRODUCERS  AND  PRODUCER  GAS. 

281.  Essentials   of   Producer-gas   Apparatus.       (a)    Broadly 
speaking  any  apparatus  in  which  gas  is  made  is  a  "gas  producer," 
but  in  engineering  the  term  is  almost  exclusively  applied  to  a 
class  of  apparatus  producing,  gas  largely  by  a  process  of  partial 
or  incomplete  combustion.     The  gas  made  in  such  apparatus  is 
known  as  "producer  gas" 

(b)  This  gas  has  long  been  used  for  the  heating  of  furnaces, 
the  melting  of  metals,  and  a  large  number  of  similar  purposes, 
but  during  the  last  twenty  years  it  has  come  into   particular 
prominence  as  a  power  gas,  that  is,  a  gas  for  use  in  internal  com- 
bustion engines.     It  happens  to  be  so  constituted  as  to  permit 
of  high  compression  in  the  engine,  thus  giving  high    thermal 
efficiencies  and,  what  is  of  greater  importance  industrially,  it  can 
be  made  at  the  point  of  consumption  more  or  less  easily  and  very 
cheaply  as  compared  with  most  of  the  other  combustible  gases. 

(c)  Although  the  necessary  apparatus  differs  considerably  with 
the  kind  of  fuel  from  which  producer  gas  is  to  be  made  and  with 
the  purpose  for  which  the  gas  is  to  be  used,  there  are  certain 
essential  parts  which  generally  exist  in  one  form  or  another  in 
all  such  apparatus.     They  are:    (i)  The  fuel  gasifier  or  "pro- 
ducer";   (2)  some  sort  of  "preheater"  or  "economizer";    (3) 
cleaning  apparatus;   and  occasionally  (4)  a  gas  storage  reservoir 
of  some  kind,  large  or  small. 

The  first  three  parts  are  all  shown  in  Figs.  5  and  391  to  394. 
In  the  particular  types  of  plant  shown  in  Figs.  5  and  391,  the 
gas  storage  reservoir  is  practically  nonexistent  unless  the  pipe 
connecting  the  top  of  the  scrubber  with  the  engine  cylinder  be 
considered  as  partly  serving  that  purpose. 

282.  Simple  Theory  of  Producer  Action,     (a)  As  indicated 
above,  the  ideal  producer  makes  gas  by  what  is  known  as  par- 
tial or  incomplete  combustion.     In  its  simplest  conception  this 

59° 


GAS  PRODUCERS  AND  PRODUCER  GAS  591 

depends  upon  the  combustion  of  carbon  to  carbon  dioxide  and 
then  the  reduction  of  this  carbon  dioxide  to  carbon  monoxide 
by  passing  it  over  incandescent  carbon.  These  reactions  can 
be  illustrated  by  means  of  Fig.  385. 

(b)  Assume  the  vessel  there  shown  to  be 
filled  with  a  column  of  carbon,  the  lower 
part  of  which  is  heated  to  incandescence. 
If  air  enter  at  the  bottom  of  this  fuel  bed, 
as  indicated  by  the  arrows,  its  oxygen  will 
unite  there   with   carbon   to   form  carbon 
dioxide,  according  to  the  equation  (see  Eq. 
(342a)) 

C  +  02  =  C02  +  175,200  B.t.u.,    (423) 

which  means  that  twelve  pounds  of  carbon 

combine  with  thirty- two  pounds  of  oxygen  Flg'  38s' 

to  form  44  pounds  of  carbon  dioxide  and  that   (12  X  14,600  =) 

.175,200  B.t.u.  are  liberated  per  twelve  pounds  of  carbon. 

(c)  This  carbon  dioxide  would   then   be  reduced   to  carbon 
monoxide  while  passing  up   through   the  incandescent  carbon 
above,  and  the  reaction  would  occur  according  to  the  equation 

C02  +  C  =  2  CO  -  67,200  B.t.u.     .     .     .     (424) 

This  means  that  the  44  pounds  of  carbon  dioxide  formed  in  the 
lower  part  of  the  fuel  bed  unite  with  twelve  more  pounds  of 
carbon  which  will  result  in  the  formation  of  fifty-six  pounds  of 
carbon  monoxide  and  the  absorption  of  an  amount  of  heat  equal 
to  67,200  B.t.u.,  which  quantity  is  easily  obtained  analytically 
in  the  manner  described  in  the  next  paragraph. 

(d)  Imagine  the  process  occurring  in  two  steps:   First  assume 
that   the  forty-four   pounds  of  carbon  dioxide  break  up  into 
twelve  pounds  of  carbon  and  thirty- two  of  oxygen.     This  could 
only  occur  with  the  absorption  of  175,200  B.t.u.,  equal  to  the 
quantity  liberated   when   the  combination  took   place.      Then 
imagine  the  carbon  and  oxygen  to  combine  with  an  additional 
twelve  pounds  of  carbon  to  form  the  fifty-six  pounds  of  carbon 
monoxide.     This  would  be  represented  by  (see  Eq.  (343^)) 

2  C  +  02  =  2  CO  +  108,000  B.t.u.,  .  .  (425) 
which  merely  states  that  twenty-four  pounds  of  carbon  burning 
to  carbon  monoxide  liberate  (24  X  45<>o  =)  108,000  B.t.u. 


592 


HEAT-POWER  ENGINEERING" 


The  first  process  involved  the  absorption  of  175,200  B.t.u.  in 
breaking  up  CO*,  the  second  liberated  108,000  B.t.u.  in 
the  formation  of  CO,  and  the  net  result  is  the  absorption  of 
(175,200  —  108,000  =)  67,200  B.t.u.,  as  given  in  Eq.  (424).* 

(e)  The  composition  of  the  gas  formed  and  the  thermal  effi- 
ciency of  the  process  can  now  be  determined  :  — 

To  produce  the  gas  according  to  Eqs.  (423)  to  (425),  thirty- 
two  pounds  of  oxygen  are  required  per  twenty-four  pounds 
of  carbon  used  and  this  oxygen  will  bring  into  the  producer 
(32  X  77/23  =)  107.1  pounds  of  nitrogen;  hence  the  163.1  pounds 
of  gas  leaving  the  producer  will  contain  this  weight  of  nitrogen 
in  mixture  with  the  fifty-six  pounds  of  carbon  monoxide  result- 
ing from  the  partial  combustion,  and  will  therefore  have  a  com- 
position of  about  34.4  per  cent  CO  and  65.6  per  cent  N  by 
weight. 

By  volume  the  composition  would  be  practically  the  same 
because_the  densities  of  CO  and  N  are  practically  identical. 

283.  Efficiency,  Simple  Producer  Action.  (a)  Had  the 
twenty-four  pounds  of  carbon  used  in  Sect.  282  (c)  been  burned 
directly  to  carbon  dioxide,  they  could  have  liberated  24  X  14,600 
=  350,000  B.t.u.  Burned  to  carbon  monoxide  they  liberated 
only  24  X  4500  =  108,000  B.t.u.  The  difference, 

350,000  —  108,000  =  242,000  B.t.u., 

must  be  the  quantity  of  heat  which  can  be  produced  by  subse- 
quently burning  the  carbon  monoxide  of  the  producer  gas  to 
carbon  dioxide.  This  corresponds  to  10,100  B.t.u.  per  pound  of 
carbon. 

(b)  If  the  thermal  efficiency  of  the  producer  be  taken  as  the 
ratio  of  the  heat  which  can  be  obtained  by  burning  the  cold  gas 
to  the  heat  which  could  have  been  obtained  by  burning  the 
original  carbon,  it  is  in  this  case 

T?f   _  Calorific  Value  of  Gas       242,000  _       ~         .       . 
Efc  ~  Calorific  Value  of  Fuel  = 


Looked  at  in  this  way  the  process  does  not  promise  very  well 
from  a  power-engineering  standpoint.     If  the  theoretical  pro- 

*  It  will  be  shown  in  a  subsequent  paragraph  that  this  treatment  does  not  tell 
the  whole  story,  but  for  a  first  analysis  it  is  accurate  enough. 


GAS  PRODUCERS  AND  PRODUCER  GAS  593 

ducer-efficiency  is  only  69  per  cent,  the  real  efficiency  could 
hardly  be  expected  to  be  more  than  50  to  60  per  cent,  and,  with 
thermal  efficiencies  of  internal  combustion  engines  ranging  from 
20  to  30  per  cent  as  an  extreme  value,  the  overall  thermal  effi- 
ciency of  such  a  producer  in  combination  with  an  engine  would 
be  low  indeed.  It  will  be  shown  later,  however,  that  higher 
efficiencies  are  obtainable  by  modifying  the  process. 

(c)  The  efficiency  given  above  is  what  is  called  the  cold  gas 
efficiency  and  is  really  not  the  correct  efficiency  to  use  under  all 
conditions.     For  power  purposes  the  gas  must  be  cooled  approxi- 
mately to  room  temperature  before  it  can  be  advantageously 
used  in  an  engine.     This  means  removing  all  of  the  sensible  heat 
given  the  material  in  the  producer,  and  the  cold  gas  efficiency 
is  the  proper  value  to  use  under  such  circumstances. 

(d)  The  process  as  outlined  results  not  only  in  the  production 
of  163  pounds  of  gas,  which  can  liberate  242,000  B.t.u.  when 
burned,  but  also  in  the  liberation  of  108,000  B.t.u.  in  the  pro- 
ducer.    In  any  real  case  part  of  this  latter  heat  will  of  course  be 
used  to  supply  unavoidable  radiation  and  similar  losses,  but  the 
rest  will  raise  the  temperature  of  the  carbon  and  of  the  air  fed 
to  the  producer  and  of  the  gas  formed.     Hence  the  gas  would 
actually  leave  the  producer  with  a  very  high  temperature,  about 
2000°  F.  or  more,  and,  by  cooling  it  to  room  temperature,  all  of 
the  heat  liberated  in  the  producer,  and  which  was  not  lost  by 
radiation  or  in  other  ways,  could  be  obtained. 

The  temperature  rise  resulting  from  the  liberation  of  a  cer- 
tain number  of  B.t.u.  is  equal  to  this  number  divided  by  the 
sum  of  the  products  of  weight  by  specific  heat  of  all  the  gases 
resulting  from  the  combustion.  The  higher  the  temperature  of 
the  combustible  gas  and  of  the  air  before  combustion,  the  higher 
will  be  the  ultimate  temperature  attained.*  Therefore,  for  fur- 
nace and  similar  work,  where  the  object  in  burning  the  gas  is  to 
obtain  high  temperature,  it  is  decidedly  advantageous  to  have 
the  apparatus  located  near  the  producer  so  that  the  sensible  heat 
is  not  lost  by  radiation  during  transmission. 

For  such  purposes  the  thermal  efficiency  of  the  producer  is 

*  As  the  specific  heats  of  gases  increase  comparatively  rapidly  at  high  tempera- 
tures, the  temperature  ultimately  attained  by  any  combustion  will  be  lower  than 
that  given  by  the  form  of  calculations  suggested,  as  has  already  been  shown.  TV 
error  will  be  greater  the  higher  the  temperature  attained. 


594  HEAT-POWER  ENGINEERING 

correctly  taken  as  the  so-called  hot  gas  efficiency,  which  is  the 
quotient  resulting  when  the  sum  of  the  total  calorific  value  and 
the  sensible  heat  of  the  gas  leaving  the  producer  is  divided  by 
the  total  calorific  value  of  the  fuel  entering.  Remembering  that 
all  heat  which  is  liberated  within  the  apparatus,  and  not  lost  by 
radiation  and  such,  must  be  present  in  the  gas  leaving,  the  "hot 
gas  efficiency  "  must  be 

_  Total  Calorific  Value  of  Gas  +  (Heat  Liberated  in  Producer  —  Losses) .  ,        \ 
Total  Calorific  Value  of  Fuel  '  (^2/' 

and  if  all  the  losses  in  the  case  previously  considered  be  assumed 
at  20  per  cent  of  the  heat  liberated  in  the  producer,  the  hot  gas 
efficiency  for  this  case  would  be 

_,.       242,000  +  (108,000  —  0.2  X  108,000) 

rLjh  =  

350,000 

=  - — — —  =  93.5  per  cent  (approximately), 
350,000 

a  figure  which  is  evidently  much  more  promising  than  that  pre- 
viously obtained. 

284.  More  Advanced  Theory  of  Producer  Action,  (a)  If  the 
combustion  processes  indicated  in  the  equations  of  the  preceding 
section  really  occurred  as  there  given  it  would  be  possible  to 
pass  a  stream  of  carbon  dioxide  into  one  end  of  a  tube  containing 
hot  carbon  and  have  nothing  but  carbon  monoxide  issue  from 
the  other  end.  Experiment,  however,  shows  that  this  is  impos- 
sible, for,  no  matter  what  the  conditions  are,  there  will  always  be 
a  certain  amount  of  carbon  dioxide  mixed  with  the  issuing  carbon 
monoxide. 

(b)  Experiment  further  shows  that,  other  things  being  equal, 
the  higher  the  temperature  in  the  tube  the  greater  will  be  the 
proportion  of  carbon  monoxide  in  the  gas  issuing,  and  the  lower 
the  temperature  the  greater  will  be  the  proportion  of  carbon 
dioxide. 

(c)  This  is  explained  chemically  by  what  is  called  "  chemical 
equilibrium."     Briefly,  if  no  other  variables  need  be  considered, 
at  each  given  temperature,  there  are  certain  definite  proportions  of 
carbon  monoxide  and  carbon  dioxide  which  will  be  in  equilibrium 
with  carbon.     If  a  mixture  of  these  gases  in  other  proportions  is 


GAS  PRODUCERS  AND  PRODUCER  GAS 


595 


brought  into  contact  with  carbon,  reactions  will  occur  and  con- 
tinue until  the  equilibrium  proportions  corresponding  to  the 
given  temperature  are  attained.* 

(d)  This  equilibrium  is  well  shown  by  the  diagram  of  Fig.  386 
which  is  plotted  from  experimental  results  obtained  with  carbon  in 
a  tube,  as  described  in  (a)  of  this  section.  In  this  figure  theabscissas 
represent  temperatures 
in  Centigrade  and  Fah- 
renheit degrees  and  ordi- 
nates  represent  per  cent 
of  CO  by  volume.  Sub- 
tracting these  ordinates 
from  100  gives  the  per- 
centages of  C0>2,  which 
are  evidently  shown  to 
scale  by  distances  from 
the  curve  to  the  100  per 
cent  line. 


80- 


100 

/ 

^  

—       — 

/ 

0 
0 

x«, 

/ 

Ca 

Eqilili 
bonM 
ndCa 

iriuin 
noxide 
•bon  at 

)iagrail 
,  Carbc 
Aim.  I 

n   for 
n  Diox 
ressur 

jde 

20 

0 

/ 

700        800        900       1000     1100      1200      1300 
Temp.0  C. 
1292      1172      1652       1832     2012     2192      2312 
Temp.°F 

Fig.  386. 


The  curve  shows  that  for  low  temperatures  probably  a  very 
small  amount  of  carbon  monoxide  would  be  found  to  be  issuing 
from  the  tube  in  the  experiment  described  above,  while  at  high 
temperatures  it  shows  the  issuing  gas  to  be  composed  almost 
entirely  of  carbon  monoxide. 

(e)  In  giving  the  effect  of  temperature  on  the  composition  as 
deduced  from  experiment,  it  was  limited  by  the  phrase  "  other 
things  being  equal."     Experiment  shows  that  the  pressure  at 
which  the  gases  exist  also  has  a  certain  effect  upon  the  compo- 
sition.    The  higher  the  pressure  the  greater  the  percentage  of 
carbon  dioxide  in  the  equilibrium  mixture  at  any  temperature. 
Pressure  variations  are,  however,  so  slight  in  producer  work  that 
their  effect  may  be  safely  neglected. 

(f)  The  time  of  contact  is  also  of  great  importance.     Chemical 
reactions  do  not  occur  instantaneously  (that  is,  in  time  measured 
in  infinitesimals)  and  the  reactions  in  question,  which  lead  to  the 
equilibrium  conditions  plotted  in  Fig.  386,  take  a  very  appreciable 
time  for  completion.     The  higher  the  temperature  the  shorter  the 
time  necessary  for  the  attainment  of  equilibrium  conditions. 

*  Whether  reaction  then  ceases,  or  whether  counterbalancing  reactions  which 
do  not  further  change  the  proportions  of  carbon  monoxide  and  carbon  dioxide 
continue,  is  a  matter  of  indifference  for  the  present  discussion. 


596 


HEAT-POWER  ENGINEERING'' 


10        60        80       100      120 
Time  of  Contact,  Seconds 


110      160 


Fig.  387- 


This  is  well  shown  in  Fig.  387  which  gives  results  obtained  in 
experiments  with  carbon  in  the  form  of  charcoal.  In  the  figure 
each  curve  is  an  isothermal;  that  is,  it  shows  the  proportions  of 
carbon  monoxide  and  of  carbon  dioxide  that  will  exist  after 
gas,  which  was  originally  all  carbon  dioxide,  has  been  in  contact 
with  carbon  at  a  certain  temperature  for  different  lengths  of  time. 

As  before,  the  ordinates 
represent  percentages  of 
CO  and  the  distances  from 
the  curve  upward  repre- 
sent percentages  of  CO2. 
It  will  be  observed  that, 
while  it  takes  a  time 
period  of  from  120  to 
1 60  seconds  to  attain  ap- 
proximate equilibrium  at 
8oo°C.  (as  shown  by  the  tendency  of  the  curve  to  become  hori- 
zontal at  this  point),  it  requires  only  5  seconds  to  attain  equi- 
librium with  a  very  much  higher  percentage  of  CO  at  1100°  C. 

(g)  The  effects  of  both  time  and  temperature  are  well  shown  in 
Fig.  389,  in  which  the  three  coordinates  are  time,  temperature 
and  volume  per  cent,  of 
CO.  The  curves  shown 
are  those  of  Fig.  387, 
but  here  each  curve  is 
located  in  its  own  tem- 
perature plane.  A  sur- 
face can  be  imagined 
as  passed  through  these 
curves  and  the  coordi- 
nates of  any  point  in 
it  will  show  the  relative 


40- 


100 J     0 


"1100 


—  11 


A=13(X 
B=120( 
Exper 


Bxpon 


°G  (2:72°F) 
C  (2192  °F) 


with  Coke 


ith  Anthracit( 
900  °C 
1652°F) 


40         60         80         100        120       110 
Time  of  Contact,  Seconds 


Fig.  388. 


percentages  [of  CO  and  C02,   which  result  at  any  temperature 
after  any  period  of  contact. 

(h)  Unfortunately  the  surface  condition  of  the  carbon  has  an 
effect  upon  the  time  required  for  the  attainment  of  equilibrium. 
In  general  the  more  porous  the  carbon,  and  the  smaller  the 
lumps,  the  shorter  will  be  the  time  required  to  attain  the  equi- 
librium corresponding  to  the  given  temperature.  This  is  just 
what  would  be  expected,  as  carbon  of  porous  character  and  in 


GAS  PRODUCERS  AND  PRODUCER  GAS 


597 


small  lumps  will  expose  most  surface  on  which  the  reaction  may 
occur. 

The  effect  of  surface  (and  possibly  other)  conditions  is  shown 
by  a  comparison  of  Figs.  387  and  388.  The  full  lines  in  the  latter 
represents  the  results  of  experiments  made  with  carbon  in  the 
form  of  coke  in  lumps  about  the  same  size  as  those  of  the  char- 


X= Temperature,0  C. 


Fig.  389. 


coal  used  in  obtaining  the  results  shown  in  Fig.  387.  The  dotted 
lines  show  similar  curves  for  anthracite  under  approximately 
like  conditions. 

The  curved  surface  shown  in  Fig.  389  is  then  only  one  of  a 
number  which  differ  in  curvature  with  the  character  of  the  carbon. 
The  more  porous  and  the  smaller  the  lumps  the  sharper  will  be 
the  rise  of  the  curves  as  they  leave  the  temperature  axis  at  the 
front,  and  the  sooner  will  they  become  flatter  as  they  recede. 


598  HEAT-POWER  ENGINEERING  ' 

(i)  The  preceding  discussion  is  purely  theoretical  and  leads 
to  the  following  conclusions:  For  best  producer  operation  (that 
is,  the  manufacture  of  gas  containing  the  maximum  amount  of 
carbon  monoxide  and  the  minimum  amount  of  carbon  dioxide 
and  nitrogen)  the  requirements  are :  — 

(1)  High  temperature  within  the  producer; 

(2)  Long  time  of  contact  between  entering  air,  gas  in  process 

of  formation,  and  hot  carbon; 

(3)  Maximum  porosity  and  minimum  size  of  fuel ; 

(4)  Theoretical  air  supply. 

285.  Practical  Limitations,  (a)  In  the  real  producer  there  are 
a  number  of  practical  considerations  which  materially  modify 
the  conclusions  just  given  for  the  theoretical  case.  For  instance, 
all  real  fuels  contain  ash  and  this  will  fuse  and  form  clinker  if 
the  temperature  becomes  high  enough.*  Such  clinker  is  very 
undesirable  because  it  obstructs  the  gas  passages  between  the 
lumps  of  fuel,  making  it  difficult  or  impossible  for  gas  to  flow 
through  certain  areas.  This  results  generally  in  more  violent 
combustion  in  the  parts  of  the  bed  which  are  still  unobstructed, 
and  this  localized  combustion  materially  augments  the  trouble 
by  raising  the  temperature  locally  and  causing  the  rapid  forma- 
tion of  more  clinker.  The  more  or  less  complete  obstruction  of 
the  gas  passages  will  ultimately  make  continued  operation  im- 
possible. Clinker  also  gives  considerable  trouble  by  fusing  to 
the  walls  of  the  producer  itself. 

Thus,  in  actual  operation,  the  fusing  temperature  of  the  ash 
sets  the  limit  to  the  temperature  allowable  in  the  producer  and 
this  temperature  varies  considerably  with  different  fuels;  but, 
with  those  adapted  to  use  in  present-day  producers,  the  tem- 
perature can  generally  be  carried  at  such  a  value  as  to  give  a 
theoretical  proportion  of  from  96  to  98  per  cent  of  CO  (with  4  to 
2  per  cent  of  CO2)  by  volume  in  the  issuing  gas. 

(b)  Caking  fuels  also  cause  trouble  in  producer  operation. 
The  coalescence  of  the  individual  lumps  decreases  the  percentage 

*  A  number  of  experimenters  are  now  operating  producers  at  what  are  ordi- 
narily considered  exorbitantly  high  temperatures,  by  mixing  with  the  coal  some 
cheap  material,  such  as  limestone,  which  acts  on  the  ash  as  a  flux.  The  ash  is  thus 
made  very  fluid  and  is  drained  off  just  as  it  is  in  the  case  of  blast  furnaces.  Several 
plants  of  this  character  are  said  to  be  in  successful  operation  in  Europe  but  they 
iiave  not  yet  been  commercially  adopted  in  this  country. 


GAS  PRODUCERS  AND  PRODUCER  GAS  599 

of  voids  in  the  fuel  bed  and  thus  obstructs  the  flow  of  gas.  It 
also  assists  in  causing  "arching  "  so  that  the* lower  part  of  the 
fuel  column  may  burn  to  ash  and  drop  down  while  the  upper 
part  remains  suspended  above.  Constant  or  intermittent  stir- 
ring of  the  fuel  bed  (often  combined  with  the  maintenance  of  a 
fairly  low  temperature)  are  necessary  with  such  fuels,  although 
both  stirring  and  low  temperature  have  a  detrimental  effect  upon 
the  gas  made.  Stirring  is  often  improperly  done,  and  opens  up 
fairly  large  free  passages  through  the  bed,  thus  allowing  C02 
and  even  air  to  pass  through  without  coming  into  intimate 
contact  with  hot  carbon. 

(c)  The  theoretical  requirement  of  long  time  of  contact  is  more 
or  less  a  relative  consideration,  as  previously  indicated ;  and  the 
length  of  time  needed  was  seen  to  depend  both  upon  the  tempera- 
ture and  upon  the  physical  character  of  the  fuel. 

Remembering  that  a  producer  operates  with  a  continuous  flow 
of  gas  through  the  fuel  bed,  the  time  of  contact  between  gas  and 
carbon  must  be  measured  in  the  actual  case  by  the  length  of 
time  it  takes  a  given  particle  of  gas  to  pass  through  the  fuel  bed, 
and  hence  depends  on  the  velocity  of  the  gas  passing  through 
the  producer  and  the  length  of  the  passage  through  the  bed  of 
fuel. 

There  is  a  practical  limit  to  the  allowable  depth  of  fuel  bed  with 
any  given  fuel,  in  any  given  size,  with  any  given  type  of  pro- 
ducer. This  limit  is  set  by  the  difference  of  pressure  necessary 
to  cause  flow  through  the  bed.  The  length  of  the  gas  path 
through  the  producer  being  thus  limited,  the  time  of  contact 
varies  with  the  velocity  which,  in  turn,  depends  on  the  diameter 
of  the  fuel  bed.  Large  diameters  will  correspond  to  low  veloci- 
ties and  long  times  of  contact;  small  diameters  will  correspond 
to  high  velocities  and  short  times  of  contact. 

(d)  This   consideration   would    indicate   a   large   diameter   of 
producer  to  be  desirable  in  every  case,  but  there  are  two  practical 
limitations  which  must  be  recognized:    (i)  The  cost  of  the  in- 
stallation will  increase  as  the  size  of  the  apparatus  required  per 
horse  power  increases;   and  (2)  there  will  be  difficulty  in  operat- 
ing the  producer  under  light  loads,  for  when  a  producer  which 
is  of  such  diameter  as  to  have  a  low  gas  velocity  at  full  toad  is 
operated  at  a  small  fraction  of  that  load,  the  small  amount  of  air 
passing  through  may  not  be  sufficient  to  keep  the  temperature 


6oo  HEAT-POWER  ENGINEERING 

of  the  large  bed  of  fuel  up  to  that  necessary  for  the  formation 
of  a  high  percentage  of  carbon  monoxide. 

The  diameter  of  any  given  producer  must  therefore  be  a  com- 
promise between  the  large  value  desirable  at  full  load  and  the 
smaller  value  which  is  desirable  at  light  load  and  which  involves 
less  expenditure  for  equipment. 

(e)  Practice  has  shown  that  certain  proportions  are  advisable 
with  certain  types  of  producers  and  certain  kinds  of  fuel.     In 
general  it  may  be  said  that  producers  are  built  of  such  diameters 
that  the  amount  of  fuel  gasified  when  carrying  rated  load  is 
from  i  o  or  12  pounds  per  square  foot  of  cross  section  of  fuel  bed 
per  hour  in  the  simpler  types,  up  to  30  to  40  pounds  per  square 
foot  per  hour  in  the  more  complicated  types  of  producers  oper- 
ating on  particularly  suitable  fuels.     The  overload  capacity  is 
determined  by  the  blast  pressure  available,  by  the  clinkering 
temperature  of  the  ash  and  the  fusing  or  fluxing  temperature  of 
the  producer  lining. 

(f)  In  the  purchase  of  fuel,  porosity  can  hardly  be  considered 
except  in  a  general  way,  it  being  merely  incidental  to  other  con- 
siderations.    The  size  of  lumps  can,   however,   be  taken  into 
account  both  as  to  effect  on  the  operation  of  the  producer  and 
on  the  price,  the  smaller  sizes  generally  costing  less  than  the 
larger.     The  smaller  the  size  of  the  fuel,  with  a  given  depth  of 
column,  the  greater  the  difference  of  pressure  required  to  pass 
the  necessary  volume  of  gas  through  the  producer;   and  with  a 
given  maximum  blast  pressure,  the  lower  is  the  capacity  of  a 
producer,  if  the  same  depth  of  column  is  maintained.     Given 
a  certain  difference  of  pressure  it  is  of  course  possible,  by  de- 
creasing the  length  of  path  through  that  bed,  to  make  any  given 
quantity  of  air  enter  the  bed  per  square  foot  of  section  in  a  given 
time;    but  this  detrimentally  shortens  the  time  of  contact  or 
else  necessitates  an  increase  of  diameter  in  order  to  reduce  the 
velocity  of  flow  to  a  satisfactory  value. 

Furthermore,  with  very  small  sizes  the  necessary  velocity  in  a 
producer  of  a  given  diameter  may  be  so  great  that  parts  of  the 
fuel  will  be  picked  up  by  the  gas  and  be  carried  out  of  the 
producer.  This  occurs  to  a  greater  or  less  extent  with  every 
producer  in  actual  operation.  Finely  divided  ash  or  a  certain 
amount  of  finely  divided  or  powdered  fuel  is  practically  always 
carried  out  by  the  issuing  gas. 


GAS  PRODUCERS  AND  PRODUCER   GAS  6oi 

The  larger  the  size  of  fuel  the  greater  are  the  voids,  hence  the 
passages  through  the  fuel  bed  are  of  greater  cross  section  and 
the  allowable  velocity  and  blast  pressure  are  less,  but  smaller 
surfaces  are  exposed  for  reaction.  .= 

(g)  There  are  thus  practical  limits  to  the  largest  and  smallest 
sizes  of  fuel  which  can  be  satisfactorily  used  in  any  given  case. 
Sizes  commonly  used  vary  from  about  eight  inches  in  diameter 
to  pea  anthracite.  The  larger  sizes  are  generally  mixed  with 
smaller  ones  to  decrease  the  passage  areas  in  the  fuel  bed,  while 
the  smaller  sizes  very  often  have  the  finer  particles_screened  out 
to  increase  the  free  areas. 

(h)  Lastly,  practically  no  producer  can  be  operated  with  the 
theoretical  air  supply.  In  order  to  supply  the  amount  of  oxygen 
necessary  to  produce  the  required  quantity  of  CO  (and  the  C02 
which  must  necessarily  accompany  it),  air  in  excess  of  the  the- 
oretical requirement  must  be  passed  through  the  producer.  In 
general  the  smaller  the  size  of  fuel  and  the  lower  the  velocity, 
the  smaller  need  this  excess  be,  but  it  can  never  be  entirely 
eliminated.  As  a  result,  producer  gas  practically  always  con- 
tains more  or  less  free  oxygen  and  consequently  an  excessive 
amount  of  nitrogen.  The  typical  analyses  of  producer  gases  in 
Table  XXV  show  this. 

286.  Artificial  Cooling  of  Producers  (General),  (a)  In  con- 
sidering the  difference  between  cold  gas  and  hot  gas  efficiencies, 
it  was  shown  that  a  large  amount  of  heat  in  excess  of  that  re- 
quired to  supply  radiation  and  similar  losses  must  be  liberated 
within  a  producer  by  the  very  process  to  which  the  formation 
of  producer  gas  is  due.  In  actual  producers  using  any  of  the 
ordinary  fuels,  the  excess  heat  would  quickly  raise  the  temper- 
ature to  a  prohibitively  high  value.  Clinker  troubles  would 
assume  such  magnitudes  as  to  entirely  prevent  successful  oper- 
ation and  in  many  cases  there  would  even  be  danger  of  fusing 
the  refractory  lining  of  the  producer  shell. 

(b)  To  prevent  such  difficulties  producer  operation  is  modi- 
fied in  several  different  ways  by  introducing  some  heat  absorb- 
ing process  to  lower  the  operating  temperature.  Part  of  the 
excess  heat  is  absorbed  naturally  to  a  certain  extent  with  all 
real  fuels,  for  they  contain  hydrocarbons  and  water  which  are 
vaporized  (and  to  a  certain  extent  modified  chemically)  at  the 


602 


HEAT-POWER  ENGINEERING 


Remarks. 

Aver,  of  about  30  analyses. 

Aver,  of  about  40  analyses. 

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P-t  f^       O 

GAS  PRODUCERS  AND  PRODUCER  GAS        603 

temperatures  attained;  but  it  is  only  with  exceptionally  wet 
fuels,  such  as  poorly  dried  peat,  that  enough  heat  is  absorbed  in 
this  manner  to  make  operation  practical.  The  reduction  of  tem- 
perature due  to  the  presence  of  C02,  nitrogen  and  moisture  in 
the  air  (from  the  atmosphere)  is  also  slight.  Hence  in  actual 
operation  it  is  necessary  to  have  some  artificial  means  of  cooling, 
(c)  Two  methods  of  artificially  controlling  the  temperature  are 
in  use.  They  may  be  called 

1.  The  "Carbon  Monoxide"  Method,  in  which  burned  pro- 
ducer gas  is  returned  to  the  producer  in  mixture  with  the  air 
supply,  and  absorbs  heat  largely  by  the  reduction  of  contained 
C02  to  CO;  and 

2.  The  Water  Vapor  Method,  in  which  water  vapor  is  mixed 
with  the  air  supply  and  absorbs  heat  by  reduction  in  contact 
with  hot  carbon. 

The  details  of  these  two  methods  are  considered  in  the  follow- 
ing sections. 

287.  The  "  Carbon  Monoxide  "  Method  of  Temperature  Con- 
trol, (a)  Burned  producer  gas  may  be  roughly  said  to  consist 
of  carbon  dioxide  and  water  vapor,  mixed  with  nitrogen.  Re- 
turning such  material  to  the  producer  will  effect  cooling  in  two 
distinct  ways:  (i)  The  carbon  dioxide  passing  over  heated  car- 
bon will  be  more  or  less  completely  reduced  to  carbon  monoxide; 
and  (2)  the  water  vapor  in  contact  with  hot  carbon  will  be 
more  or  less  completely  broken  up  to  form  hydrogen,  carbon 
monoxide  and  carbon  dioxide. 

(b)  Under  ordinary  circumstances  the  first  way  will  be  the 
only  one  of  appreciable  magnitude  because  of  the  small  amount 
of  water  vapor  generally  present  when  this  method  of  cooling 
is  used.  The  quantity  of  carbon  dioxide  which  must  be  returned 
in  order  to  maintain  a  given  temperature  in  a  theoretical  case 
can  be  approximately  determined  if  the  amount  of  carbon  dioxide 
and  carbon  monoxide  which  will  be  in  equilibrium  at  that  tem- 
perature and  the  amount  of  heat  which  must  be  absorbed  to 
maintain  the  desired  temperature  are  known.  Knowing  the 
amount  of  heat  (see  Eq.  424)  which  is  absorbed  for  each  unit 
weight  of  carbon  present  in  carbon  dioxide  when  the  latter  is 
reduced  to  monoxide,  it  is  possible  to  determine  how  much 
carbon  dioxide  will  have  to  be  reduced  and  how  much  carbon 


604 


HEAT-POWER  ENGINEERING 


monoxide  will  result.  It  is  then  only  necessary  to  find  the 
amount  of  carbon  dioxide  which  will  be  in  equilibrium  with  this 
CO,  to  add  this  amount  to  that  used  in  forming  the  monoxide, 
and  the  result  is  the  total  quantity  of  carbon  dioxide  which 
must  be  thus  returned. 

(c)  It  is  interesting  to  note  that  nearly  all  carbon  returned  in 
the  form  of  carbon  dioxide  is  used  repeatedly,  being  reduced  to 
carbon  monoxide  in  the  producer,  burned  to  dioxide  in  the  ap- 
paratus utilizing  the  gas,  and  returned  to  the  producer  again 
for  reduction,  and  so  on.     Hence  the  carbon  furnished  by  the 
fuel  will  be  less  than  the  total  carbon  in  the  issuing  gas  by  just 
the  amount  which  is  thus  used  over  and  over  again.     It  should, 
however,  be  noted,  that  there  is  a  natural  limit  to  the  amount 
that  can  thus  be  used.     The  carbon  dioxide  can  be  reduced  to  car- 
bon monoxide  only  with  the  absorption  of  heat  and  this  heat  can 
come  only  from  fuel  carbon  burned  in  the  producer.     The  method 
is  then  simply  one  which  results  in  the  entrapping  in  available 
form  of  some  of  the  heat  which  would  otherwise  be  wasted. 
The  actual  amount  of  carbon  which  can  thus  be  used  repeatedly 

in  any  given  case  is  com- 
paratively small  and  the 
principal  advantage  of 
the  process  lies  in  the 
temperature  control  and 
uniform  composition  of 
gas  (see  (d)  below)  rather 
than  in  the  saving  of  fuel. 
The  operation  of  arti- 
ficially cooled  producers 
is  shown  diaerammati- 

rlg.  390. 

cally   in   Fig.  390  (b)   in 

comparison  with  the  uncooled  method  of  operation  shown  in 
Fig.  390  (a).  The  way  in  which  more  heat  is  made  available  at 
the  expense  of  what  would  otherwise  be  lost  is  well  shown  by  the 
width  of  the  various  streams. 

(d)  The  fact  that  the  time  of  ignition  in  internal  combustion 
engines  should  ordinarily  be  varied  with  the  composition  of  the 
fuel  was  mentioned  in  Sect.  212  (h) .     When  gas  is  made  in  a  pro- 
ducer controlled  by  the  carbon  monoxide  method  its  composi- 
tion is  remarkably  uniform  from  light  loads  to  full  loads,  hence 


Sensible  Heat 
Heat  Value  of 
Issuing  Gas 


GAS  PRODUCERS  AND  PRODUCER  GAS         605 

the  time  of  ignition  can  remain  fixed  without  danger  of  large 
variations  in  thermal  efficiency.  This  must  be  considered  an 
advantage  possessed  by  this  process  in  comparison  with  that 
considered  below. 

288.  The  Water  Vapor  Method  of  Temperature  Control,  (a) 
Experiment  shows  that  when  steam  is  passed  over  incandescent 
carbon  a  certain  amount  of  hydrogen  is  released,  that  the  oxygen 
previously  combined  with  it  unites  with  some  of  the  carbon  to 
form  carbon  monoxide  and  carbon  dioxide,*  and  that  some  of 
the  steam  will  still  remain  unchanged  regardless  of  the  tempera- 
ture attained  and  of  the  amount  of  carbon  present.  It  is  again 
a  case  of  chemical  equilibrium  similar  to  that  considered  in 
Sect.  284  and  the  resultant  composition  will  depend  largely  on 
the  temperature. 

No  matter  what  the  temperature  is,  a  certain  amount  of  heat 
will  be  absorbed  in  the  process  of  decomposing  the  water  and 
this  is  always  greater  than  that  liberated  by  the  combination  of 
liberated  oxygen  with  carbon  to  form  either  CO  or  COi.  Hence, 
the  process,  when  used  in  a  producer,  must  result  in  lowering  the 
producer  temperature,  and  by  properly  proportioning  the  amount 
of  steam  per  pound  of  air  the  temperature  can  be  directly  con- 
trolled. 

(b)  The  gas  made  by  this  process  will  contain  hydrogen,  and 
a  small  amount  of  methane  as  well  as  carbon  monoxide,  as  a  com- 
bustible constituent;    and  since  all  of  the  hydrogen  and  some 
of  the  carbon  monoxide  were  formed  in  such  a  way  as  not  to 
necessitate  the  introduction  of  nitrogen,  there  will  be  a  smaller 
percentage  of  nitrogen  in  the  resulting  gas  than  when  made  by 
either  of  the  processes  previously  described.     The  gas  may,  in 
fact,  be  considered  as  made  by  the  theoretical  process  outlined 
in  Sect.  282,  with  an  admixture  of  hydrogen,  carbon  monoxide 
and  a  small  amount  of  carbon  dioxide,  all  resulting  from  the 
action  of  the  steam. 

(c)  As  a  result  of  the  presence  of  the  hydrogen  and  of  carbon 
monoxide  not  accompanied  by  its  proportion  of   nitrogen,  the 
calorific  value  of  gas  made  by  this  process  is  higher  than  that 
made  by  those  previously  described. 

(d)  One  of  the  disadvantages  of  this  process  is  that  the  com- 

*  A  small  amount  of  methane,  CH4,  is  also  found  in  all  cases. 


606  HEAT-POWER  ENGINEERING 

position  of  the  gas  is  very  changeable,  the  hydrogen  content 
increasing  from  a  very  small  amount  at  light  loads  to  very  large 
ones  at  heavy  loads.  This  necessitates  a  constant  shifting  of 
the  time  of  ignition  if  a  uniformly  high  thermal  efficiency  is 
to  be  obtained,  —  the  ignition  occurring  earliest  with  minimum 
hydrogen  content.  Such  constant  shifting  with  rapidly  varying 
load  is,  however,  not  practicably  attainable,  hence  the  engine  is 
apt  to  operate  at  widely  varying  efficiencies,  and,  in  extreme 
cases,  may  not  even  operate  satisfactorily. 

(e)  There  are  also  many  methods  of  applying  this  process 
which  give  poor  results  because  of  the  method  rather  than  the 
intrinsic  nature  of  the  process.     Any  method  of  controlling  the 
steam  supply  which  depends  only  on  the  instantaneous  load  on 
the  engine  must  cause  unsatisfactory  operation  in  the  following 
way:   During  a  period  of  very  light  load  the  fuel  bed  has  a  ten- 
dency to  cool  down  and  if  continued  for  any  great  length  of  time 
the  temperature  drop  will  be  serious.     Imagine  full  load  to  be 
demanded  suddenly  after  such  a  period.     The  fuel  bed  tempera- 
ture is  hardly  high  enough  to  make  the  necessary  quantity  of 
monoxide,  and  if  the  producer  is  fitted  with  a  device  which  will 
immediately  throw  on  full  steam  supply  with  demand  for  full 
load,  the  fuel  bed  will  be  still  further  cooled  by  the  deluge  of 
water  vapor.     Many  failures  of  otherwise  successful  producers 
have  been  due  to  just  such  actions. 

Forms  of  steam  control  which  depend  upon  the  temperature 
of  the  gas  issuing  from  the  producer,  or  the  equivalent  of  this, 
seem  to  give  better  results. 

(f)  The  fact  that  water  must  be  vaporized  before  it  can  be 
mixed  with  the  entering  air  is  often  taken  advantage  of  to  con- 
serve some  of  the  sensible  heat  in  the  gas  leaving  the  producer. 
An  apparatus  variously  known  as  a  vaporizer,  an  economizer,  or 
by  several  other  names,  is  so  arranged  that  these  gases,  while 
passing  through  or  around  it,  heat  and  vaporize  water  contained 
within  it.     Somewhat  similar  devices  also  called  economizers, 
or,  more  correctly,  preheaters,  are  often  arranged  to  preheat  the 
air  on  its  way  to  the  producer  so  that  it  may  pick  up  more  water 
vapor  and  also  return  to  the  producer  some  of  the  heat  that 
would  otherwise  be  wasted. 

The  upper  part  or  cover  of  the  producer  shown  in  Fig.  5  forms 
a  vaporizer,  the  vapor  being  picked  up  by  the  air  supply  as  it 


GAS  PRODUCERS  AND  PRODUCER  GAS  607 

passes  over  the  surface  of  the  water.  A  somewhat  similar  de- 
vice is  shown  in  Fig.  393.  Other  forms,  better  known  as  econo- 
mizers, are  shown  in  Figs.  391  and  392. 

289.  Effects  of  Hydrocarbons  in  Fuels,  (a)  The  behavior  of 
real  fuels  in  producers  and  the  composition  of  the  resulting 
gases  are  much  modified  by  the  presence  of  volatile  hydrocarbons. 
These  are  distilled  off  within  a  producer  and  are  very  much 
modified  by  the  high  temperature  of  the  heated  fuel  and  refrac- 
tory material  before  finally  issuing  with  the  gas. 

(b)  The  tendency  of  all  such  mixtures  of  hydrocarbons  when 
heated  is  to  undergo  changes,   yielding  carbon,   hydrogen  and 
new  hydrocarbons,  some  of  which  are  more  volatile  than  the 
originals  and  others  less  volatile.     If  heating  is  continued  long 
enough  and  at  a  sufficiently  high  temperature  the  ultimate  prod- 
ucts are  practically  hydrogen,  methane  and  carbon  (lampblack). 
The  hydrogen  and  more  volatile  hydrocarbons,  such  as  methane, 
form  desirable  constituents  of  the  producer  gas  *  and  the  carbon 
can  be  gasified  if  it  remains  in  the  producer,  or  it  is  compara- 
tively easily  separated  if  it  passes  out  with  the  issuing  gas.    The 
less  volatile  hydrocarbons,  however,  if  allowed  to  issue  with  the 
gas,  will  subsequently  condense,  giving  a  thick,  viscous,  or  semi- 
solid  material  known  either  as  tar  or  pitch,  depending  upon  its 
composition   and  consistency.     Such  material  is  apt  to  cause 
pipe  stoppages,  to  clog  the  gas  cleaning  apparatus,  the  engine 
valves  and  such. 

(c)  With  anthracite  fuels  the  amount  of  tar  formed  is  com- 
paratively small  and  gives  little  trouble  as  it  is  easily  separated 
from  the  gas.     Bituminous  fuels,  on  the  other  hand,  yield  large 
quantities  of  tar  if  used  in    producers  of   the   simpler    kinds. 
Such  tar  must  be  separated  from  the  gas  if  the  latter  is  to  be 
transported  any  distance  from  the  producer,  or  is  to  be  used  in 
internal  combustion  engines  or  in  any  apparatus  requiring  it  to 
flow  through  small  orifices.     This  elimination  not  only  entails 
the  use  of  more  or  less  costly  apparatus,  which  generally  con- 
sumes power,  but  also  results  in  lowered  thermal  efficiency,  as 

*  This  statement  is  true  as  far  as  definite  knowledge  goes  at  present,  but  it 
seems  probable  that  under  certain  conditions  some  of  the  products  may  prove 
undesirable  because  of  chemical  instability  leading  to  spontaneous  ignition  at  low 
compressions. 


6o8 


HEAT-POWER  ENGINEERING 


the  calorific  value  of  the  separated  tar  represents,  in  many  cases, 
a  considerable  portion  of  that  of  the  original  fuel. 

(d)  The  most  successful  method  of  elimination  so  far  produced 
depends  upon  the  destruction  of  the  tar  within  the  producer. 
This  is  accomplished  by  passing  the  tar  forming  vapors  (dis- 
tilled off  the  freshly  charged  fuel)  through  an  incandescent 
fuel  bed  before  leaving  the  producer.  The  process  taking  place 
is  called  cracking  and  results  in  the  formation  of  hydrogen, 
methane,  small  quantities  of  other  very  volatile  hydrocarbons 
and  solid  carbon.  The  solid  carbon  largely  remains  within  the 


Gas  to  Dry  Scrubber 
— *•&  Engine  or  direct 
to  Engine 


Fig.  391.  — Up  Draft  Suction  Producer. 

producer  bed  and  is  subsequently  gasified,  while  the  hydrogen 
and  other  products  of  the  cracked  hydrocarbons  pass  off  with 
the  gas. 

(e)  This  process  can  be  carried  on  in  an  ordinary  up  draft 
producer  operating  much  like  that  of  Fig.  391,  but  modified  so 
that,  while  the  gas  to  be  used  is  drawn  off  from  the  top  of  the 
main  fuel  column,  the  volatiles  distilled  off  from  the  top  of  the 
freshly  charged  fuel  in  the  extended  hopper  are  piped  around 
and   introduced   with   the   air  entering  at   the   bottom.     This 
method  has  not  met  with  great  commercial  success,  although 
it  is  used  to  some  extent  in  Europe  for  large  installations. 

(f)  Another  and  a  very  successful  method  is  to  reverse  the 
direction  of  flow  of  gas  through  the  producer,  introducing  air 


GAS  PRODUCERS  AND  PRODUCER  GAS 


609 


6io 


HEAT-POWER  ENGINEERING 


and  fuel  at  the  top  and  removing  gas  at  the  bottom.  This  gives 
what  is  known  as  a  down  draft  producer,  one  example  of  which 
is  shown  in  Fig.  392.  In  this  particular  type,  a  bed  of  coke  is 
ignited  upon  the  brick  arch  which  forms  the  grate,  and  the  bitu- 
minous coal  is  fired  upon  this  from  above. 

(g)  Few  of  the  down  draft  producers  so  far  constructed  have 
permitted  of  continuous  operation  because  of  the  difficulty  of 
removing  the  ash  and  clinkers  without  shutting  down  the  pro- 
ducer. They  are,  therefore,  generally  operated  intermittently, 
say  for  a  week,  after  which  they  are  cleaned  out  and  restarted. 
The  type  shown  in  Fig.  393,  which  is  known  as  a  water  bottom 


Air  Supply 


Fig.  393.  — Down  Draft  Producer,  Continuously  Operated.     (Akerlund  Type.) 

producer  (see  next  section),  overcomes  this  difficulty  and  per- 
mits of  continuous  operation. 

(h)  To  circumvent  the  difficulties  met  in  attempting  to  gas- 
ify bituminous  and  similar  fuels  in  up  draft  producers,  the 
so-called  double  zone  type  of  producer  is  also  used.  One  exam- 
ple of  this  type  is  shown  in  Fig.  394.  This  producer  may 
be  regarded  as  a  down  draft  producer  superimposed  upon  one 
of  the  up  draft  kind.  Air  enters  both  top  and  bottom  and 
gas  is  drawn  off  near  the  middle  of  height.  The  only  draw- 
back is  the  necessity  of  carefully  watching  operations  so  that 
the  upper  incandescent  zone  may  remain  extensive  enough  to 
successfully  crack  the  hydrocarbons  and  so  that  the  combus- 
tion below  the  "gas  offtake  "  may  occur  at  just  the  proper  rate 
to  completely  gasify  all  the  coked  material  coming  down  from 
above. 


GAS  PRODUCERS  AND  PRODUCER  GAS 


6l2 


HEAT-POWER  ENGINEERING 


"Wafer  Sealed  Charging  Hopper 
Is  brought  over  different  parts 
of  JbecUy.rotating  top 

Sealed  Sight 
awl-Poke  Hole 

.Water  Seal  for  Top 


39S 


290.  Water  Bottom  and  Grate  Bottom  Producers,  (a)  No 
matter  what  the  type  of  producer,  the  column  of  fuel  must  be 
supported  im  some  way.  Producers  are  divided  roughly  into 
two  types  depending  upon  the  way  in  which  the  fuel  bed  is 
supported.  Producers  arranged  like  those  in  Figs.  393  and  394, 

in  which  the  bed  of  fuel  is 
supported  on  a  pile  of  its  own 
ash,  resting  in  a  saucer  shaped 
depression  filled  with  water, 
are  called  water  bottom  pro- 
ducers.  The  shell  of  the  pro- 
ducer must  dip  into  the  water 
by  a  sufficient  amount  to 
prevent  the  passage  of  air 

^tO        ^        prodUCCf,        Or       tllC 

escape  of  gas  out  of  the  pro- 
ducer, under  the  action  of  the 
greatest  difference  of  pressure 
which  will  ever  occur  during 
operation. 

Producers  of  this  kind  possess  the  great  advantage  of  permit- 
ting the  convenient  withdrawal  of  ash  at  any  time  during  opera- 
tion. They  also  dispense  with  almost  all  of  the  metal  work 
found  in  other  types  at  the  bottom  of  the  fuel  column  where  the 
temperature  is  apt  to  become  dangerously  high  if  attendants 
are  careless  and  where  the  rough  work 
and  sharp  ash  and  clinker  cause  rapid 
depreciation. 

(b)  Producers  in  which  the  column 
of  fuel  is  not  supported  by  ashes  in  a 
water  sealed  saucer  may  be  roughly 
grouped  under  the  head  of  grate  bottom 
producers.      Examples  are   shown   in 

Figs.  391,  392,  395  and  396.  The  grates  may  be  of  any  degree 
of  complexity  from  the  simple  grid  of  cast  iron  bars  or  of  plain 
iron  pipes,  or  the  arch  of  fire  brick  shown  in  Fig.  392,  to  the  most 
complicated  of  mechanical  grates,  such  as  the  rotating  and  scrap- 
ing devices  shown  in  Figs.  395  and  396,  or  a  rocking  grate  much 
like  that  used  under  steam  boilers,  as  shown  in  Fig.  391. 

(c)  Mechanical   grates,   operated  continuously  by  power  in 


Fig.  396. 


GAS  PRODUCERS  AND  PRODUCER  GAS  613 

large  sizes  and  intermittently  by  hand  in  small  ones,  are  decidedly 
advantageous.  They  make  possible  the  easy  working  down  of 
ash  and  clinker,  which  in  other  cases  would  have  to  be  barred 
down  by  poking  from  above,  from  the  sides  and  through  the 
bottom.  When  continuously  in  motion  they  tend  to,  maintain 
uniform  conditions  within  the  producer,  shaking  the  fuel  column 
sufficiently  to  keep  it  open,  to  work  down  ash  and  to  break  up 
clinker. 

Combined  with  a  depth  of  ash  sufficient  to  seal  against  leak- 
age in  or  out,  or  with  a  water  bottom,  they  afford  ideal  operating 
conditions. 

291.  Induced  Draft  and  Forced  Draft,  (a)  In  developing  the 
theory  of  the  producer  it  was  assumed  that  air  could  be  made 
to  enter  and  the  resultant  gas  to  leave.  This  flow  can  only  be 
produced  by  maintaining  a  difference  of  pressure  between  inlet 
and  outlet  orifices.  Two  distinct  methods  are  used  for  creating 
flow  in  this  way.  In  one  the  pressure  on  the  entering  side  is 
raised  above  that  of  the  atmosphere;  that  is,  air  is  pumped  into 
the  producer.  Such  producers,  which  are  operated  under  what 
corresponds  to  forced  draft  in  boiler  practice,  are  called  pressure 
producers.  The  pressure  of  air  and  gas  within  the  producer  is 
greater  than  the  atmospheric  pressure  outside  of  the  producer 
shell  by  the  amount  necessary  to  cause  flow  through  the  pro- 
ducer and  all  subsequent  apparatus.  One  great  disadvantage 
of  such  types  is  the  fact  that  a  leak  anywhere  in  the  apparatus 
results  in  the  outflow  of  poisonous  producer  gas.  Opening  of 
poke  holes  for  inspection  of  the  fire  or  for  stirring  up  the  bed 
will  result  similarly.  For  such  reasons  pressure  producers  must 
always  be  operated  in  well  ventilated  structures,  preferably  with- 
out side  walls  where  climatic  conditions  permit. 

Air  is  generally  pumped  into  such  producers  by  a  steam  jet 
blower  similar  to  that  shown  in  Fig.  395.  With  proper  propor- 
tions the  amount  of  steam  can  be  regulated  so  as  to  just  equal 
that  required  for  cooling  the  producer  by  decomposing  in  con- 
tact with  the  hot  carbon.  In  general  this  steam  must  be  under 
so  high  a  pressure  that  a  separate  boiler  is  necessary  for  its  gen- 
eration, but  in  large  plants  this  is  not  a  great  disadvantage.  In 
some  types  the  steam  is  generated  in  a  vertical  water  tube  boiler 
which  receives  the  hot  gas  coming  from  the  producer.  In  this 


HEAT-POWER  ENGINEERING 

way  part  of  the  sensible  heat  in  the  gas  is  returned  to  the  fuel 
column. 

Any  other  form  of  air  pump  can  be  used;  a  very  common 
one  is  that  shown  at  the  right  in  Fig.  394.  As  shown  it  is  used 
as  an  exhauster,  but  an  exactly  similar  device  can  be  used  as 
a  blower,  the  only  difference  being  in  its  location  and  method  of 
connection. 

(b)  The  other  method  of  operation  referred  to  above  causes 
flow  through  the  producer  and  subsequent  apparatus  by  lower- 
ing the  pressure  at  the  outlet  to  a  value  below  that  of  the  sur- 
rounding atmosphere.     Atmospheric  pressure  at  the  inlet  is  then 
sufficient  to  cause  flow.     Such  producers,  operated  under  condi- 
tions corresponding  to  induced  draft  in  boiler  practice,  are  known 
either  as  induced  draft  producers  or  as  suction  producers,  depend- 
ing upon  the  apparatus  used  for  reducing  the  pressure. 

When  an  exhauster  like  that  in  Fig.  394,  or  any  similar  appa- 
ratus, is  used  the  producer  is  called  an  induced  draft  apparatus; 
when  a  gas  engine  operated  by  the  producer  draws  its  own 
charge  through  the  system  by  lowering  the  pressure  during  each 
suction  stroke  as  shown  in  Fig.  391,  the  apparatus  is  called  a 
suction  producer. 

(c)  One  great  advantage  of  all  induced  or  suction  draft  sys- 
tems is  that  any  leak  always  results  in  the  flow  of  air  into  the 
apparatus  rather  than  escape  of  gas  out  of  the  apparatus.     Such 
air  may,  in  extreme  cases,  furnish  oxygen  sufficient  to  burn  an 
appreciable  quantity  of  the  gas  within  the  apparatus,  as  for  in- 
stance in  case  the  leak  is  immediately  above  the  fuel  bed  in  the 
producer  where  the  gases  still  have  a  high  enough  temperature  to 
ignite,  and  this  would  result  in  a  diminished  output  of  power  gas, 
but  could  not  ordinarily  endanger  human  life.     A  leak  at  a  point 
beyond  the  producer  would  result  in  the  mixture  of  air  and  cold  gas 
which  could  be  entirely  counterbalanced  by  the  admission  of  less 
air  to  the  apparatus  in  which  the  gas  is  subsequently  burned. 
However,  such  mixtures  of  air  and  gas  within  the  apparatus 
represent  a  possible  source  of  trouble  as  they  may  sometimes 
acquire  explosive  proportions  and  there  is  always  the  possibility 
of  ignition.     The  high  pressures  resulting  from  explosions  would 
endanger  the  apparatus  and  possibly  human  life,  but  can  easily 
be  guarded  against  by  providing  some  form  of  pressure  relief 
such  as  a  water  seal  or  large  flat  door,  or  pJate,  with  minimum 


Driving  Shaft 


GAS  PRODUCERS  AND  PRODUCER  GAS        615 

inertia  so  as  to  permit  of  rapid  opening  with  minimum  pressure 
rise. 

(d)  There  are  a  few  types  of  producer  plants  so  constructed 
that  they  operate  on  what  is  known  as  a  balanced  draft.  This  is 
generally  achieved  by  using  the  equivalents  of  one  blower  and 
one  exhauster.  The  combined  action  of  the  two  is  such  that 
the  pressure  within  the  producer  itself  is  not  greatly  different 
from  atmospheric,  that  on  the  outlet  side  being  generally  main- 
tained at  a  value  equal  to  atmospheric.  The  dangers  associated 
with  leakage  in  or  out  are  thus  minimized. 

292.  Mechanical  Charging,  (a)  Most  of  the  producers  used 
in  power  plants  are  charged  by  hand,  particularly  in  the  smaller 
sizes.  With  small  producers  the  shell  is  generally  made  of  such 
depth  that  it  will  hold  sufficient  fuel 
for  from  three  to  six  hours'  operation 
without  recharging.  Such  producers 
are  commonly  charged  when  starting 
in  the  morning,  again  at  about  midday 
and  finally  at  night  before  shutting 
down. 

(b)  With  large  producers  it  is  gener- 
ally found  best  to  charge  at  shorter 
intervals  because  more  uniform  results  Fig.  397. 

are  thus  obtained  and  because  the  fuel 

column  is  more  easily  handled  when  this  is  done.  Where  frequent 
charging  is  necessary  a  mechanical  device  such  as  is  shown  in  Fig. 
397  has  many  advantages,  the  most  prominent  of  which  are:  — 

(1)  Uniform    rate  of   charging   so  that  there  are  no  sudden 
fluctuations  in  quality  of  gas  as  happens  when  large  quantities 
of  green  fuel  are  charged  at  long  intervals; 

(2)  Uniform  distribution  of  fuel  over  the  entire  diameter  of 
producer,  —  a  very  difficult  matter  in  hand  charging  of  large 
producers  unless  much  hand  leveling  is  done,  which  generally 
permits  the  admission  of  considerable  quantities  of  air  or  the 
discharge  of  large  volumes  of  gas  during  the  operation;  and 

(3)  Saving  of  labor  and  hence  of  operating  expense. 


293.    Cleaning  Apparatus,     (a)  The  gas  leaving  a  producer 
has  a  comparatively  high  temperature  and  carries  in  suspension 


616  HEAT-POWER  ENGINEERING 

more  or  less  solid  matter  and  also  vapors  which,  upon  cooling, 
will  condense  to  form  water  and  tar.  The  function  of  the  clean- 
ing apparatus  is  to  cool  the  gases  and  to  remove  solids,  water 
and  tar. 

(b)  In  the  broad  sense  every  part  of  the  apparatus  beyond 
the  producer  outlet  flange  is  cooling  and  cleaning  apparatus,  but 
commercially  the  term  is  applied  to  the  several  distinct  units 
such  as  wet  and  dry  scrubbers,  tar  extractors  and  such. 

(c)  The  methods  employed  for  cooling  are  almost  obvious  from 
the  figures  of  actual  producers  shown.     A  certain  amount  of 
sensible  heat  is  removed  from  the  gas  by  air  or  water,  or  both, 
in  the  economizer  or  its  equivalent.     Part  of  the  sensible  heat 
of  the  gas  is  lost  by  radiation  from  the  pipes  connecting  the 
various  parts.     By  far  the  largest  amount  is  generally  removed 
in  wet  scrubbers,  by  bubbling  the  gas  through  water,  or  by  passing 
it  through  a  space  filled  with  a  very  fine  spray  of  water,  or  over 
water  films  on  coke  or  on  similar  solid  material,  or  by  a  combina- 
tion of  these  methods. 

(d)  The  methods  of  removing  solids  (and  in  some  cases  liquids) 
depend  upon  three  principles:    (i)  Separation  by  gravitation, 
(2)  separation  by  change  of  direction,   and   (3)  separation  by 
wetting  solid  particles  and  retention  of  such  wetted  material. 

Settling  of  solid  (and  liquid)  matter  will  result  to  a  certain 
extent  when  the  velocity  of  flow  is  sufficiently  reduced.  This 
reduction  in  flow  may  be  brought  about  either  by  an  enlarge- 
ment in  the  size  of  the  passage  or  by  decrease  in  volume  due  to 
lowering  the  temperature  of  the  gas,  or  by  both  these  processes. 
In  fact  more  or  less  separation  of  the  kind  always  occurs  in  the 
pipes  because  of  natural  cooling.  Separation  by  change  in  direc- 
tion occurs  whenever  the  gas  passes  through  an  elbow  or  similar 
fitting,  the  solids  (and  liquids)  having  a  tendency  to  travel  to 
the  outside  of  the  curve. 

Special  apparatus  for  utilizing  these  first  two  principles  is 
seldom  fitted  to  producers,  and  particularly  not  to  those  used 
for  power  work,  though  the  fact  that  such  separation  must 
always  occur  to  a  certain  extent  as  the  gas  flows  through  the 
passages  may  be  utilized  in  design  to  lighten  the  work  required 
of  the  following  apparatus.  It  should  also  be  taken  into  account 
in  designing  the  piping  by  arranging  openings  through  which 
cleaning  can  be  easily  effected. 


GAS    PRODUCERS  AND  PRODUCER  GAS  617 

By  far  the  largest  amount  of  solid  material  is  removed  by  wet 
scrubbing  which  is  also  used  for  the  cooling  effect.  The  appa- 
ratus is  so  constructed  that  the  solid  particles  are  well  wetted 
and  are  then  allowed  to  separate  out  by  gravity,  or  they  are 
" scrubbed"  out  by  bringing  them  in  contact  with  wetteAsurfaces 
to  which  they  adhere.  Separation  by  gravity  is  well  shown  in  the 
cases  where  gas  is  bubbled  through  water,  the  particles  of  dust 
on  the  surface  of  the  "bubble  "  being  wetted  and  caught  by  the 
liquid,  after  which  they  slowly  settle  to  form  a  sort  of  mud. 

Separation  by  wet  scrubbing  is  well  illustrated  by  the  opera- 
tion of  coke  or  grid  filled  towers  or  "scrubbers  "  such  as  those 
shown  in  Figs.  391  and  392. 

Even  the  best  wet  scrubbers  will  allow  a  small  amount  of 
dust  to  pass  through  them.  This  material,  together  with  me- 
chanically entrained  water  and  some  tar,  is  often  finally  sepa- 
rated in  a  "dry  scrubber  "  filled  with  excelsior  or  sawdust,  such 
as  that  shown  in  Fig.  392. 

After  the  tar- forming  vapors  have  been  condensed,  the  small 
particles  or  "  droplets  "  of  tar  behave  in  much  the  same  way  as 
do  the  dust  particles.  The  apparatus  used  for  dust  removal, 
and  in  particular  the  wet  scrubber,  removes  large  proportions  of 
tar  as  well. 

(e)  When  the  tar  content  of  the  gas  is  great,  as  when  bitu- 
minous coals  are  used  in  a  producer  which  does  not  provide  for 
breaking  up  the  hydrocarbons  within  the  fuel  bed,  it  is  often 
necessary  to  use  a  separate  "  tar  remover."  These  are  generally 
mechanically  operated  scrubbing  devices  in  which  the  gas  is 
well  wetted  by  a  spray  of  water  and  then  brought  into  forcible 
contact  with  moving  and  stationary  surfaces.  The  tar  collects 
upon  these  surfaces  and  the  liquid  is  driven  off  or  drained  off 
continuously.  Such  separators  often  take  forms  resembling  fan 
blowers,  or  series  of  propellers  or  impeller  wheels,  with  adjacent 
units  rotating  in  opposite  directions. 

294.  Producer  Gas  from  Oil.  (a)  Many  attempts  have  been 
made  to  construct  producer-gas  plants  which  would  successfully 
gasify  crude  oil  and  fuel  oil,  but  most  have  resulted  in  failure. 
There  are,  however,  a  few  plants,  of  several  different  types,  in- 
successful  operation,  which  indicates  that  the  problem  of  gasi- 
fying oil  in  a  producer  is  not  impossible  of  solution. 


6i8  HEAT-POWER  ENGINEERING 

(b)  The  difficulties  met  in  attempts  to  gasify  oil  are  similar  to 
those  experienced  with  the  gasification  of  the  volatiles  in  bitu- 
minous coals  and  similar  fuels.      Either  tar,  or  lampblack,  is 
generally  produced  in  large  quantity,  and  gives  trouble  in  clean- 
ing, besides  reducing  the  efficiency. 

(c)  One  of  the  solutions  of  this  problem  is  notable  for  its  sim- 
plicity.    The  producer  is  arranged  for  down  draft  and  is  built 
with  a  brick  arch  grate  similar  to  that  shown  in  Fig.  392.     A 
bed  of  incandescent  coke  is  maintained  on  this  arch  and  the  oil 
is  sprayed  into  the  upper  part  of  the  producer,  the  resulting  gas 
passing  downward  through  the  coke  bed.     All  tar- forming  vapors 
are  destroyed  by  cracking  and  the  resultant  lampblack  is  nearly 
all  caught  in  the  coke  bed  which  is  thus  automatically  replenished. 


CHAPTER  XXXIV. 
UTILIZATION    OF    WASTE  HEAT  —  FINANCIAL  CONSIDERATIONS. 

295.  General,     (a)  It  has  been  seen  that  in  connection  with 
steam  power  plants  very  large  amounts  of  heat  are  wasted  in 
the  flue  gas  (loss  c  in  Fig.  3)  and  in  the  exhaust  steam  (width  E 
in  Fig.  3).     The  profitable  reduction  of  these  losses  is  obviously 
of  the  greatest  importance,  and  it  is  the  object  of  this  chapter 
to  outline  briefly  the  different  methods  of  its  accomplishment 
and  some  of  the  more  important  problems  connected  therewith. 
In  most  cases  it  will  be  seen  that  some  of  the  waste  heat  is  used 
in  increasing  the  temperature  (sensible  heat)  of  the  feed  water, 
thus  reducing  the  amount  of  fuel  required  to  convert  the  feed 
water  into  steam. 

296.  Utilization  of  the  Heat  in  the  Flue  Gases,     (a)  One  very 
common  method  of  saving  some  of  the  heat  that  would  ordina- 
rily be  wasted  up  the  stack  is  to  heat  feed  water  by  passing  it 
through  tubes  which  are  surrounded  by  the  flue  gases  after  they 
have  left  the  boiler.     The  heating  apparatus  in  this  case  is 
commonly  called  an  "Economizer"     Its  use  effects  a  saving  of 
heat  which  in  exceptional  cases  may  amount  to  as  much  as  15 
per  cent  of  the  total  calorific  value  of  the  fuel.     The  apparatus, 
its  method  of  operation,  advantages  and  disadvantages,  etc., 
will  be  discussed  in  detail  later. 

(b)  In  certain  instances,  some  of  the  heat  of  the  flue  gas  can 
be  used  profitably  for  heating  the  air  used  in  the  furnace;  and 
if  the  local  conditions  are  favorable,  the  hot  gases  may  be  used 
in  drying-kilns  and  such. 

But  in  all  cases  where  the  temperature  of  the  flue  gas  is  de- 
creased there  is  a  detrimental  effect  on  the  draft  (if  natural), 
to  offset  which  entails  an  additional  expense  for  an  increased 
height  of  stack,  or  for  artificial  draft  apparatus  and  its  opera- 
tion. 

6lQ 


620  HEAT-POWER  ENGINEERING 

297.  Utilization  of  the  Heat  in  the  Exhaust  Steam,  (a)  It 
has  been  seen  that  lowering  the  pressure  of  the  exhaust  steam 
issuing  from  a  prime  mover  results  in  an  increase  of  the  available 
percentage  of  the  total  heat  furnished  by  the  boiler  and  hence 
reduces  the  proportion  wasted  in  the  exhaust.  This  decrease  of 
pressure  is  commonly  effected  by  using  a  condenser,  of  which 
there  are  many  types.  But  there  is  in  each  power  plant  a  limit 
of  vacuum  beyond  which  it  does  not  pay  to  go;  and  even  where 
the  best  vacuums  are  used,  the  exhaust  steam  still  contains  the 
larger  part  of  the  heat  that  is  brought  from  the  boiler,  and  this 
heat  is  nearly  all  surrendered  to  the  condensing  water.  How- 
ever, some  of  this  heat  may  be  returned  to  the  boiler  with  the 
feed  water  (this  being  saved)  but  the  proportion  is  generally 
quite  small  if  the  vacuum  is  good.  In  Fig.  3  this  return  is  shown 
by  the  lower  stream  line,  for  one  particular  arrangement  of 
plant.  Condensers  and  methods  of  supplying  the  feed  water 
With  heat  from  the  exhaust  steam  will  be  discussed  more  in 
detail  later. 

(b)  When  the  steam  is  exhausted  at  atmospheric  pressure, 
the  feed  water  can  be  heated  nearly  to  212°  by  it  and  thus  quite 
a  considerable  saving  may  be  accomplished;  but  only  a  small 
percentage  of  the  total  exhaust  steam  of  the  entire  plant  can  be 
profitably  utilized  in  this  manner.     Frequently  the  main  prime 
mover  is  operated  condensing  and  the  auxiliary  apparatus  non- 
condensing,  the  exhaust  steam  of  the  latter  being  used  for  feed- 
water  heating.     This  results,  in  most  instances,  in  more  profit 
than  arises  from  operating  the  auxiliaries  condensing.    The  pieces 
of  apparatus  in  which  the  feed  water  is  heated  by  the  exhaust 
steam  are  called  feed-water  heaters;   they  will  be  discussed  in  de- 
tail later. 

(c)  When  the  local  conditions  are  suitable,  some  of  the  heat 
of  the  exhaust  steam  can  be  used  in  industrial  processes  which 
require  temperatures  lower  than  that  corresponding  to  the  ex- 
haust pressure.     Thus,  for  example,  a  steam  prime  mover  might 
furnish  power  for  an  industry  in  which  the  heat  of  the  exhaust 
steam  could  be  utilized 'in  dryers,  or  in  kettles  used  for  digesting 
various  materials,  and  the  condensate,  with  its  sensible  heat, 
might  be  returned  as  feed  water  to  the  boiler.     In  other  indus- 
tries in  which  solutions,  having  temperatures  of  vaporization 
below  212°,  are  evaporated  in  "evaporating  pans  "  at  atmospheric 


UTILIZATION  OF  WASTE  HEAT  621 

pressure,  or  in  "vacuum  pans  "  under  partial  vacuums,  the  latent 
heat  of  the  exhaust  steam  can  be  used  to  supply  the  heat  neces- 
sary to  evaporate  the  water  from  the  solution;  and  in  such 
cases  not  only  may  the  vacuum  pan  act  as  a  condenser  for  the 
power  plant  and  thus  reduce  the  back  pressure  on  the  prime 
mover,  but  the  hot  condensate  may  be  returned  as  boiler  feed. 

(d)  Many  plants  are  situated  in  localities  where  the  artificial 
heating  of  buildings  is  necessary  for  a  large  portion  of  the  year. 
For  such  heating,  low-pressure  steam,  i.e.,  steam  at  or  near 
atmospheric  pressure,  is  satisfactory;  hence,  the  exhaust  steam 
from  engines  suitably  located  can  often  be  used  for  heating  pur- 
poses for  many  months  in  each  year. 

As  in  the  case  of  vacuum  pans,  the  heating  system  can  some- 
times act  as  a  condenser  for  the  power  plant,  but  in  such  cases 
the  vacuum  carried  (if  any)  is  very  imperfect,  the  pressure  not 
being  much  below  atmospheric.  Such  "vacuum  systems  "  are 
generally  operated  at  a  pressure  of  but  I  or  2  pounds  below 
atmospheric,  despite  the  fact  that  the  lower  the  pressure  of 
condensation,  the  greater  is  the  latent  heat  surrendered  by  the 
steam.  The  reasons  for  not  using  greater  vacuums  are:  (i) 
Lowering  the  temperature  of  the  steam  in  the  radiator  neces- 
sitates a  greater  amount  of  radiating  surface  (which  involves 
greater  first  cost) ,  and  (2)  lowering  the  pressure  makes  it  more 
difficult  to  keep  the  joints  tight  (that  is,  to  prevent  the  inflow  of 
air),  for  even  if  the  heating  system  is  of  only  moderate  extent, 
there  are  hundreds  of  joints  and  it  is  difficult  to  insure  perma- 
nent tightness  in  all  of  them. 

In  other  heating  systems,  called  Pressure  Systems,  the  steam 
is  at  a  pressure  somewhat  above  atmospheric,  the  back  pressure 
on  the  engine  being  generally  from  5  to  20  pounds  gauge  pres- 
sure. 

(e)  Supposing  that  the  condensate  from  the  heating  system 
is  used  for  feed  water  (without  loss  of  temperature)  and  that  all 
the  heat  in  the  exhaust  steam  above  feed-water  temperature 
can  be  used  for  heating  purposes,  then,  in  the  ideal  case,  the 
efficiency  of  the  combined  system  is  100  per  cent,  for  all  of  the 
heat  which  is  given  to  the  steam  by  the  boiler  and  not  converted 
into  useful  work  is  utilized  in  heating.     In  the  actual  case  some 
of  the  heat  is  lost  by  cylinder  radiation,  by  mechanical  friction 
of  engine  and  driving  machinery,  and  by  useless  radiation  in 


622  HEAT-POWER  ENGINEERING 

pipes  between  engine  and  heating  system;  but  even  then  the 
efficiency  of  the  combination  is  relatively  high  while  it  is  in 
operation.  In  fact,  the  cylinder  radiation  and  dissipation  of 
heat  due  to  friction  and  work  may  not  be  waste  if  the  same 
amount  of  heat  would  otherwise  have  to  be  used  for  warming 
the  engine  room. 

Whether  or  not  it  would  pay  financially  to  utilize  the  exhaust 
steam  for  heating  buildings  depends  on  the  location  of  the  power 
plant,  the  length  of  the  annual  period  of  time  during  which  the 
heating  is  necessary,  the  percentage  of  the  total  steam  that  can 
be  used  during  such  periods,  the  excess  cost  of  equipment  over 
that  otherwise  required  and  many  other  items  which  need  not 
be  considered  in  this  brief  discussion. 

298.  Heat  Transmission.  —  In  order  to  transfer  the  heat  from 
the  hot  gases,  or  steam,  to  the  feed  water  or  other  absorbing 
media,  some  kind  of  heat  transmission  must  occur.     Hence  to 
properly  understand  the  operation  of  condensers,  economizers, 
feed-water   heaters   and   similar   apparatus,   one   must   have   a 
knowledge  of  the  general  theory  of  the  transmission  of  heat. 
The  subject  will,  therefore,  be  discussed  (in  the  next  chapter) 
before  such  apparatus  is  considered  in  detail. 

299.  Financial  Considerations,     (a)  Suppose  the  installation 
of  certain  apparatus  would  effect  a  substantial  saving  in  the 
weight  of  coal  used ;   then  from  the  standpoint  of  heat  utilization 
there  would  be  a  gain.     But  suppose,  further,  that  the  expense 
chargeable  against   the   installation   and   the  operation   of   the 
apparatus  itself  would  be  more  than  the  saving  in  the  cost  of 
coal;    then,  of  course,  the  installation  would  not  be  profitable 
financially. 

Obviously  the  advisability  of  the  adoption  of  additional  equip- 
ment depends  on  whether  it  will  effect,  in  the  long  run,  a  saving 
greater  than  all  expenses  in  any  way  chargeable  against  it. 

(b)  The  capital  invested  in  apparatus  must  be  guarded  against 
fall  in  value  in  order  to  protect  the  investor;  but  the  apparatus 
is  subject  to  decrease  in  value  because  of  wear  and  possible  acci- 
dents, and  also  because  it  may  become  obsolete  by  the  introduc- 
tion of  improvements.  This  decrease  in  value  is  called  "depre- 
ciation" Therefore,  each  year  there  must  be  set  aside  a  certain 


FINANCIAL  CONSIDERATIONS  623 

sum  (a)  so  that  the  amount  thus  accumulated  plus  the  remaining 
market  value  of  the  apparatus  will  at  least  equal  the  investment. 
The  more  rapidly  the  apparatus  deteriorates  or  becomes  obso- 
lete the  greater  is  the  annual  depreciation  to  be  set  aside. 

Furthermore,  the  capital  must  receive  yearly  interest  (b)  to 
be  profitable;  and  as  the  investment  increases  so  also  do  the 
expenditures  for  taxes  (c),  and  insurance  (d)\  and  should  addi- 
tional space  be  demanded  by  the  apparatus,  there  may  be  in- 
creased annual  rent  (e)  to  pay.  These  items,  and  perhaps  some 
others,  constitute  what  are  called  the  Fixed  Charges  against  the 
apparatus. 

(c)  Besides  these  items,  the  yearly  cost  of  operating  the  appa- 
ratus must  be  considered,  the  principal  items  of  such  additional 
expense   being   some   or   all   of    the   following: — (i)  Labor   or 
attendance;    (2)  fuel  consumption;    (3)  water  used;    (4)  oil,  waste 
and  other  supplies;    (5)  repairs  and  maintenance,  and  possibly 
other  items. 

If  the  saving  in  expenditure  for  fuel  per  year  should  be  greater 
than  the  sum  of  items  (a)  to  (e)  and  of  (i)  to  (5)  and  of  any 
others  not  included,  the  installation  of  the  apparatus  will  be  a 
source  of  profit,  otherwise  not. 

(d)  It  is  not  within  the  scope  of  this  book  to  enter  into  the  de- 
tailed discussion  of  the  financial  problems  connected  with  power- 
plant  engineering;   but  it  is  deemed  necessary  to  show  that  the 
heat  saving  is  not  the  final  criterion.     The  foregoing  very  brief 
discussion  is  given  for  that  purpose  and  to  make  clear  to  the 
reader  what  is  meant  when  such  phrases  as  "aside  from  the 
financial  considerations  involved  "  are  used  in  the  chapters  which 
follow. 


CHAPTER  XXXV. 
HEAT  TRANSFER. 

300.  General,     (a)    In  previous  chapters  it  has  been  assumed 
possible  to  transfer  heat  from  body  to  body  at  will,  limited  only 
by  the  law  that  a  body  cannot  gain  heat  from  one  at  a  lower 
temperature  unless  energy  is  expended  to  cause  the  transfer. 
It  is  now  necessary  to  investigate  more  closely  the  phenomena 
connected  with  the  "flow  "  of  heat  under  the  "driving  force  "  of 
a  temperature  difference. 

(b)  At  the  outset  it  must  be  clearly  understood  that  from  the 
engineer's  viewpoint  the  whole  subject  of  heat  transfer  is  in  a 
most  undeveloped  state.  Many  experiments  have  been  made, 
numerous  laws  have  been  suggested,  and  much  that  is  true  has 
been  recorded ;  but  there  are  still  many  points  about  the  subject 
which  are  matters  of  dispute  and  the  settlement  of  which  is 
anxiously  awaited.  It  will  be  shown  later  that  this  is  not  so 
much  due  to  the  lack  of  scientific  knowledge  as  to  the  lack  of 
means  of  applying  known  facts,  and  of  inability  to  analyze  the 
exact  conditions  under  which  the  heat  transfers  occur. 

301.  Heat  Conduction,     (a)  Assume  the  metallic  bar  shown 
in  Fig.  399  to  be  so  insulated  along  its  entire  length  that  no  heat 

can  be  dissipated  by  it  to  the  surrounding 

g      atmosphere.    Assume  further  that  the  ends 
are  so  arranged  that  heat  can  be  continu- 
ously supplied  to  the  bar  at  end  A  and  the 
Fig  300  same  amount  continuously  removed  from 

end  B.   Under  these  circumstances  the  heat 

supplied  will  all  flow  along  the  length  of  the  bar,  i.e.,  flow  through 
the  bar.  Experience  shows  that  under  such  conditions  the  tem- 
perature at  B  will  always  be  lower  than  the  temperature  at  A ,  that 
is,  that  there  must  be  a  temperature  difference  if  heat  is  flowing. 
This  is  very  similar  to  the  phenomena  met  in  the  flow  of  electric 
currents  in  similar  conductors.  It  is  necessary  that  a  difference 

624 


BEAT  TRANSFER  625 

of  potential  exist  between  two  points,  A  and  B,  if  an  electric 
current  is  to  flow  between  them.  In  the  one  case  then  electricity 
flows  "  because  "  of  a  difference  of  electrical  potential  or  electro- 
motive force,  in  the  other  heat  flows  "because  "  of  a  difference 
of  temperature,  or,  paralleling  the  above,  a  difference  of  "heat 
potential." 

(b)  Since  it  is  supposed  that  the  molecules  of  a  substance 
move  faster  when  at  a  high  temperature  than  when  at  a  low  one, 
the  sensible  heat  associated  with  the  substance  may  therefore 
be  conceived  as  being  measured  by  the  intensity  of  molecular 
motion,  and  heat  conduction  may  be  considered  as  merely  the 
imparting  of  such  motion  to  successive  groups  of  molecules  along 
the  path  of  heat  flow.  According  to  this  view  when  one  end  of 
a  solid  body  is  heated  the  molecules  begin  to  vibrate^  more  and 
more  rapidly  but  they  impart  some  of  their  energy  to  those 
molecules  immediately  adjacent  to  them,  and  these  in  turn  pass 
on  some  to  their  neighbors,  and  so  on  through  the  entire  sub- 
stance. 

'  (c)  The  laws  governing  this  sort  of  heat  flow  are  compara- 
tively simple.  To  develop  them  assume  the  two  parallel  planes 
A  and  B,  in  the  conducting  body  shown  in 
Fig.  400,  to  each  have  unit  area,  to  be  unit 
distance  apart  and  to  be  maintained  at 
temperatures  Ta  and  J&,  the  former  being 
one  degree  Fahrenheit  greater  than  the  Fig.  400. 

latter.     Then  there  will  be  a  flow  of  heat 
from  A  to  B\  and,  assuming  no  loss  from  the  walls  of  the  inter- 
vening body,  heat  will  have  to  be  supplied  at  A  and  removed  at 
B  at  exactly  the  same  rate  as  it  flows  between  these  points,  if 
these  temperatures  and  the  flow  are  to  be  maintained  constant. 

(d)  Experiment  shows  that  under  such  conditions  a  very  defi- 
nite amount  of  heat  will  flow  from  A  to  B  per  unit  of  time  in 
any  given  material  and  this  quantity  is  called  the  Specific  Heat 
Conductivity.  It  will  hereafter  be  designated  by  the  Greek  let- 
ter «,*  and,  as  used  in  most  engineering  calculations,  it  is  the 
number  of  B.t.u.  flowing  per  hour  in  the  material  between  two 
parallel  planes  with  area  of  each  equal  to  one  square  foot,  with 

*  The  letter  X  is  very  commonly  used  for  this,  but  because  it  has  already  been 
employed  in  this  book  to  represent  another  equally  important  quantity  it  is  thought 
best  to  prevent  confusion  by  adopting  the  above  unusual  symbol. 


626  HEAT-POWER  ENGINEERING 

one  inch  space  between  and  with  a  difference  of  temperature  of 
one  Fahrenheit  degree* 

(e)  It  is  easy  to  see  that  if  planes  having  areas  of  twice  this 
amount,  i.e.,  two  square  feet,  are  assumed,  twice  as  much  heat 
would  flow  between  them  in  a  given  time.  The  heat  flow,  or 
conductivity,  therefore  varies  directly  as  the  cross  section,  in 
the  same  way  that  electrical  conductivity  does. 

Similarly,  to  cause  heat  in  quantity  a  to  flow  between  two 
planes  of  unit  area,  but  at  two  units  distance  apart,  will  require 
twice  the  temperature  difference  that  is  needed  when  they  are 
but  one  unit  apart.  This  can  easily  be  seen  by  imagining  an 
intermediate  plane  at  unit  distance  from  each  of  the  others.  One 
degree  of  temperature  difference  will  cause  a  heat  units  to  flow 
from  plane  A  to  the  intermediate  one  and  plane  B  must  be  one 
degree  lower  than  the  intermediate  to  maintain  the  same  rate 
of  flow.  In  other  words  heat  conductivity,  like  electrical  con- 
ductivity, varies  inversely  as  the  length  of  the  conductor. 

A<2  =  the  heat  flow  between  two  parallel  planes  of  equal 

area  in  a  given  material  in  one  hour, 
B  =  the   temperature   difference   in   Fahrenheit  de- 

grees, 

5  =  area  of  each  of  the  two  planes  in  square  feet,  and 
5  =  distance  apart  of  the  planes  in  the  conductor,  in 
inches, 

then,  from  the  two  statements  in  (e)  above, 


(428) 


And,  if  Sa/d  be  called  the  conductivity  of  the  heat  path,  its 
reciprocal  d/Sa  may  be  called  the  heat  resistance,  R,  just  as  the 
reciprocal  of  electrical  conductivity  is  called  the  electrical  re- 
sistance. If  this  is  done  equation  (428)  may  be  written 

A<2  =  0  -  (5/Sa)  =  0/R, 

the  last  term  of  the  expression  resembling  Ohm's  Law,  but  giving 
the  heat  flowing  in  unit  time  in  terms  of  temperature  difference 
divided  by  heat  resistance,  instead  of  electrical  flow  in  unit  time 
in  terms  of  voltage  difference  divided  by  electrical  resistance. 

*  This  curious  mixture  of  units  is  of  convenience  in  engineering  calculations. 
t  For  flow  between  inner  and  outer  surfaces  of  a  cyclindrical  wall  see  Appendix. 


HEAT  TRANSFER 

This  form  of  expression  can  be  used  to  find  heat  flow  with  any 
complicated  combination  of  resistances  just  as  is  done  in  elec- 
trical problems,  and,  in  general,  paths  with  resistances  in  parallel 
or  in  series  might  be  considered.  However,  in  practical  cases 
resistances  in  series  are  generally  the  only  ones  of  importance, 
and  for  such  instances 

A<2  =  0-  (2R).  :  ....    4   ."  .     .     (429) 

(g)  The  specific  heat-conductivity,  a,  varies,  in  general,  with 
the  kind  of  conductor  in  about  the  same  way  as  does  electrical 
conductivity;  thus,  good  conductors  of  electricity  are  generally 
good  conductors  of  heat,  and  vice  versa.  It  also  varies  with 
purity  of  material,  being  different  for  instance  for  pure  copper 
and  copper  containing  small  quantities  of  other  metals,  and  with 
temperature  much  as  does  electrical  conductivity.  The  con- 
ductivity at  at  any  temperature  above,  or  below,  a  chosen  datum 
can  be  expressed  in  terms  of  the  conductivity  aQ  at  datum  tem- 
perature by  the  equation 

at  =  «0(l  +  00; 
and  with  32°  F.  as  datum  this  becomes 

at  =  «32  {I  +£(/-  32)1,      ....      (430) 

in  which  0  is  a  constant  which  has  values  varying  with  the  mate- 
rial, being  positive  with  some  and  negative  with  others. 

The  values  of  a;32  and  0  are  given  in  Table  XXVI  for  some  of 
the  common  heat  conductors  used  by  the  engineer. 

Comparison  of  the  specific  conductivities  tabulated  will  show 
thnt  for  metals  they  are  several  hundred  times  as  great  as  for 
water,  and  that  for  this  latter  substance  the  conductivity  is 
several  times  the  value  for  gases.  Stagnant  gases  are  about  the 
poorest  conductors,  and  stagnant  water  is  nearly  as  bad. 

302.  Heat  Transfer  by  Convection,  (a)  When  fluids  (liquids 
and  gases)  have  their  temperatures  raised  locally,  the  heat  energy 
is  distributed  through  the  mass  of  fluid  not  only  by  conduction, 
such  as  was  just  considered,  but  also  by  what  is  known  as  "con- 
vection." Most  liquids  are  comparatively  poor  heat  conductors 
and  practically  all  gases  are  very  bad  ones,  but  under  proper 
conditions  heat  may  be  transferred  to  distant  parts  of  the  fluid 
very  quickly  by  convection. 


628 


HEAT-POWER  ENGINEERING  '' 


TABLE  XXVI.*— SPECIFIC  CONDUCTIVITY  OF  VARIOUS 
MATERIALS. 


Materials. 

*»*• 

0t- 

Cast  iron.        

330.00 

—  0.0004 

Average  values  for  gray  iron. 

Wrought  iron 
(unworked)  

450.00 

—  0.0009 

Variations     with     composition 
very  great. 

See  next  below  as  indication  of 

Wrought  iron 
(worked)  
Steel  (soft)  

240.00 
300.00 

—  O.OOO6 
—  0.0003 

variation. 
See  below  as  indication  of  vari- 

Steel (mod.  hard)  . 

240  .  oo 
1  80 

—  0.0003 

ations. 

Copper  (pure)  
Copper 
(commercial)  .  .  . 

Brass  (yellow)  .... 
Brass  (red)  

2400 

2IOO 

42O 
^40 

—  O.OOO2 
+  O.OOOI 

+O.OOI4 
+0.0008 

Values  given  by  different  experi- 
menters   vary    considerably. 
Probably  due  to  variations  in 
purity  and  condition. 

1  Varies   greatly   with   composi- 
'     tion. 

Aluminum  (pure).. 
Aluminum 

•HEIS 

Cylinder  oil. 

750 

IO4I 
0.784 

+0.0003 

+O  .  OOO2 
—  O.OOI5 

Naturally  varies  with  kind  of 

Water  

2.6158 

+O.OO53 

oil,  cylinder  oil  not  being  a 
definite  compound. 
These  values  seem  best  authen- 

Air 

o  11080 

+o  0017 

ticated.      Authorities    differ 
greatly. 
Varies  with  humidity,  etc. 

Hydrogen 

O   7IQ33 

Fire  brick 

6.948  at  1300°  F.     Varies  con- 

" Insulating  " 
materials  

O.4  tO  1.2 

siderably  with  composition  of 
brick. 

Such  materials  as  cork,  cellular 
paper,  asbestos  mixtures,  etc. 

*  Compiled  largely  from  the  Landolt-Bornstein-Myerhoffer  Tabellen,  and  from 
"Hutte,"  Des  Ingenieurs  Taschenbuch. 

There  is  still  considerable  uncertainty  and  disagreement  regarding  the  specific 
conductivities  of  the  various  substances  and  the  U.  S.  Bureau  of  Standards  is  now 
carrying  on  investigations  on  this  subject.  The  results  will  presumably  be  pub- 
lished eventually  in  a  bulletin. 

t  a  is  heat  in  B.  t.  u.  conducted  per  square  foot,  per  degree  difference,  per 
hour,  per  inch  thickness  of  material.  /3  is  the  constant  in  Eq.  (430). 


BEAT  TRANSFER  629 

(b)  Practically  all   fluids   increase   in  volume  when  heated, 
that  is,   their  density  decreases.     Local  heating  will  therefore 
cause  local  decrease  of  density;    but  this  will  disturb  the  me- 
chanical equilibrium  of  the  fluid  and  there  will  be  a  tendency  for 
the  heated  portions  to  rise.     This  will  be  more  marked  the  more 
intense  and  local   the  heating,  and  it   results  in  the 

flow  of  the  heated  material  through  the  rest,  that  is, 
currents  are  formed,  or  "circulation  "  occurs.  This 
process  very  rapidly  distributes  heat  energy  to  all  parts 
of  the  mass  even  though  the  fluid  be  a  poor  conductor 
of  heat.  Examples  of  convection  currents  caused  by 
local  heating  are  shown  by  the  arrows  in  Figs.  401 
and  350. 

(c)  The  marked  distinction  between  heat  conduction   Fjg.~40I. 
and  heat  convection  can  now  be  clearly  shown,  if  the 

views  expressed  are  assumed  correct:  Heat  conduction  is  due 
to  the  individual  motions  of  single  molecules,  while  heat  con- 
vection is  the  common  transportation  of  groups  of  molecules. 

(d)  No  attempt  will  be  made  to  give  an  expression  for  the 
rate  at  which  heat  is  distributed  through  a  fluid  by  convection, 
as  it  would  be  very  complicated  and  of  little  use  at  best.     It 
would  at  least  involve  differences  of  temperatures  and  densities, 
specific  heats,  viscosity  and  molecular  friction.     In  general  it 
may  be  said  the  heat  transfer  by  convection  will  increase  with 
temperature  difference,  or  with  the  intensity  of  local  heating, 
and  will  be  greater  the  less  the  viscosity  of  the  material. 

303.  Heat  Transfer  by  Radiation,  (a)  Experiment  shows 
that  bodies  at  all  temperatures  radiate  energy  at  the  expense  of 
their  associated  heat,  which  energy,  when  stopped  or  absorbed 
by  another  body  or  medium,  becomes  evident  as  heat  energy. 
This  does  not  mean  that  the  radiated  energy  is  in  the  form  of 
heat  when  on  the  way  between  the  two  bodies;  in  fact,  if  heat 
energy  is  to  be  considered  as  connected  with  the  motion  or  con- 
dition of  molecules,  radiant  energy  of  this  kind  cannot  be  heat 
as  it  will  pass  through  a  vacuum  devoid  of  molecules  of  any  kind. 

(b)  Like  light,  radiant  energy  is  supposed  to  be  transmitted 
by  the  hypothetical  "ether,"  and  to  be  a  vibratory  form  of 
energy.  It  is  further  commonly  supposed  that  the  molecules 
of  a  body  start  such  vibrations  in  the  ether  at  the  expense  of 


630  HEAT-POWER  ENGINEERING 

part  of  their  energy,  and  that  the  energy  associated  with  mole- 
cules of  other  bodies  can  be  augmented  at  the  expense  of  these 
ether  vibrations.  Whether  the  ether  exists  or  not,  and  whether 
the  process  goes  on  in  this  way  or  not,  is  really  immaterial.  The 
facts  remain  that  a  body  can  lose  heat  by  radiating  energy, 
which  is  not  what  is  commonly  called  heat  after  leaving  that 
body,  and  that  substances  can  be  raised  in  temperature,  vapor- 
ized and  so  on,  by  receiving  such  radiated  energy.  This  energy 
will  hereafter  be  called  radiant  energy  * 

(c)  The  rate  at  which  heat  energy  is  radiated  by  a  body  in- 
creases very  rapidly  as  the  absolute  temperature  is  raised.     Un- 
fortunately the  exact  law  governing  has  not  yet  been  definitely 
determined,  but  it  seems  probable  that  the  amount  of  energy 
radiated  varies  with  the  fourth  power  of  the  absolute  tempera- 
ture.    The  heat  AQ/g  radiated  per  unit  of  surface  per  unit  of 
time  by  a  body  maintained  at  a  constant  absolute  temperature 
T  is  then  given  by  the  equation 

&QR  =  kT*,      .  .  .     .     .  -?"-.     (431) 

in  which  k  is  a  constant,  which  depends  on  the  character  of  the 
material. 

The  net  loss  of  heat  from  the  body  by  radiation  is  not  given 
by  this  equation  however.  As  any  radiating  body  must  be  sur- 
rounded by  others  with  definite  temperatures,  it  must  be  receiving 
radiant  energy  as  well  as  sending  it;  hence,  the  net  result  of  such 
an  interchange  would  be  a  loss  or  gain  of  heat  equal  to  the  dif- 
ference between  that  sent  and  that  received.  On  this  basis  the 
net  heat  lost  per  unit  of  time  by  unit  surface  of  a  body  main- 
tained at  temperature  7\  (abs.),  radiating  to  another  parallel 
surface  maintained  at  lower  temperature  T2  (abs.),  and  with 
vacuous  space  between  the  two  surfaces,  would  be 

WRN  =  &7Y  -  £7Y  =  k  (TV  -  TV).    .    .     (432) 

which  is  known  as  Stefan's  Law. 

(d)  Since  the  radiant  energy,  like  light,  travels  or  radiates  in 
all  directions  from  the  surface  of  the  body  which  serves  as  its 
source,  equations  like  those  just  given  must  be  used  with  a  certain 

*  The  name  "radiant  heal"  is  often  given  to  what  is  here  called  radiant  energy. 
It  is  not  adopted  in  this  book  because  of  the  confusion  of  ideas  which  may  result 
from  its  use.;  see  (i)  of  this  section. 


HEAT   TRANSFER  631 

amount  of  care.  The  radiating  and  receiving  surfaces  may  be  so 
arranged  that  all  energy  lost  by  one  is  received  by  the  other  (in 
which  case  Eq.  (432)  applies),  or  they  may  be  so  arranged  that 
part  of  the  energy  is  not  caught  (and  Eq.  (432)  should  then  be 
modified) . 

In  Fig.  402  the  hot  surface  under  consideration  is  supposed 
to  be  a  small  area  S  in  the  plane  ab,  which  is  of  infinite  area 
and  has  the  same  temperature  throughout.  &/////////////////^//////////////////b 
The  plane  AB  is  a  similar  one  of  infinite  -- -  ^<6-^lLlIL^^ 

extent  having;  a  uniform  but  lower  tern- 

Fig.  402. 
perature.      It  is  obvious  that   the   solid 

angle  <f>,  representing  the  extreme  angle  with  which  the  rays 
from  surface  S  strike  plane  AB,  approaches  180°  as  a  limit,  and 
that  all  energy  radiated  from  .S  must  be  intercepted  by  AB  or 
pass  through  it.  In  such  case  the  hot  surface  6"  is  said  to  "see '' 
nothing  but  the  cold  surface  and  the  radiant  energy  received 
from  5  by  the  cold  surface  is  given  in  Eq.  (431). 

If,  however,  the  surfaces  are  arranged  as  in  Fig.  403,  in  which 

the  cold  surface  is  again  represented  by  AB,  it  is  evident  that 

,   the  solid  angle  d>  is  considerably  less  than 

W/////////////////5^///////////////////,0 

/   \  180°.     All  rays  from  S  passing  outside  of 

/^\  this  angle  miss  the  cold  surface  entirely  and 

J|^^%.  are  lost  in  the  space  beyond.     The  part  of 

^F.       *  the  total  radiant  energy  intercepted  by  the 

cold  surface  would  then  be  equal  to  that 

given  by  Eq.  (431)  multiplied  by  the  ratio  of  the  solid  angle  </ 
to  the  solid  angle  180°.  Note,  however,  that  this  does  not  give 
the  net  heat  lost  by  the  hot  surface,  for  this  will  be  all  that  can 
be  lost  through  the  solid  angle  180°  minus  all  that  is  gained 
through  that  same  angle.  Other  cases  can  be  analyzed  in  similar 
manner,  the  amount  of  radiant  energy  received  by  a  body 
depending  on  the  angle  <f>.  * 

(e)  The  condition  of  the  surface  of  a  body  determines  to  a 
considerable  extent  the  rate  at  which  it  will  'give  off  or  absorb 
radiant  energy.     Dull  black  surfaces  are  excellent  radiators  and 
absorbers.     Polished   metallic  surfaces  are   very  poor  in  both 
respects. 

(f)  Some  few  substances  are  practically  transparent  to  radiant 
energy,  that  is,  they  allow  practically  all  of  it  to  pass  through 
their  structure  without  absorption,  but  all  absorb  more  or  less. 


632  BEAT-POWER 

Every  substance  will  absorb  radiant  energy  with  the  same  wave 
lengths  as  that  which  it  radiates,  and  the  theoretical  limit  of 
transparency  to  radiant  energy  would  be  attained  with  a  body 
which  radiated  energy  of  one  wave  length  only  and  hence  ab- 
sorbed radiant  energy  of  that  wave  length  only. 

Most  solid  substances  radiate  energy  of  many  different  wave 
lengths  and  absorb  in  an  equally  broad  fashion.  Gases  on  the 
other  hand  radiate  energy  of  only  one  or  very  few  wave  lengths 
and  are  proportionately  transparent  to  radiant  energy. 

(g)  In  the  case  of  two  dull  black,  parallel  surfaces  of  the 
same  material  and  with  vacuous  space  between,  Eq.  (432)  will 
give  the  approximate  net  number  of  B.t.u.  of  radiant  energy 
interchanged  per  hour  per  square  foot  of  surface,  if  k  has  the 
value  of  about  16  X  io~10,  the  temperatures  being  on  the  Fah- 
renheit scale.* 

No  real  body  has  exactly  the  properties  of  the  ideal  black  one, 
but  sooted  and  lamp-blackened  surfaces  generally  approach  the 
ideal  case  within  5  per  cent  or  less. 

(h)  In  connection  with  Eq.  (432)  it  should  be  noted  that  even 
if  the  two  radiating  surfaces  are  so  arranged  that  each  "sees  " 
only  the  other,  &7Y  will  represent  all  the  heat  lost  by  body  I, 
but  &7Y  will  not  necessarily  represent  all  lost  by  body  2,  by 
radiation  in  the  direction  toward  body  I ;  this  would  be  true 
only  if  the  vibrations  caused  by  both  parallel  surfaces  were 
exactly  alike. 

(i)  In  connection  with  the  subject  of  heat  radiation  it  may  be 
well  to  call  attention  to  an  anomalous  expression  in  common 
engineering  usage.  All  apparatus  which  is  maintained  at  a 
temperature  higher  than  that  of  the  surrounding  atmosphere 
loses  heat  to  the  latter  and  this  loss  is  commonly  spoken  of  as 
heat  lost  by  "radiation."  As  a  matter  of  fact  only  part  of  it 
is  lost  in  such  manner,  the  major  portion  being  dissipated  by 
convection,  and  a  smaller  part  by  conduction  through  the 
atmosphere. 

304.  Heat  Transfer  in  Engineering  Apparatus,  (a)  The  three 
distinct  methods  of  heat  transfer  so  far  considered  are  never 

*  For  detailed  discussion  of  the  subject  see  Bull.  2,  U.  S.  Bureau  of  Standards, 
IQOS;  Pg-  107  of  Bull.  18,  U.  S.  Bureau  of  Mines;  and  Dalby,  Heat  Transmission, 
British  Inst.  of  M.  E.,  1909,  the  latter  containing  references  to  over  500  papers 
on  the  general  subject  of  heat  transmission. 


HEAT   TRANSFER 


633 


fe. 


really  found  existing  separately  in  any  actual  engineering  prob- 
lem, for,  in  general,  all  three  methods  of  transfer  are  operating 
at  the  same  time.  Nor  does  the  engineer  as  a  rule  have  to  deal 
with  heat  transfer  in  or  through  but  one  substance,  or  from  a 
single  simple  substance  to  another  single  simple  substance.  In 
general,  his  problems  are  so  complicated  that  in  the  end  it  is 
found  simpler,  in  the  present  state  of  knowledge,  to  design  by 
the  use  of  empirical  or  semi-empirical  equations  rather  than  to 
attempt  a  rational  treatment  of  each  case. 

(b)  An  idea  of  the  sort  of  problems  which  occur  can  be  given 
by  considering  a  single  case  analogous  to  practice  and  developing 
the  ideal  equations  for  it,  in  so  far  as  this  can  be  done. 

Imagine,  for  example,  a  sheet  of  metal  separating  two  mediums 
at  different  temperatures,  as  is  shown  semidiagrammatically  in 
Fig.  404,  in  which  B  is  a  section  through  the 
metal  perpendicular  to  its  surfaces  bb'  and  ccf, 
while  A  and  C  represent  sections  through  the 
mediums  on  each  side  of  the  plate.  The 
dotted  lines  aaf  and  dd'  represent  isothermal 
planes  in  these  mediums,  the  material  in  plane 
aa'  having  a  temperature  ti,  and  that  in  plane 
dd'  having  a  lower  temperature  /2- 

From  what  has  already  been  said  about  con- 
duction, it  is  evident  that  heat  will  flow,  or 
be  conducted,  from  the  plane  aa'  through  the 
mediums  A,  B  and  C  to  the  plane  dd'  so  long  as  the  tempera- 
ture difference  is  maintained.  If  the  only  method  of  heat 
transfer  be  assumed  to  be  conduction,  the  heat  flow  can  be  cal- 
culated by  Eqs.  (428)  and  (429). 

(c)  The  problem  of  conduction  may  be  considered  to  be  the 
determination  of  the  amount  of  heat  which  can  be  made  to  flow 
by  the  temperature  difference  (/i  -  J2),  through  the  three  prisms 
with  lengths  5t,  52  and  53  inches,  arranged  in  series  as  shown  in 
perspective  in  Fig.  405  (a),  in  which  the  planes  aa'  and  dd,'  are 
similar  to  those  in  Fig.  404. 

(d)  Investigating  now  in  detail  the  assumed  problem  of  heat 
conduction  in  connection  with  Fig.  405  (a) ,  it  is  evident  that  there 
must  be  a  constant  drop  of  temperature  along  the  length  61,  if 
heat  is  flowing  along  this  first  prism.     This  is  shown  graphically 
by  the  line  from  h  to  &  at  (b)  in  the  figure,  the  temperatures  being 


634 


HEAT-POWER  ENGINEERING 


(a) 


represented  by  ordinates  above  an  arbitrary  chosen  line  which 
is  not  shown.  The  temperature  drops  steadily  from  a  value  t\ 
at  the  plane  aa'  to  a  value  tb  at  the  surface  W. 

At  this  surface  there  is  an  abrupt  and  marked  temperature 
drop  to  tb  which  is  necessary  to  overcome  the  surface  resistance 
and  make  the  heat  enter  the  second  medium,  for  careful  experi- 
ment shows  that  a  surface  offers  a  certain  resistance  to  heat  flow, 
as  it  is  found  that  a  temperature  drop  must  occur  at  a  surface 
to  cause  heat  to  enter  any  given  mate- 
rial. This  so-called  surface  or  contact 
resistance  is  often  compared  with  that 
offered  by  a  joint  in  an  electrical  cir- 
cuit. But  while  there  are  points  of 
resemblance,  there  are  also  many  dif- 
ferences between  the  two  cases,  hence 
the  parallel  should  not  be  carried  too 
far. 

There  is  then  a  steady  drop  through- 
out the  length  52  of  the  second  prism 
until  the  temperature  tc  is  reached,  the 
line  from  4'  to  tct  in  general,  having  a 
different  slope  from  the  line  titb  because 
of  difference  in  the  specific  conductiv- 
ity. At  the  surface  ccf  there  is  again  an 
abrupt  drop  from  tc  to  tc'  and  then  the 
temperature  decreases  through  the  third 
medium  until  the  assumed  temperature 
/2  is  reached  in  the  plane  dd'  . 
In  the  example  illustrated  in  the  figure,  gas  and  water  are 
the  mediums  on  the  opposite  sides  of  the  plate,  as  is  the  case 
with  boiler  heating  surface.  But  in  the  boiler  there  are  addi- 
tional resistances  due  to  the  soot  on  the  external  surfaces  and 
scale  and  grease  on  the  interior  walls. 

(e)  Since  heat  flow  is  equal  to  temperature  difference  divided 
by  resistance,  the  amount  of  heat  per  hour  could  be  found  in 
this  case  if  all  the  resistances  were  known.  The  resistances 
being  in  series  they  are  additive,  as  previously  indicated  in 
Eq.  (429),  and  therefore  in  this  case 

e\ 


Fig.  405. 


R' 


R" 


HEAT   TRANSFER  635 

in  which  RI,  R2  and  R&  are  the  resistances  of  the  paths  61,  62  and 
63,  and  R'  and  R"  are  the  contact  resistances  of  the  planes  W 
and  cc'  respectively.  Then,  remembering  that  unit  cross  section 
has  been  assumed,  and  that  R  =  5/Sa,  this  equation  may  be 
written 


'  "  (4M> 


ai       a        0:2       a          0:3 

in  which  subscripts  are  used  as  in  Eq.  (433)  and  the  symbols  have 
the  same  meaning  as  in  Eq.  (428)  excepting  that  no  idea  of 
length  is  attached  to  the  specific  heat-conductivities  a'  and  a". 
Evidently  the  total  conductivity  per  unit  area  is  the  reciprocal 
of  the  denominator  in  Eq.  (434).  If  this  is  represented  by  K, 
then  for  any  area  S,  the  equation  becomes 

&Q  =  KSe.      ......     (435) 

(f)  Such  equations  as  Eq.   (434)  or  (435)  can  of  course  be 
solved  for  any  given  case  if  the  values  of  the  specific  conductivi- 
ties (a)  or  the  total  conductivity  (K)  are  known  ;   but  in  any  real 
case  such  a  calculation  would  be  of  little  value  as  heat  transfer 
will  also  be  produced  simultaneously  by  radiation  and  convec- 
tion, the  latter  generally  being  forced  to  a  certain  extent.     So 
great  is  the  effect  of  convection  in  most  engineering  problems 
that  it  is  often  the  most  important  consideration  as  can  be  well 
shown  numerically.     If  heat  is  transferred  from  a  metal  plate  to 
quiescent  water  under  such  conditions  that  convection  currents 
are  practically  eliminated,  the  amount  of  heat  transferred  per 
square  foot  per  hour  per  Fahrenheit  degree  difference  of  tem- 
perature will  be  of  the  order  2.8  B.t.u.  (=  at).     If  on  the  other 
hand  the  water  be  in  violent  motion,  or  in  ebullition  so  as  to 
assist  convection  as  much  as  possible,  the  heat  transferred  may 
be  of  the  order  1500  B.t.u. 

(g)  It  has  already  been  seen  that  stagnant  gases  and  water 
have  conductivities  several  hundred  times  poorer  than  metals. 
Hence  the  stagnant  film  of  fluid  that  adheres  to  the  surfaces  of 
the  metal  plates  increases  greatly  the  difficulty  of  heat  trans- 
mission to  and  from  such  plates.     These  surface  films  may  be 
regarded  as  being  constituted  of  the  molecules  of  fluid  caught 
in  the  microscopic  irregularities  of  the  plate's  surface,  or  of  those 
which  they  entangle  or  retard.     They  act  as  heat  insulators 


636  HEAT-POWER  ENGINEERING 

which  prevent  the  hotter  particles  of  one  fluid,  and  the  colder 
particles  of  the  other,  from  coming  in  contact  with  the  plate. 
Obviously  violent  agitation  of  the  fluids  tends  to  destroy  or  re- 
duce the  thickness  of  the  films  and  thus  makes  the  conditions 
more  favorable  for  heat  transmission.  Therefore  the  more  vio- 
lent the  circulation  or  convection  currents  (within  reason)  the 
more  rapid  will  be  the  heat  transfer  per  square  foot  of  surface; 
and  this  is  not  only  because  of  the  effect  on  the  film,  but  also 
because  the  hotter  portions  of  the  fluid  are  brought  to  the  plate 
at  a  more  rapid  rate.  If  gas  and  water  are  the  two  fluids,  as  in 
the  steam  boiler,  the  temperature  drop  A/i  (in  Fig.  405  (6))  neces- 
sary to  pass  the  heat  through  the  gas  film  is  relatively  very  much 
greater  than  the  drop  A/2  through  the  metal  of  the  plate  and 
through  the  water  film;  in  some  cases  it  may  represent  98  per 
cent  of  the  difference  between  the  temperatures  of  the  hot  gas 
and  the  water. 

The  important  part  played  by  such  films  can  be  shown  by 
an  example:  If  a  bunsen  flame  is  placed  below  a  metallic  vessel 
containing  boiling  water  the  flame  will  not  quite  touch  the  metal 
but  will  spread  out  into  a  sheet  at  a  distance  of  about  5V  to  ¥V  of 
an  inch  from  the  plate.  Because  of  its  high  conductivity  the 
plate  on  the  gas  side  can  be  only  a  few  degrees  higher  in  temper- 
ature than  the  water,  hence  through  the  very  short  distance  of  ^V 
to  £$  of  an  inch  there  must  be  a  drop  of  temperature  from  that 
of  a  bunsen  flame  to  a  value  only  slightly  above  that  of  water 
boiling  at  atmospheric  pressure. 

(h)  Some  of  the  difficulties  which  arise  in  actual  engineering 
problems  involving  the  transmission  of  heat,  and  the  reason  for 
using  empirical  or  semi-empirical  formulas,  will  now  be  apparent. 
These  problems  are  still  further  complicated  by  the  coatings  of 
scale,  grease,  soot,  paint  and  other  material  on  the  surfaces  of  the 
transmission  plates  and  by  the  relative  directions  of  the  flow  of 
the  fluids  on  the  opposite  sides  of  the  plates.  The  effect  of  this 
flow  can  be  analyzed  quite  accurately,  as  will  be  seen  in  the  suc- 
ceeding sections.  It  will  first  be  discussed  in  a  general  way  and 
later  the  mathematical  treatment  will  be  given  in  more  detail. 

305.  Effectiveness  of  Heat  Transmitting  Surfaces,  (a)  It 
has  been  seen  that  the  rate  of  transmission  of  heat  through  a 
plate  depends  directly  on  the  difference  between  the  tempera- 


HEAT   TRANSFER  637 

tures  of  its  two  surfaces.  Obviously  when  the  temperatures  of 
the  fluids  on  either  side  of  the  plate  are  maintained  constant, 
the  temperature  drop  is  the  same  at  all  points  over  the  surface, 
hence  the  rate  of  transmission  and  effectiveness  of  surfaces  is 
uniform  over  the  whole  area.  But  when  there  is  flow  of  one  or 
both  of  the  fluids,  the  conditions  are  quite  different. 

(b)  Imagine,  for  instance,  that  the  tube  in  Fig.  406  is  sur- 
rounded with  boiling  water  (temperature  constant)  and  that  hot 
gas  flows  from  a  to  b,  becoming  cooler  as  it 

progresses.  Then  the  average  tempera- 
ture drop  (difference  of  temperature)  (0mi) 
through  the  wall  back  of  surface  Si  is 
greater  than  that  (0™2)  at  surface  S2,  and 
this  latter  is  greater  than  that  (0TO3)  at  sur- 
face Ss  and  so  on  through  the  length  of  the 

tube.  With  a  tube  of  infinite  length  the  gas  could  theoretically 
be  cooled  to  the  temperature  of  the  water  and  the  temperature 
difference  at  the  end  b  would  be  zero.  Thus  dmi  >  0W2  >  0™3  > .  .  .  6mn 
and  each  portion  of  the  surface  is  less  effective  than  those  pre- 
ceding and  more  so  than  those  following.  The  nearer  the  tem- 
perature of  the  gas  approaches  that  of  the  water  the  less  effective 
is  the  adjacent  heating  surface,  although  it  costs  as  much  per 
square  foot  as  the  more  effective  portions.  Hence,  as  was  seen 
in  Sect.  261(0),  there  is  in  each  case  some  particular  extent  of 
surface  which  will  give  the  greatest  financial  return. 

Obviously  as  the  curve  of  temperature  change  of  the  gases  is 
not  straight,  the  mean  temperature  difference  for  the  surface 
as  a  whole  is  not  one-half  the  sum  of  the  initial  and  final  differ- 
ences. Before  the  case  can  be  analyzed  mathematically  it  will 
be  necessary  to  find  the  true  value  of  the  mean  temperature 
difference. 

(c)  Besides  the  foregoing  case,  the  cold  fluid  may  flow  and  the 
hot  one  may  be  at  constant  temperature,  or  both  the  cold  and 
hot  fluids  may  be  flowing  and  the  currents  may  be  either  in  the 
same  direction  or  in  opposite  directions.     In  each  of  these  addi- 
tional cases  the  temperature  difference  varies  over  the  surfaces, 
but  the  methods  of  variation  are  quite  different  from  the  case 
described  in  the  preceding  paragraph.     All  these  cases  will  be 
considered  in  detail  in  later  sections. 

(d)  In  all  cases  of  heat  transmission  through  plates  from  hot 


638  HEAT-POWER  ENGINEERING 

fluids  to  cold  ones  it  may  be  noted  that,  neglecting  radiation 
losses,  the  heat  surrendered  by  the  hot  fluid  must  equal  that 
received  by  the  cold  one  and  must  also  equal  that  flowing 
through  the  intervening  material ;  hence 

ChWh  (Ta  -  Tb)  =  A<2  =  CCWC  (tb  -  ta),    .     .     (436) 
in  which 

A<2  =  heat  transmitted  in  a  unit  of  time. 
Ch  and  Cc  =  the  specific  heats  of  the  hot  and  cold  fluids. 
Wh  and  Wc  =  weights  of  the  fluids  flowing  per  unit  of  time. 
ta  and  k  =  temperatures  of  cold  fluid  at  ends  a  and  b  (Fig. 

406). 

Ta  and  Tb  =  temperatures  of  hot  fluid  at  ends  a  and  b  (meas- 
ured on  the  same  temperature  scale  as  that 
used  for  ta  and  4)-* 

If  the  object  is  to  have  the  cold  fluid  abstract  a  certain  quantity 
of  heat  A<2  in  a  given  time  with  initial  temperature  tai  it  may  be 
accomplished  with  large  weight  Wc  of  material  leaving  at  low 
temperature  4,  or  by  a  small  weight  leaving  at  high  tempera- 
ture, and  similarly  in  regard  to  the  quantity  of  heat  supplied 
by  the  hot  fluid.  Obviously  the  final  temperature  attained 
by  either  fluid  may  be  controlled  by  regulating  the  weight  of 
material  flowing  per  unit  of  time. 

(e)  Again,  in  all  cases  of  heat  transmission  (neglecting  radia- 
tion losses),  the  heat  given  up  by  one  medium  and  received  by 
the  other  must  equal  the  conductivity  of  the  path  multiplied  by 
the  area  of  surface  transmitting  heat  and  by  the  temperature 
difference,  as  in  Eq.  (435).  However,  in  case  one  or  both  fluids 
flow,  the  temperature  difference  is  not  constant  but,  as  has  just 
been  seen,  varies  from  point  to  point,  hence  a  mean  temperature 
difference  6m  must  be  used.  For  all  conditions,  then, 

A<2  =  KSdm, (437) 

in  which 

A<2  =  heat  transmitted  (B.t.u.  per  hour) 
=  heat  lost  by  hotter  medium 
=  heat  gained  by  cooler  medium. 

*  T  is  not  here  used  to  represent  absolute  temperature  but  merely  that  of  the 
hotter  medium  measured  on  the  same  temperature  scale  as  /.  Its  use  avoids  the 
employment  of  primes,  additional  subscripts,  or  other  complications  that  would 
be  necessary  to  distinguish  between  the  temperatures  of  the  hot  and  cold  bodies 
if  the  same  letter,  such  as  t,  were  used  for  both. 


HEAT   TRANSFER  639 

•K  =  conductivity  of  heat  path  (B.t.u.  per  sq.  ft     per  hr 

per°F.). 

6"  =  total  surface  (sq.  ft.). 
6m  =  mean  temperature  difference  (°  F.) 
=  6  when  no  flow  occurs. 

(f)  But  before  Eq.  437  can  be  used  6m  must  first  be  deter- 
minecl.  As  will  be  shown  later  it  is  given  for  all  cases  by  the 
equation  0a  -  0b 

Bm  =  ioge(ea/eb)>  ......    (438) 

in  which 

Ba  =  temperature  difference  at  end  a  of  the  surface. 
0b  =  temperature  difference  at  end  b  of  the  surface. 

Therefore,  no  matter  what  the  conditions  of  flow, 


or 


306.  Cases  of  Heat  Transmission  through  Plates,  (a) 
There  are  five  cases  of  heat  transmission  through  plates,  and 
Eqs.  (436)  to  (440)  apply  to  all  of  them.  They  will  be  described 
briefly  in  this  section  and  in  more  detail  later. 

(b)  Case  I.  (T  =  const.)  A  hot  substance  at  constant  tem- 
perature T  surrenders  heat  to  a  flowing  cold  substance,  whose  tem- 
perature t  is  increased.  Surface  condensers  and  feed  water 
heaters  are  examples  of  this  case,  for  in  both  of  these  heat  of 
the  exhaust  steam  (at  constant  temperature)  T=con8t 

is  surrendered  to  water   which   is   raised  in 
temperature    as  it  flows   through   the   appa-      "-         ^"" 
ratus.     This  case  is  shown  by  the  curves  in 
Fig.  407,  in  which  ordinates  are  temperatures 
and   abscissas   are   extent   of   surface.      The  pjg 

upper  curve  is  for  the  hot  fluid  and  the  lower 
for  the  cold  one,  the  flow  being  toward  the  right.  It  will  be  seen 
that  the  final  temperature  of  the  cold  body  depends  on  the  total 
length  of  surface,  and  that,  as  the  flow  progresses,  the  tempera- 
ture /  of  the  cold  medium  gradually  approaches  that  (T  =  const.) 
of  the  hot  fluid,  and  the  temperature  difference  and  value  of  the 
surface  (per  square  foot)  becomes  less. 


640  HEAT-POWER  ENGINEERING 

The  efficiency  of  the  heating  surface  is  evidently 

Ef .  =  'Heat  transmitted  -r-  maximum  amount  absorbable 


0, 


(440 


—  1 

t 

=  Const. 

f                     °                      > 

Fig.  408. 


(c)  Case  II.  (/  =  const.)  A  substance  at  constant  tempera- 
ture (t)  receives  heat  from  a  hotter  flowing  substance  whose  tempera- 
ture (T)  decreases.  An  example  of  this  is  the  steam  boiler,  in 
which  the  boiling  water  (at  constant  temperature  /)  receives 
heat  from  the  hot  gases  which  decrease  in  temperature  T  as 
they  progress.  This  case  is  the  reverse  of 
Case  I,  and  Eq.  (441)  applies  except  that 
ChWh  would  be  substituted  for  CCWC.  Fig. 
408  is  the  diagram  for  this  case. 

(d)  Case  III.  Parallel  Flow.  The  term 
is  understood  by  engineers  to  mean  parallel 
flow  in  the  same  direction  on  opposite  sides 
of  the  plate.  The*Kdt  and  cold  substances  both  flow  in  the  same 
direction,  their  temperatures  converging  nearer  to  equality  as  they 
progress,  as  shown  in  Fig.  409  in  which  the  arrows  show  the 
direction  of  flow. 

With  finite  surface  the  heat  transmitted  is 
=  CCWC  (tb  -  to).  If  the  object  is  to  absorb 
heat,  the  maximum  amount  which  the  cold 
fluid  could  receive  is  CcWc6a,  and  the  Com- 
parative Efficiency  (to  be  used  in  comparisons 
with  other  cases)  is  therefore 

—  ta)          tb  —  ta 


(Ta  — 


CEfc 


(442) 


Fig.  409- 


ccwcea  Ba 

But  if  the  object  is  to  cool  the  hot  fluid  the  maximum  amount  of 
heat  that  could  be  surrendered  is  ChWhOa  and  in  that  case  the 
Comparative  Efficiency  is 

ChWh  (Ta  -  Tb)      Ta  -  Tb 


CEfh 


ChWh0c 


ef. 


(443) 


No  matter  how  extensive  the  surface,  Tx,  in  the  figure,  is  the 
limit  of  temperature  to  which  the  hot  fluid  can  be  cooled  and 
the  cold  one  heated.  The  heat  available  for  transmission  is 
(or  CcW<0a)  and  with  infinite  surface  only  the  part 


BEAT  TRANSFER  641 

CkWk  (Ta  -  r,)f  or  CCWC  (Tx  -  ta),  could  be  transmitted. 
Hence  the  maximum  possible  efficiency  is 

Efh  =  (Ta  -  T,)  +  Oa,    .     .     .    .;     .     (444) 
or  Efe  =  (Tx  -  ta)  -5-  Oa,   '  .     .     .     .     .     (445) 

which  is  less  than  that  attainable  in  any  of  the  other  cases.  It 
would  therefore  appear  that  this  arrangement  should  always  be 
avoided ;  however,  if  only  a  relatively  small  portion  of  the  avail- 
able temperature  head  0a  is  to  be  utilized,  parallel  flow  may  be 
advantageously  used,  as  under  these  conditions  it  requires  less 
heating  surface  (and  hence  the  initial  cost  is  less)  to  produce  the 
same  result  than  is  required  in  some  other  arrangements. 

(e)  Case  IV.     Counter  flow.     The  hot  and  cold  substances  flow 
in  opposite  directions,  the  temperature  of  the  former  approaching 
the  lowest  temperature  of  the  latter,  and  vice  versa,  as  they  proceed. 
This  is  shown  in  Fig.  410,  in  which  the  directions  of  flow  are 
shown  by  the  arrows,  Ta  being  the  initial  tern-  Tfl 

perature  of  the  hot  fluid  and  /&  being  that  of 
the  cold  one.  The  relation  between  the  h<  c 
absorbing,  or  surrendering,  capacities  of  the 
two  fluids  is  given  by  the  ratio  of  CCWC  to  ChWh 
and  this  determines  whether  the  two  curves 
diverge  or  converge  or  are  parallel.  With  infi-  Fig.  410.* 

nite  surface  it  can  be  shown  that  the  hot  medium 
would  be  cooled  to  the  initial  temperature  4  of  the  cold  one  if 
ChWh  <  CCWC',  or  the  cold  medium  will  be  raised  to  the  initial 
temperature  Ta  of  the  hot  fluid  if  CCWC  <  ChWh\  and  in  this  ideal 
case  the  efficiency  is  unity,  since  all  the  heat  possible  is  trans- 
mitted with  the  materials  in  question.  Hence  the  only  limit  to 
the  efficiency  is  the  extent  of  the  heating  surface.  But  a  com- 
parison of  Fig.  410  with  Fig.  409  will  show  that  the  mean  tem- 
perature head  is  less  with  counter  current  flow  than  with  parallel 
flow,  hence  to  accomplish  the  same  degree  of  heating  (or  cooling), 
and  to  obtain  the  same  efficiency,  more  extensive  surface  (at 
greater  cost)  is  required.  Counter  current  apparatus  is  there- 
fore characterized  by  high  possible  efficiency  and  by  economy  of 
amount  of  heating  or  cooling  material,  as  an  offset  for  the  greater 
surface  necessary. 

(f)  CaseV.     (T  and  t  both  constant.}     Transmission  of  heat 
from  a  hot  fluid  of  constant  temperature  (T)  to  a  cold  one  which 

*  Fig.  410  is  for  CCWC  >  ChWh.    If  CcWc  <  ChWh  then  6b  >  Ba. 


642 


HEAT-POWER  ENGINEERING 


remains  at  constant  temperature  (t).  The  vacuum  pan  is  an  ex- 
ample of  this  case,  since  the  latent  heat  of  the  steam  (at  constant 
temperature)  furnishes  the  heat  for  evaporating  (at  constant 
temperature)  the  other  medium. 

(g)  The  mathematical  treatment  of  these  five  cases  will  now 
be  discussed  in  the  succeeding  sections.* 

307.  Case  I.  (T  =  Const.)  A  Hot  Substance  at  Constant 
Temperature  Surrenders  Heat  to  a  Cold  Fluid  which  Flows, 
(a)  Assume  the  conditions  shown  in  Fig.  411  and  imagine  that 

Wc  pounds  of  the  cooler  material 
flow  over  the  small  surface  65  in  a 
given  time  and  that  as  a  result  their 
temperature  is  raised  an  amount 
dt  (  =  60).  Then,  if  the  specific  heat 
of  the  cooler  material  be  Cc,  the 
heat  5Q  absorbed  from  the  area  5S 
per  unit  of  time  is 

6<2  =  CcWc5t=  CCWC.56; 

but  this  must  equal  the  heat  trans- 
mitted through  5S  in  the  same  time, 
hence 

dQ=  (T-t)K.5S  =  0K.8S, 
in  which  T  and  /  are  average  tem- 
peratures  (to  same   scale)   over   5S 


5S 


Fig.  411. 


and  the  other  symbols  have  the  same  significance  as  in  Sect.  305. 
Equating  the  two  values  of  5Q  in  the  two  preceding  equations 
gives 

CcWc.5d  =  OK-5S, 

Ca  fffl         K      Cb 
from  which  /    2  -  ~  I    55. 

Jb       0  CcWcJa 

Integration  of  this  gives 


KS 


(446) 


which,  rearranged  and  multiplied  by  (0«  —  0*>)  becomes 
r  w  (a        a  \       ^5  (6 a  —  Ob) 

c<w<^-        -  log,  («./*)  ' 

*  These  sections  may  be  omitted  in  a  briefer  study. 


HEAT   TRANSFER  643 

Now  from  Fig.  411  it  is  seen  that  (8a  -  db)  =  (tb  -  M  hence 


but  the  last  member  of  this  equation  is  A<2,  hence  the  equation 
above  becomes  /,,        a  •, 

~  f       x 

•     •     •     •     (447) 


which,  in  connection  with  Eq.  (437),  shows  that 

fi         (Oa  ~  Ob) 

6m-\oge(ea/eb)  ......    (448) 

as  given  in  Eq.  (438). 

(b)  For  certain  purposes,  however,  it  is  more  convenient  to 
write  the  value  of  Bm  in  another  form.  From  Fig.  411  it  is  evi- 
dent that  Ba  =  (T  -  ta)  and  6b  =  (T  -  4),  substituting  which  in 
Eq.  (448)  and  simplifying  gives  the  more  useful  expression 

a  h  —  ta  /  v 

9"=,       T-t.  .......     (449) 

log'7^4 

Transforming  Eq.  (446)  gives 


where  n  is  the  number  whose  Naperian  logarithm  is  KS/CCWC, 
as  given  by  the  Log.  Tables  in  the  Appendix. 

Hence  for  any  extent  of  area  5,  the  temperature  difference  at 
the  end  b,  in  terms  of  the  known  value  at  end  a,  is 

06  =  0«  -*-»;.     .     .     .     .     .     .     (450 

and  by  taking  different  extents  of  area  S  and  solving  for  the  cor- 
responding values  of  6b  data  may  be  obtained  for  plotting  curves 
which  show  how  the  temperature  difference  varies  as  the  flow 
progresses,  for  given  values  of  K,  Cc  and  Wc. 

(c)  The  efficiency  of  heat  transmission  (neglecting  losses)  for 
this  case  was  given  in  Eq.  (441).  Substituting  the  value  of  6b 
from  Eq.  (451)  gives 

£/=^  =  ^^  =  I-i,  .  .  .  (452) 

from  which  the  values  of  the  efficiencies  corresponding  to  dif- 
ferent extents  of  area  S  can  be  readily  computed  in  any  given 
case,  and  the  data  thus  obtained  can  be  used  for  constructing  a 
curve  to  show  the  variation  graphically. 


644 


HEAT-POWER  ENGINEERING 


308.  Case  II.  (t  =  Const.)  A  Substance  at  Constant  Tem- 
perature (t)  Receives  Heat  from  Another  Flowing  Substance 
whose  Temperature  Decreases.  This  is  the  case  shown  in 

Fig.  412  and  is  the  reverse  of  Case  I. 
The  treatment  is  similar  to  the  last 
case  except  that  T,  dT  and  ChWh  are 
substituted  for  /,  U  and  CCWC.  A<2 
is  given  by  Eq.  (447)  without  change 
and  ^by  Eq.  (448). 

Since  in  this  case  6a  =  ( Ta  —  t)  and 
Ob  =  (Tb  —  t),  substitution  of  these 
quantities  in  Eq.  (448)  gives 

Ta-Tb 


Fig.  412. 


log* 
Paralleling  Eq.  (450) 


(453) 


nt  (454) 

where  n  is  the  number  whose  loge  is  (KS/ChWh).     Using  this 
value  of  n,  Eqs.  (451)  and  (452)  can  be  applied  to  this  case. 

309.   Case  III.    Parallel  Flow  in  the  Same  Direction,     (a) 

This  case  is  shown  by  the  curves  in  Fig.  413.     As  in  the  previous 

cases  the  heat  lost  by  the  one  mate- 

rial in  passing  any  area  equals  that 

transmitted  through  the  wall  and 

also  equals   that   received   by  the  T 

second  material  (neglecting  losses). 

Therefore,  for  an  infinitesimal  area, 

dS  in  the  figure, 


dQ  =  5TChWh  =  dtCcWc 
and  for  the  entire  area 


(a) 


c,    (b) 

where  AT6  and  A  &  are  the  total 
charges  in  the  temperatures  of  the 
hot  and  cold  fluids.  It  is  also  evident  from  Fig.  413  that  for 

surface  M  &T  +  U  =  (6  -  9>)  =  W  ......     (c) 

and  that  ^  +  ^  =  ^ 


HEAT   TRANSFER  645 

Equations  (a)  and  /c)  may  now  be  used  to  derive  two  more 
which  will  be  of  value  later.     From  (a) 

dTChWh  -  dtCcWc  =  o, 
and  multiplying  Eq.  (c)  by  CCWC  gives 

dTCcwc  +  5tccwc  =  deccwc. 

Adding  these  last  two  equations  and  solving  gives,  for  the  small 
area  55, 


which  will  be  used  later. 

By  analogy  it  is  also  evident  that  for  the  total  area  S 

C  W 

' 


Substituting  now  in  Eq.  (b)  the  value  of  AjT&  just  found  gives 


which  will  also  be  used  later. 

(b)  Returning  now  to  fundamentals,  it  is  evident,  as  in  pre- 
vious cases,  that 

dQ  =  dTChWh  =  K6  •  dS. 
From  which 

8T/d=  (K'9S)/(CkWk). 

Substituting  for  5T  its  value  from  Eq.  (e)  and  rearranging  gives 


WkCcWc   I 


Ch 
and  integrating  between  the  limits  a  and  b  yields 


chwhccwc 

Multiplying  both  sides  by  (Oa  -  Ob)  and  rearranging  gives 


e  (ea/eb)  ' 

But  from  Eq.  (g)  it  is  seen  that  the  left-hand  member  is  AQ, 
hence,  as  in  the  other  cases, 

(455) 


,• 


646  HEAT-POWER  ENGINEERING 

(456) 


Comparison  with  Eq.  (437)  shows  that     m 

(oa  -  eb) 


ioge  (oa/ob)' 

as  in  the  other  cases. 

From  Eq.  (h)  ic.w.+c*w*\ 

=  v  C.W.C 


(457) 

=  0«-*-»,         ...   .     ,     ,    .,  \>,iv-  v  ••      (458) 

.    yo/ccjpc  +  qwy\- 

where    w    is   the   number  whose   loge   is   AO  1     r  W  C  W  —  /' 

This  last  equation  makes  it  possible  to  determine  6b  when  Ba  and 
S  are  known. 

(c)  From  Fig.  413  it  is  apparent  that  ATb  =  (Ta  —  Tb). 
Substituting  this  in  equation  (/),  putting  0b  =  6a  -r-  n,  and  solv- 
ing gives  .  /  j\  /  r  w  \ 

T>  =  T«-e^-^(CcWCcfChWy.    r     (459) 

And  by  analogy 

'V'ii    (460) 


Then  if  06  =  o,  which  occurs  when  5  =  oo  ,  T&  becomes  equal  to 
/&  and  equal  to  the  limiting  temperature  Tx.     Thus 


or 


Since  the  maximum  amount  of  heat  that  can  be  transmitted 
is  (ra  -  Tx)  ChWh  =  (Tx  -  to)  CCWC,  the  true  efficiency  is  there- 
fore, in  the  ideal  case, 

TFf   -  (Ta  ~  Tb>  ChWh  -  (r"  ~  T^  (A^ 

'   (Ta  -  Tx)  ChWh  ~  (Ta  -  Tx)  ' 

mf  (tb  —   ta)   CCWC  tb—ta  (     ,^ 

or  TEfc  =  ~-r=  -  .  r  ,,,-  =  7p  --  -  .....     (463) 

(1  x  —  ta)  CCWC          1  x  —  ta 

As  given  in  Eqs.  (443)  and  (442)  the  comparative  efficiency 
(for  comparison  with  the  other  cases)  is 

~,.   .'V,  i  •.   .   (464) 


^-    .......     (465) 

Va 

depending  on  whether  the  object  is  to  cool  the  hot  fluid  or  to 
heat  the  cold  one. 


HEAT   TRANSFER 


64? 


310.    Case  IV.     Counter  Flow,     (a)  This  case  is  shown   in 
Fig.  414,   the  directions  in  which  the  temperature  curves  are 
generated   being  shown   by   the   arrows.     Compared   with   the 
other  cases  it  is  a  little  more  difficult      , 
to  develop  usable  equations  for   this  a  P^||^i^  JEJ^EE 
sort  of  flow  because,  in  general,  only 
the  initial  temperatures  Ta  and  tb  at  Ta 
opposite  ends  of  the  plate  are  known 
and  both  9a  and  06  are  unknown. 

(b)  As  in  previous  cases,  however, 
5Q  =  8TChWh  =  K0.5S    .     (a) 
=  dtCcWc (b) 

Hence 


the   symbol   Z   being    introduced    as 

this  ratio  will  be  frequently  used  in 

the  following  development.     From  the  figure  it  is  seen  that  the 

change  in  temperature  difference  over  any  elementary  area  8S  is 

50  =  0i  -  02  =  8T  -  8t* 
Substituting  for  U  in  terms  of  dT  from  Eq.  (c)  and  solving  gives 

dT  =  50 /  (i  —  Z) (d) 

If  this  is  substituted  in  Eq.  (a)  there  results,  after  transforma- 

tl0n'  80       l~ZK    ^ 

J  =  ~QJVh* 

which,  being  integrated  between  limits  a  and  b,  gives 


which,  after  both  sides  are  multiplied  by  (0«  -  0&)  and  rearranged, 
Sives  CkWk       KS(da-eb) 


(ea-^l_z-  ioge(ea/eb)  ' 

(c)  From  the  figure  it  is  further  apparent  that 


(467) 


and  from  Eq.  (c),  by  analogy  A/a  = 

*  The  analysis  given  is  for  Z  <  i.  If  Z  >  i,  then  in  Fig.  414  Ob  >  0aand 
0,  >  0i.  For  this  case  substitute  (02  -  0i)  for  (0!  -  02),  (St  -  8T]  for  (8T  -  5/)f 
(Z  -  ^  for  (i  —  Z),  06/0a  for  00/0fe,  and  (06  —  0o)  for  (00  —  0b). 


648  HEAT-POWER  ENGINEERING 

substituting  from  which  in  the  last  equation  and  solving  gives 


Now  A()  =  kTbChWh  and  substituting  the  value  of    An  just 
found  gives  c*W* 


(d)  Returning  now  to  Eq.  (467)  and  comparing  with  Eq.  (g), 
it  is  obvious  that  the  left-hand  member  is  equal  to  A<2,  hence 


.V;         -     -     (468) 
and  o  _  o 

.....     (469) 


These  expressions  are  evidently  the  same  as  in  the  other  cases. 
However  they  are  not  of  value  until  0a  and  0&  have  been  deter- 
mined, either  by  the  methods  which  will  now  be  given,  or  from 
actual  experiment  with  existing  apparatus. 
(e)  From  Eq.  (466)  it  is  evident  that 

i  ~z  K3 
ea/eb  =  ec*w"      =n,    ......     (470) 

in  which  n  is  the  number  whose  Nap.  log  is  ^  ,,.   KS.     Sub- 

LhWh 

stituting  the  value  of  0&  from  this  equation  in  Eq.  (f)  gives  * 


-  (i  -Z).       .     .     .     .     (h) 

From  Fig.  414  it  can  be  seen  that  A/0  =  (Ta  —  k  —  0a),  substi- 
tuting which  in  Eq.  (e)  and  solving  gives 

An   =    (Ta  ~tb-  0a)/Z.          .        .....        (i) 

Now  subtracting  Eq.  (i)  from  Eq.  (h)  and  solving  gives 


Tg-k  .  (  I    .    * n } 

~z~  ^\z+r^~zr  -  •  •  • 


(471) 


by  which  the  temperature  difference  at  one  end  can  be  deter- 
mined in  terms  of  known  quantities. 

*  For  Z  >  i  the  footnote  on  p.  647  applies  up  to  this  point.     Change  (h)  to  be 

=  da  (n  —  i)  •«•  (Z  —  i)  and  in  (471)  substitute  [^ +  -^  )in  the  paren- 

\^  —  i      ^/ 


thesis. 


HEAT   TRANSFER  649 

(f)  With  0a  known,  the  value  of  06  follows  from  Eq.  (470);  AQ 
and  9m  can  be  determined  from  Eqs.  (468)  and  (469)  ;  and  the 
final  temperatures  of  cold  and  hot  fluids  are 


and 


Tb  =  (tb 


(473) 


(g)   It  is  important  to  note  that  the  expressions  in  (f)  can  be 
used  only  to  determine  the  conditions  at  the  ends  a  and  b  or  over 


Fig.  415- 

the  entire  length  of  area  S.  They  cannot  be  used  for  interme- 
diate points,  that  is,  for  plotting  the  curves  TaTb  or  tatb  and  the 
like. 

311.  Case  V.  (T  =  const.  &  t  =  const.)  A  Hot  Substance 
Surrenders  Heat  at  Constant  Temperature  to  a  Cold  Substance 
whose  Temperature  is  Constant,  (a)  This  case  is  exemplified 
in  vacuum  pans  in  which  steam  at  constant  temperature  (T) 
surrenders  some  of  its  latent  heat  to  evaporate  a  solution  at 
constant  temperature  (f).  The  type  of  apparatus  which  is 
known  as  a  "single  effect  vacuum  pan"  is  illustrated  in  Fig.  415 
in  one  of  its  many  forms  and  arrangements. 

(b)  In  such  case  0m  =  (T  -  t)  and  the  heat  transmitted 
through  the  heating  surfaces  is  A<2  =  KSBm  from  Eq.  (437)- 


650 


HEAT-POWER  ENGINEERING 


Neglecting  losses,  the  weight  of  steam  condensed  in  unit  time 
by  an  amount  of  heat  equal  to  A Q  is  obviously 

Wh  =  AG/r,      ......     (474) 

where  r  is  the  latent  heat  of  steam  at  temperature  T  °F. ;  and 
the  weight  of  solution  evaporated  in  unit  time  is 

Wc  -  \Q/[\  -  (/.  -  32)i,     .',,;.;     .     (475) 

where  \  is  the  total  heat  (above  32°)  per  pound  of  the  vapor 
formed  at  temperature  /  from  the  solution,  and  /o  is  the  tem- 
perature at  which  the  solution  enters  the  vacuum  pan. 

(c)  The  vapor  (at  temperature  /i)  from  the  solution  in  one 
vacuum  pan  may  be  used,  as  in  Fig.  416,  to  vaporize  (at  lower 


Condenser 


Fig.  416. 

temperature  /2)  the  solution  in  a  second  vacuum  pan,  the  latter 
acting  as  condenser  for  the  first  element;  the  vapor  from  the 
second  pan  (at  temperature  /2)  may  be  similarly  used  to  evapo- 
rate (at  lower  temperature  /3)  the  solution  in  a  third  pan,  and 
so  on,  the  vapor  from  the  last  pan  being  carried  to  a  condenser. 
When  more  than  one  pan  is  thus  used  the  arrangement  is  termed 
"multiple  effect."  Arrangements  are  called  "double  effect," 
"triple  effect,"  "quadruple  effect,"  and  so  on  according  to  the 
number  of  pans  in  the  series.  In  Fig.  416  the  weak  solution  is 
admitted  at  /  to  the  first  pan  from  which  it  is  fed  at  proper  rate 
through  valves  V\  and  V2  to  the  other  ones.  The  strong  solu- 
tion is  withdrawn  from  the  respective  pans  at  A ,  B  and  C. 


CHAPTER  XXXVI. 
APPARATUS  FOR  HEATING  FEED   WATER. 

312.  Object  of  Heating  Feed  Water,  (a)  The  principal 
advantages  to  be  derived  from  heating  the  feed  water  supplied 
a  boiler  are: 

(i)  A  decrease  in  the  amount  of  fuel  required  to  generate  the 
steam,  hence  an  increase  in  the  over-all  efficiency  of  the  plant; 

(2)  less  severe  strains  in  the  boiler  metal,  as  there  is  less  differ- 
ence of  temperature  between  boiler  shell  and  the  fresh  feed  water; 

(3)  the  partial  deposition  outside  of  the  boiler  of  scale-forming 
impurities  contained  in  the  water;    and  (4)  an  increase  in  the 
steaming  capacity  of  the  boilers  as  less  heat  need  be  transmitted 
per  pound  of  steam  generated. 

(b)  An  idea  of  the  saving  of  fuel  derived  from  the  use  of  hot 
boiler  feed  can  be  obtained  by  analyzing  an  average  case.  As- 
sume, for  instance,  that  the  water  as  received  at  the  plant  has 
an  average  temperature  of  60°  F.  with  q  =  28.08  and  that  it 
is  converted  into  steam  at  a  pressure  of  150  Ibs.  abs.  (with 
X  =  1193.4),  thus  requiring  the  addition  of  1193.4  ~~  28.08  =  1164 
B.t.u.  (approx.)  per  pound.  Assuming  the  specific  heat  of 
water  as  unity,  every  11.64  (saY  I2)  degrees  by  which  the  tem- 
perature of  the  water  is  raised  before  its  introduction  into  the 
boiler  means  i  per  cent  less  heat  to  be  added  in  the  boiler,  which 
would  roughly  correspond  to  a  saving  of  i  per  cent  of  fuel. 

Expressed  as  a  formula,  the  theoretical  saving,  due  to  using 
hot  feed  water  at  temperature  //  instead  of  cold  at  temperature 
//,  in  a  boiler  generating  dry  saturated  steam  is  approximately: 

per  cent  saving  =  ^ —  X  100,    .     .     .     (476) 

in  which  "  q/ 

q/  =  sensible    heat    of    the    hot    feed   water    above    32°  F. 

=  (//  -  32)  approx., 
qf  =  sensible    heat    of    the    cold    feed    water    above    32°  F. 

=  (//  -  32)  approx., 

X  =  total  heat  of  steam  above  32°  F.  at  boiler  pressure. 

651 


HEAT-POWER  ENGINEERING 
If  the  steam  is  superheated  in  the  boiler,  the  saving  is 


per  cent  savng  =  - 


, 

+  A  — 


X  100.    .     .     (477) 


The  savings  in  per  cent  resulting  from  different  amounts  of 
feed-water  heating  with  different  initial  temperatures  for  the 
case  of  saturated  steam  are  shown  diagrammatically  in  Fig.  417. 
These  are  obtained  by  the  method  just  given. 

(c)  Inspection  of  these  curves  will  show  that  if  water  at  as 
low  a  temperature  as  40°  F.  is  raised  to  a  temperature  of  200°  F., 


60  80  100  120  140  ICO  180  200 

Initial  Temperature  of  Feed  Water(°F.) 

Fig.  417. 

i.e.,  through  a  range  of  160°  F.,  the  saving  will  be  slightly  over 
13  per  cent;  and  a  change  from  60°  to  180°  effects  a  saving  of 
about  10  per  cent  of  the  fuel  that  would  otherwise  be  needed. 

As  the  boilers  do  not  have  to  transmit  as  much  heat  per  pound 
of  steam  generated  from  preheated  feed  water  as  from  cold 
water,  smaller  or  fewer  boilers  may  be  used  for  a  given  output, 
when  other  considerations  permit. 

313.  Feed-Water  Heaters  in  General,  (a)  One  method  of 
heating  the  boiler  feed  water  is  by  using  for  that  purpose  some 
of  the  latent  heat  in  the  exhaust  steam  from  a  steam-driven 
prime  mover  (as  has  already  been  explained  in  Section  297),  the 
apparatus  in  which  the  transmission  occurs  being  called  a  Feed- 
Water  Heater,  or  an  Exhaust  Steam  Feed-Water  Heater. 


APPARATUS  FOR  HEATING  FEED  WATER  653 

(b)   If  w  pounds  of  steam  are  utilized  for  heating  per  pound 
of  raw  feed  water  which  is  at  temperature  /,,  then 

(//  -tf)  =w[\-  (t/  -  32)]  X  £/, 

in  which  t/  =  temperature  finally  attained  by  the  feed  water 

and  condensed  steam, 
X  =  total  heat  above  32°  of  i  Ib.  of  steam  used  for 

heating,  and 
Ef  =  efficiency  of  heater. 

Then  the  temperature  of  the  feed  water,  when  w  Ibs.  of  steam 
are  used  per  pound  of  feed,  is 


,  _ 

i+wEf     ~  .....     (478' 

and  to  attain  a  temperature  of  t/  the  weight  of  steam  required 
per  pound  of  raw  feed  is 


In  the  foregoing  it  has  been  assumed  that  the  condensed  steam 
is  finally  cooled  in  the  heater  to  the  temperature  of  the  outgoing 
feed  water.  Any  error  which  is  thus  introduced  is  corrected  by 
the  efficiency  factor. 

(c)  //  the  condensed  steam  is  not  returned  to  the  boiler  with 
the  feed,  this  expression  for  w  also  gives  the  maximum  propor- 
tion of  the  total  steam  generated  which  can  be  utilized  for  heat- 
ing an  equivalent  weight  of  feed  water.  For  example,  if  feed 
water  at  60°  is  heated  to  212°  F.  by  steam  from  an  engine  ex- 
hausting at  atmospheric  pressure,  and  if  Ef  =  .90,  the  maximum 
possible  weight  of  steam  so  utilized  is  found  to  be  about  17  per 
cent,  or  about  Jth  of  all  that  is  available.  It  is,  of  course,  de- 
sirable that  the  heat  in  the  remaining  portion  (£)  should  be 
utilized  in  some  other  way  as  far  as  is  possible. 

In  plants  in  which  the  main  units  are  operated  condensing,  the 
auxiliary  engines,  which  generally  use  less  than  £  of  the  total 
steam,  are  operated  noncondensing  and  their  exhaust  steam  is 
utilized  for  feed  heating.  This  results  in  greater  thermal  effi- 
ciency of  the  plant  as  a  whole  than  would  exist  if  the  auxiliaries 
were  connected  to  the  condenser,  since  all  the  heat  of  the  steam 
not  used  for  power  is  then  theoretically  returned  to  the  boiler. 


654  HEAT-POWER  ENGINEERING 

(d)  When  the  condensed  steam  (at  //)  is  returned  to  the  boiler 
with  the  feed,  the  total  weight  of  feed  per  pound  of  raw  feed 
is  (i  +  w),  and  the  proportion  of  raw  to  total  is   i/(i  +  w), 
where  w  is  the  weight  of  steam  condensed  per  pound  of  raw  feed, 
as  given  by  Eq.  (479).     Then  the  steam  condensed  per  pound 
of  total  feed  water  is 

w'  =  w/(i  +  w) (480) 

which  is  the  maximum  proportion  of  the  total  steam  generated 
that  can  be  utilized  for  feed  heating  in  such  cases. 

(e)  If  the  heater  is  located  in  the  exhaust  system  between  the 
prime  mover  and  the  condenser,  it  is  called  a  (i)  Vacuum  Heater, 
and  the  maximum  temperature  which  the  feed  water  can  theoreti- 
cally attain  is  that  corresponding  to  the  vacuum.     When  located 
in  the  exhaust  system  of  a  noncondensing  unit,  it  is  termed  an 
(2)  Atmospheric  Heater,  and  the  theoretical  temperature  attain- 
able with  sufficient  steam  is  212°.     Should  the  heater  take  steam 
from  the  auxiliary  apparatus  of  the  power  plant  it  may  be  named 
an  (3)  Auxiliary  Heater.     If  the  condensate  from  the  main  units 
is  not  used  as  feed  and  there  is  not  enough  steam  from  the 
auxiliary  apparatus  to  raise  the  temperature  to  the  maximum 
otherwise   attainable,    the   vacuum   and    auxiliary   heaters   are 
sometimes  arranged  in  series  —  the  water  first  passing  through 
the  former,  which  is  then  called  a  (4)  Primary  Heater,  and  finally 
through  the  latter,  which  becomes  the   (5)   Secondary  Heater. 
When  the  pressure  of  the  steam  used  for  heating  is  considerably 
above  atmospheric,  the  apparatus  is  a  (6)  Pressure  Heater. 

When  the  arrangement  is  such  that  the  feed  water  and 
steam  intermingle  in  the  same  chamber  the  heater  is  said  to 
be  of  the  (7)  Open  Type;  and  when  the  two  substances  are 
kept  separate  by  heat-transmitting  surfaces  it  is  of  the  (8) 
Closed  Type. 

314.  Open  Heaters,  (a)  Heaters  of  this  type  are  generally 
in  the  form  of  rectangular  boxes,  or  circular  shells,  fitted  with 
coarse  cascading  or  spraying  devices  to  break  up  the  water  as 
it  passes  through  and  thus  bring  it  into  more  intimate  contact 
with  the  steam.  They  usually  contain  a  filtering  bed  or  settling 
chamber  in  which  the  solids  carried  in  suspension  or  in  solution 
are  more  or  less  completely  removed  after  heating.  When 
necessary,  they  are  also  fitted  with  oil  separators  in  the  steam 


APPARATUS  FOR  HEATING  FEED   WATER 


655 


inlet  for  removing  the  cylinder  oil  from  the  steam  before  it  comes 
in  contact  with  the  water.  This  oil,  if  carried  over  to  the  boiler, 
would  seriously  reduce  the  transmission  of  heat  in  that  apparatus 


Water  Inlet 


Vent 


and  deposits  scale  on  those 
i  well  as  within  the  pans 


[Water  Outlet 


Fig.  418.  —Open  Heater. 


and  might  even  cause  overheating  of  the  metal  parts  subjected 
to  high  temperatures.  Two  of  the  great  variety  of  heaters  of 
this  type  are  shown  in  Figs.  418  and  419,  the  water  level  in  the 
latter  being  automatically  regulated  by  a  float. 


Fig.  419.  —Open  Heater. 

(b)  The  main  advantages  of  Open  Atmospheric  Heaters  are: 
(i)  the  feed  water  can  be  heated  nearly  to  212°  F.  if  sufficient 
steam  is  available,  and  surplus  steam  can  be  utilized  for  heating 


656 


HEAT-POWER  ENGINEERING 


buildings  and  in  industrial  processes  where  conditions  permit; 
(2)  scale  and  oil  do  not  affect  the  surrender  of  the  heat ;  and  (3) 
the  hot  condensed  steam  is  returned  to  the  boiler  with  the  raw 
feed,  but  should  be  purified  of  oil  (if  any  is  brought  over  from 
the  engine  cylinder  by  the  steam). 

The  open  heater  may  be  arranged,  as  in  Fig.  419,  to  include  in 
its  structure  (a)  an  oil  separator,  which  is  usually  located  in  the 
exhaust  pipe  at  entrance  to  heater,  (b)  a  filter  for  removing 
sediment,  part  of  which  may  be  precipitate  brought  down  by 
heating,  and  (c)  a  hot  well,  which  may  also  receive  the  returns 
(condensate)  from  systems  for  heating  buildings  and  such.  As 
the  feed  water  is  hot  and  at  pressure  near  atmospheric  these 
heaters  should  be  located  above  the  feed  pump  and  this  latter 


Miscellaneous  ."Losses 


Useful 


Fig.  420. 

should  be  suitable  for  pumping  hot  water.  If  the  raw  water  is 
not  available  under  sufficient  head  to  flow  into  the  heater,  a 
second  or  cold-water  pump  must  be  added. 

(c)  The  proportion  of  the  total  steam  generated  that  can  be 
used  for  heating  the  feed  water  is  obtainable  from  Eq.  (479), 
being  about  &th  in  ordinary  cases,  and  the  saving  of  fuel  effected 
is  given  by  Eq.  (476)  or  (477),  the  maximum  being  about  Jth. 
Fig.  420  shows  in  full  lines  the  energy  stream  for  a  power  plant 
having  all  units  exhausting  to  atmosphere  but  using  as  much 
waste  heat  as  is  possible  in  a  feed -water  heater;   and  in  dotted 
lines  it  illustrates  the  same  case  when  no  heater  is  used.     In  the 
first  case  the  over-all  thermal  efficiency  is  A  /B  and  in  the  second 
A/B',  the  heat  supplied  to  the  prime  mover  being  C  in  both 
cases. 

(d)  If  the  main  engines  are  condensing,  and  the  steam  from 
steam-driven  auxiliary  apparatus  is  used  for  feed  heating,  the 


APPARATUS  FOR  HEATING  FEED  WATER 


657 


stream  line  is  that  illustrated  in  Fig.  421  by  the  heavy  lines.  A 
is  the  heat  utilized,  B  is  the  heat  value  of  the  fuel  used,  C  is 
the  heat  supplied  to  the  main  and  auxiliary  ^engines,  and  the 
ratio  A/B  is  the  over-all  thermal  efficiency. 


Miscellaneous  Losses 


GT\    Power  for 

Auxiliaries 


!  Water  Outlet. 
irfa.ce 
Blow-off 


Expansion, 
Joint 


But  if  the  auxiliaries  are  power  driven,  the  energy  being  fur- 
nished by  the  main  units,  then  the  case  is  shown  in  the  same 
figure  by  the  dotted  lines;  the  useful  output  is  A  (as  before), 
B'  is  the  heat  value  of  the  fuel  used,  and  C'  is  the  heat  furnished 
to  the  main  units,  its  amount  being 
less  than  C  because  the  water  rates 
of  the  larger  units  are  lower  than 
those  for  the  small  auxiliary  engines. 
The  over-all  thermal  efficiency  in  this 
case  is  A/Bf  which  is  less  than  when 
the  auxiliaries  are  driven  by  steam  and 
their  exhaust  is  used  for  feed  heating. 


3i5»  Closed  Heaters,  (a)  Heaters 
of  this  type  are  so  arranged  that  the 
steam  does  not  come  in  contact  with 
the  water.  They  are  generally  con- 
structed with  straight  or  coiled  tubes 
contained  in  a  shell  of  some  sort,  with 
proper  provision  being  made  for  in- 
equalities in  expansion.  The  water 
generally  passes  through  the  tubes  or 
coils  and  the  steam  fills  the  envelop- 


Fig.  422.  — Closed  Heater. 


ing  space,  the  condensation  being  drained  off  as  it  collects.  The 
three  most  common  of  the  many  possible  arrangements  are 
shown  in  Figs.  422  to  424. 


658 


HEAT-POWER  ENGINEERING 


(b)  Closed  heaters  are  comparatively  difficult  to  clean  as  a 
large  part  of  the  impurities  in  the  water  is  deposited  on  the  inside 
of  the  tubes  and  forms  a  coating  similar  to  boiler  scale.  To 
counteract  this  effect,  the  water  is  often  forced  through  the 
tubes  at  enormously  high  velocity,  tending  to  keep  them  clean 
by  "scouring."  However  the  power  required  for  pumping 
places  a  practical  limit  to  the  velocities  used  and  the  method  is 
only  partly  successful.  If  the  steam  contains  oil,  and  it  is  not 
removed  before  entering  the  heater,  the  tubes  will  become  coated 


Water  Inlet 


Fig.  423.     Coil  Heater. 


Fig.  424.  —  Closed  Heater. 


with  this  material,  which  is  of  low  conductivity,  and  the  rate 
of  heat  transmission  will  be  greatly  impaired. 

(c)  These  heaters  are  generally  placed  between  the  feed  pump 
and  the  boiler,  hence  the  former  deals  with  cold  water  only  and 
but  one  pump  is  required  (not  considering  reserve  pumps  for 
emergencies)  as  against  two  with  open  heaters  which  do  not 
receive  the  raw  water  under  head.  The  feed  water  is  free  from 
oil,  but  the  condensate  is  generally  wasted.  Figs.  420  and  421 
apply  equally  well  to  this  case  except  that  the  heater  loss  E 
includes  the  sensible  heat  of  the  condensate  (measured  above 
the  temperature  of  the  raw  feed)  unless  there  is  more  than 
enough  steam  to  raise  the  feed  temperature  to  the  maximum 
possible  value.  The  maximum  temperature  attainable  is  gen- 


APPARATUS  FOR  HEATING  FEED  WATER 


659 


To  Aim. 


Normally  Closed  S 
;  Steam 


Feed 
Water 


To  Boiler 


W  Normally 
Closed 


Fig.  425. 


erally  2  degrees  or  more  below  the  steam  temperature,  which 
latter  depends  on  the  pressure  of  the  steam  used. 

(d)  In  all  such  cases,  the  auxiliary  apparatus,  such  as  heaters, 
should  be  so  piped  that  when  out  of  commission  the  steam  can  be 
exhausted   to  atmosphere  direct,   and  the  feed  water  can  be 
by-passed  around  the  heater.     The  piping  is  therefore  arranged 
somewhat  as  in  Fig.  425,  5  and 

W  being  the  steam  and  water 
by-pass  valves  which  are  nor- 
mally closed. 

(e)  The    saving    effected    by 
closed  heaters  can  be  found  from 
Eqs.  (476)  and  (477),  the  tem- 
perature  attained    by   the   feed 
water  is  given  by  Eq.  (478),  and 
the  proportion  of  the  total  steam 
generated,  that  can  be  used  for 
heating  the  raw  feed,  is  given  by 
Eq.  (479). 

(f)  The  heat  transmission  falls  under  Case  I  of  Sections  (306) 
and    (307).      The   mean   temperature   head    is   given    by   Eqs. 
(438)  or  (449)  and  the  number  of  square  feet  of  heating  surface 
can  be  found  from  Eq.  (440)  when  K  is  known.     For  feed -water 
heaters  K  varies  widely  with  the  kind  of  material,  character  of 
surface  (scale,  oil  film,  corrugations,  etc.),  with  the  velocity  of 
flow  of  feed  water  and  with  other  factors.     It  ranges  ordinarily 
with  copper,  or  brass,  tubes  from  175  with  velocity  of  12  J  feet 
per  minute  and  single  pass,  to  250  with  velocity  of  50  ft.  per  min. 
and  multipass;  with  a  velocity  of  150  ft.  per  min.  through  coils 
it  reaches  300  B.t.u.  per  square  foot  per  hour  per  degree  differ- 
ence in  temperature,  while  under  very  favorable  conditions  much 
higher  values  are  attainable. 

(g)  Closed  heaters  with  copper  tubes  are  sometimes  rated  in 
terms  of  "heater  horse  power"  \  square  foot  of  surface  being 
allowed  per  rated  horse  power.      On  this  basis,  if  the  steam 
pressure  is  atmospheric  and  if  K  =  192,  the  30  Ibs.  (approx.)  of 
feed  water  required    per  so-called  boiler  horse  power  will   be 
heated  from  60°  to  194°  (134°  increase)  by  the  J  square  foot  of 
surface  — or  I  sq.  ft.  will  heat  about  90  Ibs.  of  water  (the  amount 
required  for  3  boiler  h.p.)  through  this  temperature  range, 


66o 


BEAT-POWER  ENGINEERING 


316.  Economizers,  (a)  The  function  of  the  economizer  is  to 
abstract  a  portion  of  the  heat  from  the  flue  gases,  and  to  deliver 
it  to  the  feed  water  on  its  way  to  the  boiler,  thereby  somewhat 
reducing  the  large  loss  c  in  Fig.  3.  The  energy  stream  for  this 


Economizer  Loss 
F 


Boiler  and  Furnace  Losses 

Fig.  426. 


Heat  Lost 

in  Exhaust 

Steam 


case  is  shown  by  the  full  lines  in  Fig.  426,  in  which  the  case 
without  the  economizer  is  that  with  dotted  lines,  the  boiler  per- 
formance being  assumed  to  remain  unchanged.  For  the  same 
boiler-output  the  fuel  used  is  in  the  ratio  of  B  to  Bf. 


Safety 
Valve 


Urayjn >s  Gear 


Fig.  427.  — Economizer. 

(b)  One  form  of  economizer  is  shown  in  Fig.  427.  The  appa- 
ratus usually  consists  of  nests  of  staggered,  vertical,  cast-iron 
tubes  fitted  into  top  and  bottom  headers  (with  metal  to  metal 


APPARATUS  FOR  HEATING   FEED   WATER 


66l 


joints),  each  set  of  headers  being  connected  together  by  longi- 
tudinal branch  pipes  having  handholes  which  give  access  to  the 
interior  for  washing  out  deposits.  In  the  upper  headers  are 
located  removable  lids  opposite  the  ends  of  the  tubes  in  order 
to  give  access  to  the  latter,  and  power-driven  scrapers  constantly 
move  along  the  external  surfaces  of  the  tubes  to  remove  the 
deposit  of  soot,  the  scrapings  falling  to  a  pit  below,  from  which 
they  are  withdrawn  from  time  to  time.  The  water  is  preferably 
introduced  at  the  end  farthest  from  the  boiler  and  discharged 
from  the  nearer  end;  for  its  direction  of  flow  is  then  counter  to 
that  of  the  flue  gases,  thus 
obtaining  the  counterflow 
of  Case  IV,  discussed  in 
Chapter  XXXV.  The 
setting  is  either  of  brick 
or  of  sheet  steel  lined  with 
nonconducting  material 
(magnesia  or  asbestos) ; 


Boiler 
Rear 


\^  Economizer  , 


To  Stack 


Access  Side 

Fig.  428. 


the  arrangement  of  flues 

is  such  (see  Fig.  428)  that 

the  gases  from  the  boilers  can  be  by-passed  direct  to  the  stack 

when  the  economizer  is  out  of  commission,  and  the  water  can  be 

delivered  direct  to  the  boiler. 

(c)  In  some  instances  the  flue  gases  are  cooled  from  ordinary 
stack  temperature  of  550°  to  650°  F.  to  as  low  as  240°  F.  and  the 
water  is  heated  to  270°  or  more;  temperatures  much  higher  than 
can  be  obtained  with  an  atmospheric  feed-water  heater.     But 
because  the  temperature  of  the  stack  gases  is  low  and  because 
of  the  additional  resistance  in  the  flues  due  to  the  presence 
of  the  economizer  tubes,  the  natural  draft  must  generally  be 
assisted  in  some  manner.     Hence,  in  connection  with  the  finan- 
cial problem   involved,   the  cost  of  such  draft  apparatus  and 
the  annual  expenses  chargeable  against  it  must  be  added  to 
the  charges  against  the  economizer  itself,  including  those  for  the 
space    it   occupies    and    the    power   required    for   driving    the 
scrapers.     As  the  economizer  occupies  a  great  deal  of  space  it 
is  frequently  placed   either  above  the  boiler  or  outside  of  the 
building. 

(d)  In  addition  to  the  four  advantages  accruing  in  all  cases 
from  heating  feed  water,  as  given  in  Section  312  (a),  the  econo- 


662  HEAT-POWER  ENGINEERING 

mizer  has  (5)  a  great  reserve  of  hot  water  near  the  vaporizing 
point,  ready  to  meet  sudden  demands  on  the  boiler;  (6)  its  use 
may  make  it  possible  for  the  boiler  itself  to  operate  with  higher 
efficiency,  and  (7)  it  is  especially  advantageous  when  the  boilers 
are  being  forced,  for  then  the  flue  gases  are  hottest  and  the 
stack  waste  is  ordinarily  the  greatest.  Owing  to  the  higher  tem- 
perature attained  by  the  water,  some  scale-forming  materials 
are  deposited  which  are  not  precipitated  in  atmospheric  feed 
heaters. 

(e)  If  the  counterflow  principle  is  used  in  the  economizer 
the  equations  of  Section  310  apply.  A  simple  approximation 
can  be  made  however  by  assuming  the  two  curves  in  Fig.  414  to 
be  straight  lines,  then,  at  the  middle  of  the  curves, 

6m  =  (Ta  -  A7V2)  -  (tb  +  A/«/2)  =  Ta  -  tb  -  J  (An  +  A*a).  (a) 
But  CpGkTb  =  wkta  ..  J'  .  .  .  .  .  (b) 

where  Cp  =  specific  heat  of  gas  (=  0.24), 

G  =  weight  of  gas  per  boiler  h.p.-hr., 
w  =  pounds  of  water  per  boiler  h.p.-hr. 
Solving  (b)  for  A7\  and  substituting  in  (a)  gives 

i  +W/GCP).   .    .    .    (c) 


But  the  heat  absorbed  in  the  economizer  by  the  water  used 
per  boiler  horse  power  is  Q  —  w&tat  hence  Eq.  (437)  becomes 
(per  boiler  h.p.) 

=  KSSm  ........     (d) 


Substituting  the  value  of  Om  from   (c)   and   solving  gives   the 
increase  in  the  temperature  of  feed  water  as 

(approx.)-  (481) 


In  practice  S  ranges  from  2\  to  5  square  feet  per  boiler  horse 
power.  Corresponding  to  gas  temperatures  of  300°  and  600°  F. 
respectively  K  has  values  of  about  2\  and  3i  B.t.u.  per  square 
foot  per  degree  difference  of  temperature  per  hour.  The  weight 
of  water  (w)  per  boiler-horse-power  hour  is  generally  taken  at 


APPARATUS  FOR  HEATING  FEED  WATER  663 

about  30  Ibs.;  and  the  weight  of  gas  (G)  per  boiler-h.p./hr.  as 
G=(i  +  n.6x)  X  F, 

where  x  =  excess  coefficient, 

F  =  weight  of  combustible  per  boiler-h.'p./hr. 
=  3  to  4  Ibs. 

G  is  ordinarily  from  80  to  120  Ibs.  per  boiler  h.p./hr. 
Then  the  final  temperature  of  the  feed  water  is 

tf  =   tb  +  A/a, (482) 

and  the  final  temperature  of  the  flue  gas  is 

Tb=  ra-An, (483) 

in  which  An  =  ^2; (484) 

(jfLp 

and  if  w  —  30,  G  =  So,  and  Cp  =  0.24 

An=i.56A/« (485) 

(f)  The  per  cent  saving  effected  by  raising  the  feed  temperature 
by  the  amount  A/a  may  be  obtained  from  Eqs.  (476)  and  (477)  by 
substituting  A/a  for  the  numerator.  The  actual  saving  of  boiler 
and  economizer  taken  together  may  be  still  more,  since  the 
boiler  may  have  higher  efficiency  because  of  the  better  conditions 
of  operation. 

NOTE:  See  "Economizer  Equation"  and  curves,  by  A.  W.  Smith  in  Sibley 
Journal,  Jan.,  1916,  and  the  later  discussion  in  the  June  issue. 


CHAPTER  XXXVII. 
CONDENSERS  AND  RELATED  APPARATUS. 

317.  Advisability  of  Condensing.     The  principal  advantages 
accruing  from  the  use  of  condensers  in  connection  with  steam- 
driven  prime  movers  are:  (i)  Improved  thermal  efficiency  of  the 
unit  (except  in   the  smaller  sizes);  (2)  greater   power  from    a 
given  size  of  prime  mover;    and,  when  the  condensate  is  used 
for  feed  water,  there  are  the  additional  advantages  of  (3)  the 
thermal  gain  from  using  hot  feed  water  and   (4)   the   freedom 
from  deposits  of  scale  in  the  boiler  because  the  feed  water  is 
distilled. 

However,  despite  the  apparent  advantages,  it  is  not  always 
desirable  to  operate  condensing,  for  financial  and  other  reasons. 
The  additional  expense  for  the  extra  equipment,  its  installation, 
attention  and  upkeep,  the  expenditure  for  condensing  water,  for 
pumps  and  their  operation,  and  the  additional  space  required  by 
the  apparatus  may  in  some  caseswholly  offset  the  advantages.  It 
is  generally  not  considered  profitable  to  operate  condensing  with 
small  engines,  or  with  simple  engines  of  the  ordinary  types  (some 
special  types,  such  as  the  unidirectional  flow  engine,  operate 
to  best  advantage  when  condensing) ;  nor  should  condensers 
ordinarily  be  used  when  a  considerable  part  of  the  exhaust 
steam  can  be  employed  for  heating  or  for  industrial  purposes. 

318.  Condensers  in  General,     (a)  The  two  main  classes  into 
which  all  types  of  condensers  may  be  divided  are:   (i)  Direct- 
contact  Condensers  and  (2)  Surface  Condensers.     In  the  former, 
the  steam  and  condensing  water  mingle  in  the  same  chamber, 
while  in  the  latter  type  they  are  kept  separated  by  heat-trans- 
mitting surfaces.     In  each  class  there  are  many  different  arrange- 
ments possible  and  some  of  these  will  be  considered  in  detail 
later. 

(b)  Theoretically,  the  material  handled  by  a  condenser  is  low- 
pressure  steam;  actually  it  is  a  mixture  of  water,  water  vapor 

664 


CONDENSERS  AND  RELATED  APPARATUS  66$ 

and  air.  Part  of  this  air  comes  from  the  boiler,  being  carried  into 
that  vessel  in  solution  in  the  feed  water,  and  part  of  it  leaks  into 
the  system  through  the  stuffing  boxes  surrounding  the  piston 
and  valve  rods,  through  the  joints  of  pipes  and  of  such  other 
parts  of  the  equipment  as  are  handling  the  material  betow  atmos- 
pheric pressure.  Also  the  water  used  for  condensing  carries  air 
in  solution  when  under  atmospheric  conditions,  and  in  direct-con- 
tact condensers  this  air  is  released  under  diminished  pressure  and 
is  added  to  that  which  enters  in  the  various  ways  just  outlined. 

(c)  Then,  according  to  Dalton's  law,  the  total  pressure  within 
the  condenser  is  the  combination  of  the  pressures  of  the  air  and 
vapor,  i.  e.,  it  is  the  sum  of  their  partial  pressures.  The  import- 
ance of  this  fact  is  best  appreciated  from  an  example. 

Assume  the  temperature  within  a  condenser  to  be  H5°F. 
Then  if  the  condenser  contained  only  water  and  saturated  steam 
at  this  temperature  the  pressure  within  the  enclosure  would  be 
2.99  inches  of  mercury,  corresponding  to  a  vacuum  of  26.93 
inches.  If,  however,  every  pound  of  steam  has  mixed  with  it 
one-quarter  of  a  pound  of  air,  which  is  not  at  all  uncommon,  the 
pressure  due  to  this  air  can  be  found  as  follows: 

One  pound  of  saturated  steam  at  a  pressure  of  2.99"  Hg.  occu- 
pies a  volume  of  231.9  cu.  ft.  This  must  also  be  the  volume 
occupied  by  the  0.25  Ibs.  of  air  mixed  with  it,  and  the  tempera- 
ture of  this  air  is  that  of  the  steam  (115°).  Then  from  the  law 
of  ideal  gases,  the  pressure  of  the  air  in  the  condenser  is 

P  = 


or  p  =  0.46  inches  of  mercury. 

Thus,  the  total  pressure  in  the  condenser  will  then  be  2.99" 
+  0.4.6"  =  3.45  in.  Hg.  and  the  vacuum  will  be  29.92  —  3.45 
=  26.47  in.  Hg.  The  back  pressure  on  the  prime  mover  is 
slightly  higher  than  this,  as  a  pressure  drop  must  exist  between 
that  piece  of  apparatus  and  the  condenser  in  order  to  cause  the 
steam  to  flow  through  the  exhaust  pipe. 

With  one  pound  of  air  per  pound  of  steam,  which  is  a  possible 
condition,  the  pressure  due  to  the  air  would  be  1.84  inches  of 
mercury,  under  the  same  circumstances,  and  the  vacuum  would 
only  be  25.09  inches. 

The  air  is  thus  seen  to  have  a  very  appreciable  effect  upon  the 


666  HEAT-POWER  ENGINEERING  r 

vacuum  and  every  precaution  should  therefore  be  taken  to 
prevent  an  excessive  amount  of  it  entering  the  apparatus.  If 
allowed  to  accumulate  it  would  gradually  increase  in  pressure 
and  destroy  the  vacuum.  It  must  therefore  be  removed  as 
rapidly  as  it  collects.  Before  it  can  be  discharged  from  the 
condenser,  however,  its  pressure  must  be  raised  to  that  of  the 
atmosphere  (or  slightly  above)  which  is  done  by  an  air  com- 
pressor or  pump  having  terminal  pressures  sufficiently  above 
atmospheric  to  effect  a  discharge.  When  this  pump  handles 
only  the  air  it  is  called  an  "Air  Pump"  or  "Vacuum  Pump." 

In  some  cases  where  the  water  is  discharged  from  the  condenser 
with  considerable  velocity,  the  arrangement  is  such  that  the  air 
is  ejected  by  the  water,  no  separate  air  pump  being  needed. 

(d)  Condensers  in  steam-power  plants  practically  always  use 
water  as  the  condensing  medium,  but  any  liquid  or  gas  that 
could  be  obtained  cheaply,  in  sufficient  quantities  and  at  a  low 
temperature,  could  be  used;  in  fact  air  has  been  so  utilized  in  a 
number  of  special  instances. 

It  is  seldom  that  water  is  available  under  a  head  sufficient  to 
cause  it  to  flow  into  or  through  a  condensing  apparatus.  It  is 
therefore  generally  delivered  to  the  condenser  by  a  "Circulating 
Pump"  which  may  be  independently  driven  by  steam,  by  electric 
motor  or  by  belt,  or  may  be  operated  by  links  driven  by  the 
prime  mover.  These  pumps  generally  have  comparatively  low 
lifts  and  handle  large  volumes,  hence  the  centrifugal  type  is 
commonly  used,  although  there  are  many  cases  where  the  rotary 
or  the  reciprocating  types  have  the  advantage  and  are  installed. 

In  apparatus  in  which  condensing  water  and  steam  mix  and 
form  a  vacuum,  the  condensing  water  is  often  forced  into  the 
condenser  by  the  atmospheric  pressure  acting  on  the  surface  of 
the  water  outside,  no  circulating  pump  being  used.  This  is  very 
common  practice  where  the  suction  head  is  not  over  15  feet, 
and  it  is  used  even  with  greater  heads  in  some  instances. 
1  (e)  The  removal  of  the  water  from  the  vacuum  chamber  of 
the  condenser  may  be  accomplished  in  several  ways.  If  the  hot 
well,  which  receives  the  condensate,  can  be  located  with  water 
level  at  least  34  feet  below  the  condenser,  the  water  can  be 
discharged  by  gravity  through  a  "Tail  Pipe,"  or  "  Barometric 
Tube,"  whose  lower  end  is  submerged  in  the  hot  well  (the 
34-foot  column  of  water  corresponding  to  a  30  inch  column  of  Hg. 


CONDENSERS  AND  RELATED  APPARATUS  667 

on  the  barometer).  In  other  cases  it  is  necessary  to  have  pumps 
which  raise  the  water  from  condenser  pressure  to  atmospheric. 
Such  pumps  are  called  "Tail  Pumps"  "Hot-well  pumps''  etc., 
when  they  handle  only  water  (and  whatever  air  it  happens  to 
have  entrapped).  In  many  instances,  however,  the  same  pump 
plunger  discharges  both  the  water  and  the  free  air,  in  which  case 
the  one  pump  serves  both  as  hot-well  pump  and  as  air  pump, 
and  is  then  called  a  "  Wet  Vacuum  Pump  "  or  "  Wet  Air  Pump." 

(f)  Each  prime  mover  may  have  its  independent  condenser  or 
there  may  be  a  central  condensing  equipment  for  a  number  of 
units.  In  the  former  case  the  exhaust  piping  may  be  made 
short,  direct  and  with  few  joints;  in  the  latter,  because  of  the 
greater  length  of  pipe  and  larger  number  of  joints,  there  is  more 
opportunity  for  air  infiltration  and  more  resistance  to  flow,  but 
larger  and  more  economical  auxiliaries  may  be  used. 

In  order  to  permit  of  operating  noncondensing  when  the  con- 
densing apparatus  is  out  of  commission,  the  exhaust  pipe  should 
contain  a  valve  which  can  be  opened  to  the  atmosphere.  This 
valve  is  usually  arranged  to  open  automatically  when  the  con- 
denser ceases  to  operate.  To  permit  of  repairs  while  the  engine 
is  running  there  should  be  a  shut-off  valve  in  the  exhaust  pipe 
leading  to  the  condenser;  and  should  several  condensers  dis- 
charge to  a  common  main  there  should  also  be  shut-off  valves 
between  them  and  that  pipe. 

319.  Contact  Condensers,  (a)  There  are  several  different 
kinds  of  contact  condensers  only  a  few  of  which  will  be  described. 
That  in  Fig.  429  is  known  as  the  "Ordinary  Jet  Condenser"* 
In  it  the  injection  water  entering  at  /and  the  steam  entering  at  5 
mingle  in  the  conical  condenser  head  B  and  the  resulting  mixture 
of  condensate,  injection  water  and  noncondensable  gases  is  raised 
to  atmospheric  pressure  and  discharged  by  the  wet  air  pump 
located  below,  the  flow  of  injection  water  being  regulated  by 
handwheel  H.  At  (a)  in  Fig.  429  is  a  diagram  of  the  piping  for 
such  a  condenser.  It  includes  an  atmospheric  relief  valve  (4) 
which  will  automatically  open  to  the  atmosphere  when  the  valve 
V  is  closed  for  making  repairs  to  the  condenser,  or  when  the 
vacuum  is  "broken,"  as  when  the  injection  water  fails. 

*  The  term  "  Jet  Condenser  "  is  also  used  as  being  synonymous  with  "  direct 
contact  condenser." 


668 


HEAT-POWER  ENGINEERING 


If  the  suction  lift  for  the  injection  water  is  not  too  great  this 
water  may  be  siphoned  into  the  condenser  by  the  vacuum  after 
it  has  been  established  by  priming  and  starting  the  pump.  In 
such  cases  this  lift  may  be  as  much  as  15  to  1 8  feet,  provided  the 
piping  is  short  and  not  restricted.  When  the  water  is  supplied 
in  this  manner  there  is  danger  of  flooding  and  wrecking  the 
engine  in  case  the  pump  ceases  to  operate  before  valve  C  is  closed, 
or  if  it  runs  so  slowly  that  it  cannot  discharge  the  water  as  fast 
as  it  collects.  To  prevent  the  possibility  of  such  disaster  various 


Fig.  429. — Jet  Condenser. 

expedients  are  adopted,  such  as  providing  a  float  (F  in  Fig.  429) 
which,  when  the  water  level  becomes  dangerously  high,  will  be 
raised  and  open  a  valve  v  to  admit  the  atmosphere  to  the  con- 
denser and  thus  "break"  the  vacuum  and  stop  the  flow  of 
injection  water. 

If  a  pump  is  used  for  the  injection  water  the  head  against  which 
it  operates  is  the  difference  between  the  total  head  and  that 
through  which  the  water  would  be  "drawn  "  by  the  vacuum. 


CONDENSERS  AND  RELATED  APPARATUS 


669 


Atmospheric 
Relief  Valve 


(b)  The  term  "  Barometric  Condenser  "  may  be  applied  to  any 
form  of  direct-contact  condenser  having  the  barometric  tube. 
Fig.  430  shows  one  arrangement  commonly  called  the  "  Siphon  " 
Type*  The  injection  water  entering  the  condenser  head  B 
from  pipe  /  passes  downward  in  a  thin  annular  sheet  around  the 
hollow  cone  in  the  condenser  head  and  unites  with  the  steam 
which  passes  through  the  cone.  The  mixture  is  discharged 
through  the  neck  or  throat  N  with  sufficient  velocity  to  carry 
with  it  the  noncondensable  gases.  A  is  an  atmospheric  relief 
valve  and  H  is  a  handwheel  for  regulating  the  injection  water. 
The  water  level  L  in  the  tail 
pipe  depends  on  the  vacuum 
maintained,  but  for  safety  the  tail 
pipe  is  extended  34  feet  above 
the  water  level  in  the  hot  well. 

If  injection  water  is  available 
at  a  head  h  (in  the  figure)  of  not 
over  1 8  feet,  it  may  be  "drawn 
in  "  by  the  vacuum  after  this  has 
once  been  established  by  opening 
the  lower  valve  shown  dotted,  or 
in  some  other  manner,  and  in 
such  case,  the  pump  P  can  be 
dispensed  with.  At  the  foot  of 
the  exhaust  pipe  there  should  be 
either  a  drain,  or  an  "entrainer," 
the  latter  being  so  arranged  that 
the  exhaust  steam  impinges  on 
the  surface  of  the  water  which 
has  collected  in  a  pocket,  and 
gradually  picks  it  up  in  small 
particles  and  disposes  of  it  by 
entrainment.  Because  of  the 


Fig.  430.     Siphon  Condenser. 


great  head  room  required  by  these  condensers  they  are  fre- 
quently located  outside  of  the  power  house;  and  sometimes  a 
Tail  Pump  is  substituted  for  the  tail  pipe,  as  in  Fig.  431. 

(c)  Fig.  431  shows  a  direct-contact  condenser  somewhat  simi- 

*  All  direct-contact  condensers  can  be  used  to  siphon  the  condensing  water, 
but  the  term  "Siphon  Condenser"  is  generally  applied  only  when  there  is  the 
neck  N  shown  in  Fig.  430. 


670 


HEAT-POWER  ENGINEERING 


lar  to  the  one  just  discussed  except  that  it  uses  a  u dry  air 
pump"  for  removing  the  air.  As  the  volume  of  air  to  be 
handled  will  increase  with  its  temperature,  and  as  the  size 
of  the  dry  air  pump  will  increase  with  the  volume  of  the 
air,  the  latter  is  usually  cooled  in  some  manner  before  it 
goes  to  the  air  pump.  In  the  arrangement  shown  this  is  done 
by  passing  it  through  a  spray  of  cold  water,  in  the  upper 
part  of  the  condenser  head,  on  its  way  to  the  discharge  opening. 


Fig.  431. — Condenser  with  Dry  Air  Pump. 

(d)  TheE/ec/0r  Condenser,  shown  diagrammatically  in  Fig.  432, 
operates  on  the  same  principle  as  the  steam  ejector  which  is  used 
for  forcing  water  into  boilers  against  the  pressure  of  the  steam. 
The  injection  water  enters  at  /  and  passes  through  the  neck  of 
the  combining  tube  B,  where  it  rapidly  condenses  the  exhaust 
steam  which  passes  through  small  nozzles  in  the  wall  of  this 
tube.  Some  of  the  heat  surrendered  by  the  condensed  vapor 
is  converted  into  kinetic  energy  of  the  steam  jets  flowing  through 
these  nozzles  and  the  momentum  acquired  propels  the  water 


CONDENSERS  AND  RELATED  APPARATUS 


671 


with  high  velocity  through  the  neck.  This  velocity  is  reduced 
in  the  expanding  tube  below  so  that  the  pressure  is  raised  to 
atmospheric  when  the  end  E  is  reached. 

To  start  the  flow  of  injection  water  with  the  arrangement 
shown,  boiler  steam  may  be  admitted  through  the  smarting 
valve  C.  This  steam  then  issues  through  the  check  valve  D 
and  partly  exhausts  the  atmosphere  from  the  injection  pipe,  thus 
causing  the  water  to  rise  and  enter  the  condenser.  The  valve 

Starting  Valve 
C 


Fig.  432. — Ejector  Condenser. 

C  may  then  be  closed,  the  exhaust  steam  continuing  the  circu- 
lation of  the  water  in  the  manner  just  described.  The  siphoning 
of  injection  water  can  also  be  started  by  admitting  high  pressure 
water  through  the  starting  valve  C,  in  which  case  valve  D  can  be 
omitted. 

The  operation  of  the  condenser  ceases,  of  course,  when  the 
supply  of  exhaust  steam  is  discontinued,  hence  this  arrangement 
of  condenser  cannot  be  used  for  intermittent  service,  nor  is  it 
satisfactory  if  the  load  varies  widely  and  frequently.  With 
steady  load  the  "  suction  lift  "  may  be  16  feet;  with  variable  loads 
it  is  limited  to  a  smaller  value. 


f 


672  HEAT-POWER  ENGINEERING 

The  combining  tube  may  be  arranged  with  adjustable  internal 
throttling  device  and  external  sleeve  to  permit  the  regulation  of 
the  water  and  steam  openings  to  suit  the  load.  Should  the 
water  contain  foreign  matter  a  strainer  should  be  located  in  the 
injection  pipe. 

If  the  condensing  water  is  supplied  under  a  head  of  20  feet,  or 
more,  a  slightly  modified  arrangement  can  be  used  and  a  more 
certain  vacuum  obtained  even  with  wide  variations  in  load. 

(e)  With  all  types  of  contact  condensers  the  weight  of  water 
required  per  pound  of  dry  steam  for  any  vacuum  is 

.   \x~qm   _  \x  -  (tm  -  32)  *  ( 

"-ST^o"     fc-w"       '   '   '   (486) 

where     Xz   =  total  heat  above  32°  F.  per  pound  of  steam  at  ex- 
haust pressure. 

Qt  =  heat  of  liquid  of  injection  water,  at  temp.  t°  F. 
qm  =  heat  of  liquid  of  mixture  at  temp.  tm°  F.     (tm  is 
from  5  to  15°  less  than  the  temperature  of  the 
exhaust  steam.) 

The  temperature  of  the  water  in  the  hot  well  is  practically 
that  of  the  mixture,  and  this  water  is  available  for  boiler  feed 
when  the  character  of  condensing  water  permits.  The  weight 
of  water  to  be  handled  by  the  circulating  pump  per  hour  is 
w  X  weight  of  steam  condensed  in  that  time,  and  the  weight 
delivered  by  the  discharge  pump  is  (w  +  i)  X  wt.  of  steam. 

(f)  The    principal    advantages    of    direct-contact   condensers 
are:     (i)  Their   simplicity;    (2)  low  first  cost;  (3)  low  cost  of 
upkeep;   and   (4)   small  space  required.     They  have,  however, 
certain  detrimental  features  which  in  some  instances  may  partly 
or  wholly   counterbalance    these   advantages:     (a)    If    the   in- 
jection water  is  sea  water,  or  has  scale-forming  impurities,  or  is 
otherwise  unsuitable  for  boiler  feed,  none  of  the  heat  in  the 
condenser  discharge  can  be  returned  to  the  boiler;    (b)  the  dis- 
tilled water  resulting  from  the  condensation  of  the  steam  is  lost 
since  it  is  mixed  with  the  injection  water,  whereas  with  surface 
condensers  it  is  available  for  boiler  feed;    (c)  the  temperature  of 
the  hot-well  water  used  for  boiler  feed  is  lower  than  that  from  a 
surface  condenser  of  proper  design;    (d)  it  is  more  difficult  to 
obtain  a  good  vacuum  than  with  surface  condensers,  because  of 

*  A  correction  of  from  5  to  15  per  cent  must  be  made  to  allow  for  cooling  the 
air  and  entrained  moisture  and  for  the  inefficient  heat  absorption. 


CONDENSERS  AND  RELATED  APPARATUS 


673 


the  air  introduced  by  the  injection  water;    and  (e)  larger  air 
pumps  are  therefore  required. 

320.  Surface  Condensers,  (a)  A  water-cooled  surface  con- 
denser is  essentially  an  enlargement  in  the  exhaust  piping  through 
which  pass  tubes  which  contain  the  flowing  condensing  water. 
If  this  water  flows  merely  from  one  tube  header  to  the  other,  the 
apparatus  is  called  a  "single  pass"  condenser,  and  "multipass 
condenser  "  is  the  general  term  applied  when  the  water  flows 
across  the  steam  chamber  two  or  more  times.  A  double-pass 
condenser  of  the  ordinary  type  is  shown  in  Fig.  433,  with  cooling 


Discharge  {-P"-" 


Fig.  433-  — Double  Flow  Surface  Condenser. 

water  flowing  from  the  lower  part  (^4)  of  one  head  to  the  other 
head  (B)  and  then  back  to  the  upper  part  (C)  of  the  first  one. 

The  arrangement  of  piping  for  a  surface  condenser  resembles 
that  for  the  jet  condenser  in  Fig.  429(0).  In  order  to  insure 
the  flooding  of  all  the  condenser  tubes  at  all  times  the  condensing 
water  is  usually  introduced  at  the  bottom  of  the  condenser  and 
discharged  at  the  top. 

(b)  The  surface  condenser  has  certain  advantages  over  the  di- 
rect-contact type.  The  principal  ones  are  as  follows:  If  the  con- 
densate  is  used  as  boiler  feed,  (i)  substantially  all  of  the  available 


674  HEAT-POWER  ENGINEERING^ 

sensible  heat  of  the  exhaust  steam  is  returned  to  the  boiler; 
(2)  the  same  water  is  used  repeatedly,  thus  avoiding  the  ex- 
pense for  new  water  (which  is  of  importance  only  when  suitable 
water  is  difficult  to  obtain  or  when  its  cost  is  high)  ;  (3)  the 
feed  water  is  distilled  and  free  from  scale-forming  impurities; 
(4)  less  air  is  carried  into  the  boiler  by  the  feed  water;  and  (5) 
sea  water  or  any  other  water  which  is  unsuitable  for  boiler  feed 
can  be  used  for  cooling  and  yet  the  available  sensible  heat  of  the 
exhaust  steam  is  returnable  to  the  boiler;  (6)  better  vacuums 
are  generally  obtainable  with  smaller  air  pumps  and  less  power 
for  same,  because  of  (4)  and  because  the  air  entrained  in  the 
condensing  water  is  kept  separated  from  the  steam:  and  (7) 
there  is  no  possibility  of  the  circulating  water  flooding  and  wreck- 
ing the  prime  mover. 

The  principal  disadvantages  are  the  relatively  large  (a)  first 
cost,  (b)  space  occupied,  (c)  upkeep  expense  (the  latter  being 
largely  due  to  the  corrosion  and  deterioration  of  condenser  tubes 
and  to  the  multitudinous  joints  which  must  be  maintained  free 
from  leakage),  and  (d),  in  the  case  of  steam  engines,  the  presence 
of  oil  in  the  condensate.  The  latter  item  does  not  hold  with 
turbines.  The  surface  condenser  requires  at  least  two  pumps 
(the  wet  air  and  the  circulating  water  pumps)  and  may  use  a 
third  (a  separate  dry  air  pump)  when  the  best  results  are  desired. 
In  contrast,  some  direct-contact  condensers  have  no  pumps,  and 
others  only  a  wet  or  dry  air  pump. 

(c)  The  weight  of  condensing  water  required  per  pound  of  ex- 
haust (with  quality  unity)  is  evidently 


.        m    .    (87) 


where   Xz  =  total  heat  above  32°  F.  per  Ib.  of  exhaust  steam. 

qc  =  heat  of  liquid  of  condensate  leaving  condenser  at  tc°. 

tc  =  from  o°  to  20°  F.  below  the  exhaust  temperature  tx. 

g<  =  heat  of  liquid  of  condensing  water  at  inlet,  at  /». 

qd  =  heat  of  liquid  of  condensing  water  at  discharge,  at  td. 

td  =  from  5°  to  10°  F.  below  exhaust  temperature  tx. 
With  from  25  to  26  inches  of  vacuum  w  is  from  25  to  30  Ibs. 
depending  on  the  value  of  /»  ;  and  with  better  vacuums  w  is  from 
45  to  55  Ibs.  and  even  more. 

(d)    The  heat  transmission  in  Surface  Condensers  is  according 
*  See  footnote  on  page  672. 


CONDENSERS  AND  RELATED  APPARATUS 


675 


to  Case  I  of  Sections  306  and  307  and  the  amount  of  condensing 
surface  required  to  condense  w,  Ibs.  of  exhaust  steam  per  hour 
(quality  unity)  is  from  Eq.  (437). 


BmK 
=  w.\\x-  (tc  -  32)}  -s-  0JC,  .     .     .  ~  .     (488) 

where  the  symbols  in  the  bracket  have  the  same  meaning  as  in 
Eq.  (487) ;  and  from  Eq.  (438) 

/  4      *  \ 

....          (489) 


The  value  of  K  depends  on  the  surface  coating  on  the  tubes 
(scale  and  oil),  on  the  velocity  of  the  water,  on  the  air  present 
in  the  steam,  on  the  material  of  the  tubes  (although  this  is 
usually  negligible)  and  on  other  items.  It  ordinarily  ranges 
from  250  to  300  B.t.u.  per  square  foot  per  degree  F.  per  hour  in 
the  simpler  types  of  condensers  under  ordinary  conditions,  but 
with  the  best  designs,  well  drained,  and  with  good  air  pumps, 
the  rate  of  transmission  may  be  from  two  to  three  times  these 
values.  For  ordinary  condensers  with  from  24  to  26  inches 
vacuum  about  10  Ibs.  of  steam  are  condensed  per  square  foot 
of  heating  surface  per  hour. 

For  small  turbines  with  high  vacuums  from  2\  to  4  square  feet 
of  condensing  surface  are  ordinarily  used  per  kilowatt  rating  of 
the  generator;  and  with  large  turbines  from  I  to  2j  sq.  ft.  are 
found  with  the  best  types  of  condensers. 

(e)  The  essentials  which  make  Surface  Condensers  most  effec- 
tive are:  (i)  All  the  tube  surface  should  be  available  for  heat 
transmission;  none  of  it  should  be  air-bound 
either  on  the  steam  or  water  side.  (2)  The 
falling  condensate  should  not  "drown  "  any 
tubes,  for  then  (a)  the  surface  is  only  about 
10  per  cent  as  effective,  (b)  the  condensate  is 
cooler,  hence  not  so  valuable  as  feed  water, 
and  (c)  more  condensing  water  is  required. 
(3)  The  velocities  of  the  steam  and  water 
should  be  high  enough  to  break  up  the  surface 
films.  As  the  transmission  is  largely  depend- 
ent on  the  heat-absorbing  ability  of  the  water, 
the  more  rapidly  the  latter  is  brought  in  contact  with  the  tube 
surfaces,  the  greater  the  rate  of  transmission.  (4)  The  air  in 


Fig.  434- 


676 


HEAT-POWER  ENGINEERING 


the  condensate  should  be  cooled  as  much  as  possible  to  decrease 
the  volume  to  be  handled  by  the  air  pump  and  to  reduce  its  par- 
tial pressure  acting  on  the  prime  mover.  (5)  There  should  be 
suitably  arranged  baffles  to  so  distribute  the  steam  that  all  parts 
of  the  condensing  surface  are  equally  effective. 

(f)  Fig.  434  shows  one  form  of  dry-tube  condenser  with  ar- 
rangement for  preventing  the  lower  tubes  of  the  condenser  from 


Circulating 
Water 


Fig.  435- 

being  drowned  and  from  serving  as  condensate  coolers.  This 
is  accomplished  by  the  baffles  A,  B,  which  are  arranged  to  collect 
and  draw  off  the  condensate  from  the  tubes  immediately  above 
as  rapidly  as  it  is  formed.  Baffle  pans  somewhat  similarly 
arranged  (with  drains)  are  used  in  like  manner  in  other  con- 
densers of  this  type. 

(g)  In  some  condensers  the  counter-current  principle  is  used 


CONDENSERS  AND  RELATED  APPARATUS  677 

as  regards  the  condensate.  In  such  cases  the  exhaust  steam 
enters  the  condenser  at  the  bottom,  hence  the  falling  condensate 
passes  downward  through  this  upflowing  steam  and  becomes 
heated  thereby,  the  feed  water  then  being  substantially  at 
exhaust  temperature. 

(h)  As  a  cubic  foot  of  air  is  heavier  than  a  like  volume  of 
steam  at  the  temperatures  existing  in  condensers,  and  as  it  is 
coolest  and  most  dense  at  the  bottom  of  the  shell,  it  tends  to 
gravitate,  hence  the  wet  air  pump  placed  below  the  condenser 
is  correctly  located  for  receiving  the  air  as  well  as  the  con- 
densate. 

(i)  Fig.  435  shows  the  piping  of  a  condenser  having  separate 
dry  air  and  hot-well  pumps.  The  arrangement  includes  an  air 
cooler  through  which  the  air  passes  on  its  way  to  the  dry  air 
pump,  the  condensed  vapor  from  this  cooler  being  passed  through 
a  water  seal  to  the  hot  well  where  the  condensate  collects. 

321.  Air  Pumps,  (a)  As  has  already  been  seen  a  Dry  Air 
Pump  is  an  air  compressor  which  receives  the  air  (and  its  en- 
trained moisture)  at  condenser  pressure 

and  compresses  it  sufficiently  to  permit          ^ Atmt 

of  discharge  to  the  atmosphere,  the  com- 
pressor card  resembling  Fig.  436  in  the 
best  instances.  As  the  compression  ratio 
is  high,  the  clearance  volume  must  be 
small,  for  no  air  can  be  received  from  F-  6 

the  condenser  until  that  in  the  clearance 

space  is  expanded  to  condenser  pressure.  To  increase  the  volu- 
metric efficiency  the  three  expedients  most  commonly  used  are: 
(i)  The  air  may  be  compressed  in  two  stages;  (2)  an  equalizing 
passage  (as  a  in  Fig.  437)  may  be  so  arranged  that  at  the  end  of 
the  stroke  the  clearance  air  may  at  the  proper  time  be  moment- 
arily exhausted  into  the  other  end  of  the  cylinder  which  is  filled 
with  air  at  condenser  pressure,  thus  when  the  stroke  begins  the 
clearance  space  is  under  pressure  nearly  equal  to  the  vacuum; 
and  (3)  the  clearance  space  may  be  filled  with  water,  as  is  the 
case  in  wet  air  pumps. 

Air  pumps  as  well  as  the  other  pumps  are  usually  steam  driven, 
as  the  exhaust  steam  can  ordinarily  be  advantageously  used  fo* 
feed-water  heating. 


HEAT-POWER  ENGINEERING 

(b)  A  Wet  Air  Pump  of  the  ordinary  horizontal  reciprocating 
type  is  shown  at  the  left  in  Fig.  433,  -s  indicating  the  suction 
valves  and  d  the  discharge  valves.  One  of  the  vertical  types  is 
illustrated  in  Fig.  438  with  foot  valves,  bucket  valves  and  dis- 
charge valves  as  shown.  In  the  Edwards  type,  shown  in  Fig.  439, 
the  foot  and  bucket  valves  are  dispensed  with,  and  whatever 
condensate  collects  in  the  base  of  the  pump  is  displaced  and 
forced  into  the  pump  cylinder  by  the  conical  end  of  the  plunger 
as  it  approaches  the  bottom  of  its  stroke.  This  water  and  the 
air  above  are  then  caught  above  the  plunger  when  it  ascends  and 
are  discharged  in  the  usual  manner.  As  in  most  pumps,  there 
is  a  lip  around  the  upper  valve  deck  so  that  the  valves  will  always 


To  Eccentric 


Fig.  437.  — Dry  Air  Pump  with  Equalizing  Passage. 

be  water  sealed  to  prevent  air  leakage.  Other  single-acting 
vertical  pumps  and  double-acting  horizontal  ones  are  somewhat 
similarly  arranged  to  operate  without  foot  and  bucket  valves. 

A  wet  air  pump  of  the  Rotary  Type  is  shown  in  Fig.  440,  it 
being  so  arranged  that  the  water-sealed  lobed  wheels  not  only 
discharge  the  water  but  also  carry  along  the  air  which  is  intro- 
duced at  A  below  the  wheels. 

(c)  The  Leblanc  type  of  dry  air  pump  is  shown  in  Fig.  441. 
Water  in  chamber  A,  "drawn  in  "  by  the  vacuum,  is  discharged 
at  B  and  is  projected  downward  by  the  vanes  on  the  rotor  R  in 
a  series  of  layers  which,  acting  as  pistons,  entrap  the  air  entering 
at  C  and  force  it  through  the  neck  N  against  the  atmospheric 
pressure.  To  start  the  vacuum  live  steam  may  be  temporarily 
admitted  at  S. 


CONDENSERS  AND  RELATED  APPARATUS  679 

(d)  The  volume  of  condensate  (Vc)  and  that  of  condensing 
water  (Vw)  used  per  minute  can  be  readily  estimated  and  the 
necessary  size  of  pumps  can  then  be  determined  if  water  alone 
is  to  be  handled.  If,  however,  air  is  to  be  pumped  there  is  no 
exact  method  of  arriving  at  the  volume  (7«)  to  be^discharged 
per  minute  and  the  proportions  of  the  pump  are  based  on  rough 


barge 


harge 


Fig.  438.  —Wet  Air  Pump. 

Air] 


Fig.  439.  —Wet  Air  Pump,  Edwards  Type. 


Fig.  440.  —  Rotary  Type  of 
Air  Pump. 


estimates.  Surface  water  under  atmospheric  conditions  may 
contain  by  volume  from  2  to  5  per  cent  of  air,  and  the  leakages 
may  increase  the  percentage  of  "atmospheric  air"  in  the  con- 
densers to  from  7  to  10  per  cent.  Under  partial  pressure  and 
higher  temperature  conditions  the  volume  of  this  air  is  greatly 
increased  and  its  value  can  be  readily  computed,  and  serves  as 
a  rough  basis  for  determining  the  size  of  the  pump. 


68o 


HEAT-POWER  ENGINEERING 


According  to  Gebhardt*  single-acting  wet  vacuum  pumps  for 
jet  condensers  ordinarily  have  plunger  displacements  per  minute 
of  about  3  Vw,  where  Vw  is  the  volume  of  the  injection  water 
pumped  in  that  time,  and  double-acting  pumps  have  displace- 
ment 3J  V»,  the  piston  speeds  being  about  50  feet  per  minute. 
With  reciprocating  engines  the  wet  air  pump  for  a  surface  con- 


Fig.  441.  — Leblanc  Air  Pump. 

denser  ordinarily  has  a  displacement  of  10  Vc,  where  Vc  is  the 
volume  of  condensate,  and  for  steam  turbines  it  is  about  20  Fc, 
these  values  being  the  average  of  two  hundred  plants.  For  dry 
air  pumps  the  displacement  of  the  plunger  ranges  from  20  to  30  Vc 
with  vacuum  below  27  inches,  up  to  50  Vc  for  28  inches  and  over, 
these  values  being  based  on  an  investigation  of  fifty  installations. 

*  Gebhardt's  "  Steam  Power  Plant  Engineering,"  published  by  John  Wiley 
and  Sons. 


CONDENSERS  AND  RELATED  APPARATUS  68 1 

322.  Recovery  of  Condensing  Water,  (a)  The  amount  of 
water  required  in  a  plant  for  condensing  purposes  is  relatively 
very  great,  varying,  as  shown  in  Sec.  320(0),  from  about  25  to 
55  pounds  per  pound  of  steam  condensed.  After  being  used 
this  water  is  generally  wasted,  hence  a  continuous  supply  of 
fresh  water  is  required  in  such  cases.  When  a  plant  owns  its 
own  water  supply  or  is  situated  near  a  large  river,  or  other  body 
of  water,  from  which  it  can  pump  condensing  water,  the  cost  of 
the  water  is  practically  only  that  of  pumping.  Many  plants  are 
so  situated,  however,  that  the  only  source  is  the  city  mains  and 
in  such  cases  the  continuous  expenditure  for  condensing  water 
may  be  far  in  excess  of  the  saving  effected  by  its  use.  Methods 
of  cooling  and  storing  condensing  water  have  been  developed, 
therefore,  so  that  the  same  water  can  be  used  repeatedly  and 
thus  make  it  possible  to  obtain  the  benefit  of  condensing  opera- 
tion in  cases  where  the  cost  of  a  continuous  supply  of  fresh 
water  would  be  prohibitive. 

(b)  For  cooling  the  water,  various  evaporative  cooling  devices 
are  in  use.     They  all  operate  by  exposing  large  surface  of  water 
(sometimes  in  thin  sheets  or  in  drops)  to  air  currents,  the  cooling 
being  effected  both  by  the  direct  contact  of  the  cooler  air  with 
the  hot  water  and  by  the  evaporation  of  part  of  the  water.     For 
this  purpose  (i)  a  pond  having  relatively  large  exposed  surface 
may  be  used ;  or  (2)  the  water  may  be  sprayed  into  the  air  and 
allowed  to  fall  into  a  pond;   or,  (3)  it  may  be  passed  through  a 
cooling  tower,  such  as  described  in  the  following  paragraphs. 

(c)  Cooling  towers  are  roughly  divided  into  two  classes: 

1.  Natural  draft  cooling  towers,  and 

2.  Fan  towers  or  forced  draft  towers. 

In  the  natural  draft  type,  a  vertical,  rectangular  or  cylindrical 
shell  is  filled  with  some  material  or  structure  (trays,  slats,  wire 
screens,  etc.)  adapted  to  spread  the  water  into  thin  sheets  or 
streams.  The  water  is  introduced  at  the  top,  gravitates  over 
this  filling  to  a  reservoir  in  the  base  of  the  tower  and  is  then 
returned  to  the  condenser. 

Air  enters  at  the  bottom  of  the  tower  and  passes  upward 
through  the  filling  so  that  cooling  takes  place  on  the  counterflow 
principle.  The  upward  motion  of  the  air  in  the  tower  is  due  to 
the  fact  that  its  temperature  and  humidity  are  greater  than 


682 


HEAT-POWER  ENGINEERING 


those  of  the  outside  air  and  it  is  therefore  constantly  displaced 
upward  by  fresh,  cool  air  entering  at  the  bottom.  This  effect 
(the  "draft")  is  increased  by  lengthening  the  column  of  hot  moist 
air  by  the  addition  of  a  "flue,"  or  "stack,"  above  the  filling. 

(d)  A  fan  type  of  tower  is  essentially  the  same  as  one  with 
natural  draft  so  far  as  filling  and  cooling  are  concerned;  the 
stack  is  omitted,  however,  and  the  draft  is  assisted  by  fans 


\  Fig.  442. 

which  force  air  in  at  the  bottom  of  the  tower.  Such  a  struc- 
ture, of  which  there  are  many  arrangements,  is  shown  in  Fig. 
442.  This  type  of  tower  has  the  disadvantage  of  requiring  an 
expenditure  of  power  to  operate  the  fans,  but  is  independent  of 
atmospheric  conditions  so  far  as  draft  is  concerned. 

A  combination  of  both  types  is  occasionally  used,  the  stack 
supplying  draft  when  possible  and  being  helped  out  by  the  fans 
when  necessary. 


CONDENSERS  AND  RELATED  APPARATUS  683 

(e)  Neglecting  losses,  the  heat  abstracted  in  a  given  time 
from  the  exhaust  steam  in  condensing  it  equals  the  weight  of 
the  condensate  (wx)  times  the  latent  heat   (rx)  of  the  exhaust 
steam  at  its  partial  pressure,  and  this,  of  course,  is  the  amount  of 
heat  absorbed  by  the  cooling  water.     Hence,  if  this-  water  is 
used  repeatedly,  it  must  first  be  cooled  by  the  surrender  of  this 
same  amount  of  heat  before  its  return  to  the  condenser.     This 
cooling  is  accomplished    principally  by  the  evaporation   of  a 
portion  of  the  water,  the  heat  carried  away  in  this  manner  being 
equal  to  the  product  of  weight  (wv)  vaporized  in  the  given  time, 
by  the  latent  heat  (rv)  at  the  partial  pressure  existing  at  the 
surface  exposed  to  the  atmosphere.     Then,  considering  that  the 
cooling  is  effected  entirely  by  evaporation  and  neglecting  losses, 

it  follows  that  ,     N 

(wr)x  =  (wr)v ; (492) 

or,  the  weight  of  cooling  water  evaporated  in  a  given  time  is 

approximately 

10,  =  wxrx/rv.      ......     (493) 

But,  as  rx  and  rv  do  not  differ  greatly,  it  is  roughly  true  that 
wv  =  wx,  —  that  is,  under  the  conditions  assumed,  the  weight  of 
condensing  water  vaporized  in  the  cooling  device  is  about  equal 
to  the  amount  of  condensate  formed  in  the  same  interval  of 
time  in  the  condenser  in  which  that  water  is  used.  Thus,  if  all 
the  steam  generated  is  condensed  in  a  surface  condenser  and 
returned  to  the  boiler,  no  new  water  (theoretically)  is  needed 
for  boiler  feed,  but  about  an  equal  weight  of  make-up  water 
must  be  constantly  added  to  the  supply  of  cooling  water;  and 
with  surface  condensers  this  water  may,  of  course,  be  of  quality 
unsuitable  for  use  in  the  boilers.  This  is  theoretically  the  maxi- 
mum amount  that  need  be  lost  in  the  process  of  cooling. 

(f)  If  the  air  were  so  fully  saturated  that  it  could  receive  no 
more  moisture,  none  of  the  water  would  vaporize  and  no  cooling 
would  be  effected  in  the  manner  just  described.     In  such  case 
heat  could  still  be  abstracted  from  the  water  by  bringing  cooler 
air  and  its  moisture  in  contact  with  it.     The  cooling  media 
would  then  have  their  sensible  heat  raised  by  absorbing  heat 
from  the  water,  but  it  would  take  a  great  quantity  of  air  to 
effect  the  cooling  in  this  manner. 

(g)  The  actual  case  is  intermediate  between  the  two  extremes 
just  discussed.     The  atmospheric  air  is  practically  never  fully 


684  HEAT-POWER  ENGINEERING 

saturated  but  nearly  always  has  some  humidity.  In  the  aver- 
age cooling  tower  from  J  to  £  of  the  heat  is  carried  away  by  the 
increase  in  the  sensible  heat  of  the  air  and  its  vapor,  and  the 
rest  by  evaporation.  The  actual  operation  of  the  cooling  de- 
vice is  dependent  on  the  humidity,  temperature,  amount  and 
distribution  of  the  air  and  on  the  temperature  and  extent  of 
exposed  surface  of  the  water.  Ordinarily,  under  unfavorable 
conditions,  one  cubic  foot  of  air  entering  can  be  expected  to 
remove  at  least  2\  B.t.u.  as  sensible  heat  of  the  air  and  latent 
heat  of  vaporized  water;  from  2  to  4  per  cent  of  the  condensing 
water  is  all  that  need  be  lost  by  evaporation ;  and  the  condensing 
water  can  be  readily  cooled  40  to  50  Fahrenheit  degrees. 


CHAPTER  XXXVIII. 

WATER  PURIFICATION 

323.  Impurities  in  Natural  Waters,  (a)  Waters  available  for 
power  plant  use  are  never  the  simple  H2O  of  chemistry  but 
always  carry  certain  impurities  in  suspension  and  in  solution. 
When  taken  from  streams  or  lakes  the  water  generally  has  large 
quantities  of  mud  and  silt  in  suspension  at  certain  periods  of 
the  year;  in  some  cases  at  all  periods.  Water  taken  from 
sources  which  receive  large  deposits  of  leaves,  twigs  and  other 
vegetable  and  animal  remains  will  always  carry  certain  organic 
substances  in  solution  and  sometimes  in  suspension  as  well. 
Practically  all  waters  found  on,  or  below,  the  earth's  surface 
contain  inorganic  salts  and  gases  in  solution  and  sometimes  free 
acids  as  well. 

(b)  All  such  impurities  are  liable  to  cause  trouble  in  power 
plants,  either  (i)  by  clogging  tubes  and  pipes,  or  (2)  by  corroding 
metal  surfaces,  or  (3)  by  incrusting  heat-transmitting  surfaces, 
or  (4)  by  causing  foaming  within  boilers  and  similar  apparatus. 

(c)  When  solid  material  in  suspension  is  of  large  size  it  can 
often  be  separated  by  simple  mechanical  means,  as  by  screening, 
by  settling,  or  by  filtering  through  beds  of  coke,  broken  rock,  or 
sand.     When  fine  it  can  be  removed  by  first  entangling  it  in  a 
flocculent  precipitate  and  then  filtering,  as  is  done  with  municipal 
supplies. 

In  general,  however,  after  such  treatment  average  water  will 
still  contain  in  solution  quite  a  quantity  of  material  which  will 
cause  trouble  if  allowed  to  enter  the  apparatus  of  a  power  plant. 
The  greatest  difficulty  is  experienced  in  steam  boilers  and  in  the 
jackets  of  internal-combustion  engines  because  of  the  deposition 
of  such  dissolved  material  upon  the  metal  surfaces,  thus  forming 
a  crust,  or  a  scale,  which  materially  decreases  heat  conductivity, 
clogs  the  passages,  and  may  lead  to  the  overheating  of  metal 
plates  or  surfaces.  Acids  in  solution  may  cause  corrosion  of 
such  surfaces. 

685 


686  HEAT-POWER  ENGINEERING 

(d)  To  prevent  troubles  of  this  character  water  is  often 
"treated,"  "softened,"  or  "purified,"  before  use.  The  problem 
of  water  treatment  is  very  large  and  by  no  means  entirely  solved 
as  yet.  In  the  following  paragraphs  the  fundamental  principles 
and  the  most  common  methods  of  treatment  of  boiler  feed 
waters  will  be  very  briefly  considered. 

324.  Troubles  from  Untreated  Feed  Water,  (a)  If  untreated 
water  is  fed  to  a  boiler  the  following  troubles  may  ensue: 

(1)  Corrosion  may  occur  because  of 

(a)  Free  acid,  such  as  HzSO*  and  HNOS,  which  will  not  only 

attack  the  metal  of  the  boiler,  but  if  present  in  larger 
quantities  than  5  parts  per  1 ,000,000  *  will  often 
corrode  or  pit  the  metal  parts  of  the  engine  with 
which  the  steam  comes  in  contact;  and  because  of 

(b)  Organic  material,  such  as  infusions  of  leaves,  sewage  and 

such,  which  acts  as  though  acids  were  formed  within 
the  boiler. 

(2)  Incrustation  may  occur  because  of 

(a)  The  deposition  of  suspended  matter,  such  as  mud,  in  parts 

of  the  boiler  in  which  the  circulation  is  not  sufficiently 
rapid  to  maintain  it  in  suspension; 

(b)  Tke  concentration  of  salts  brought  into  the  boiler  with 

the  feed  water  and  left  behind  by  the  issuing  steam; 

(c)  The  deposition  of  decomposed  salts,  such  as  the  soluble 

bicarbonate  of  calcium,  Ca(HCOs)»,  which  when 
heated  loses  one  molecule  of  COz  and  one  of  H^O, 
leaving  insoluble  CaCOz ; 

(d)  The  deposition  by  heating  of  salts  which  are  less  soluble 

in  hot  water  than  in  cold,  as  calcium  sulphate,  CaSO^, 
the  solubility  of  which  at  ordinary  steam  tempera- 
tures is  only  about  one-fourth  as  great  as  at  ordinary 
atmospheric  temperatures;  and 

(e)  The  deposition  of  soaps  formed  by  the  saponification  of 

greases  and  organic  oils  by  alkalies  present  in  the 
feed  water. 

*  Parts  per,  1000,  100,000  and  1,000,000  are  the  terms  commonly  used  for 
expressing  the  results  of  water  analyses.  Since  one  U.  S.  gallon  of  water  at  60 
degrees  F.  weighs  58,335  grains,  one  part  per  100,000  is  equal  to  0.584  grain  per 
U.  S,  gallon. 


WATER  PURIFICATION  687 

(3)  Foaming  may  be  caused  by 

(a)  The  decomposition  or  modification  of  salts  to  form  floc- 

culent  precipitates  which  collect  as  a  scum  on  and 
near  the  surface  of  the  water;  and  by 

(b)  Organic  matter,   grease,  soaps  and  such,  which  form 

similar  scums. 

(b)  By  far  the  most  troublesome  salts  commonly  found  in 
feed  waters  are  those  of  calcium  and  magnesium.  They  are 
generally  either  the  carbonates  or  the  sulphates  of  these  metals. 
The  carbonates  of  calcium  form  a  more  or  less  granular  scale 
which  it  is  not  very  difficult  to  remove  with  the  tools  used  for 
cleaning  boilers.  The  sulphate  of  calcium  forms  a  very  hard, 
porcelain-like  scale  which  is  removed  only  with  great  difficulty. 
Magnesium  carbonate  generally  gives  rise  to  a  scum,  causing 
priming,  and  also  forms  a  hydrate  which  serves  to  cement  to- 
gether other  scale-forming  materials.  The  sulphate  of  this  metal 
decomposes  at  high  temperatures,  liberating  sulphuric  acid  which 
may  cause  corrosion  and  forming  the  hydrate  which  acts  as  a 
cement. 

325.  Methods  of  Treating  Feed  Waters,  (a)  A  large  quan- 
tity of  the  material  carried  in  solution  in  boiler  feed  waters  can 
often  be  precipitated  by  simply  raising  the  temperature.  This 
should  be  done  in  open  type  heaters  using  exhaust,  or  live  steam, 
whichever  is  necessary  to  attain  the  necessary  temperature. 
The  impurities  which  are  precipitated  either  remain  fastened 
to  the  pans  and  other  parts  of  the  heater  or  are  separated  by 
filtering  through  a  bed  of  coke,  or  other  material,  contained 
within  the  heater  itself. 

(b)  Where  the  use  of  live  steam  is  not  desirable  or  where  the 
water  contains  salts  that  are  not  readily  precipitated  by  simply 
raising  the  temperature,  certain  chemicals  can  be  added  to  the 
water.  These  chemicals  should  be  so  chosen  as  to  react  with 
the  majority,  or  with  the  most  harmful,  of  the  impurities  to  form 
insoluble  precipitates,  or  to  form  less  harmful,  soluble  com- 
pounds. By  far  the  most  common  chemical  in  use  for  this 
purpose  is  soda  ash  (impure  sodium  carbonate)  although  various 
other  inorganic  and  organic  compounds  are  also  utilized.  Soda 
ash  has  the  advantages  of  very  low  cost,  small  weight  required, 


688  HEAT-POWER  ENGINEERING 

applicability  to  most  waters  and  formation  of  compounds  which 
are  easily  disposed  of  in  the  heaters  and  in  the  boilers. 

(c)  In  many  cases,  particularly  where  steam  is  not  available, 
or  where  special  conditions  are  to  be  met,  cold  methods  are 
used.     In  such  cases  a  solution  of  the  proper  chemical,  or  chemi- 
cals, is  fed  in  measured  quantities  to  the  raw  water,  and  any 
precipitates  formed  are  settled  or  filtered  out,  after  which  the 
treated  water  passes  to  some  sort  of  storage  to  await  use. 

i  Apparatus  of  this  type  is  generally  made  wholly  or  partly 
automatic.  It  is  always  of  large  size  and  therefore  costly,  and 
because  of  the  low  temperature  many  reactions  which  may  be 
easily  carried  out  in  heaters  are  either  entirely  absent  or  are 
very  incomplete. 

(d)  Many  "  boiler  compounds,'1  some  of  secret  composition, 
are  in  use.     They  are  mixed  with  the  feed  water  on  its  way  to 
the  boiler  and  are  supposed  to  prevent  or  mitigate  the  formation 
of  scale.     It  should  be  remembered  that  no  solid  material  which 
enters  the  boiler  can  leave  with  the  steam  and  hence  it  must  all 
remain  within  the  vessel  unless  removed  by  other  means,  such 
as  blowing  down,  skimming,  etc. 

This  being  the  case,  all  that  can  be  expected  of  a  boiler  com- 
pound is  that  it  will  react  with  the  most  troublesome  impurities 
so  as  to  change  them  to  less  troublesome  ones  which  can  be 
removed  as  sludge  through  the  blow-off  valve,  rather  than  as  a 
hard  scale  adhering  to  the  metallic  surfaces.  In  any  event  the 
amount  of  solid  to  be  removed  from  the  boiler  will  be  greater 
when  a  compound  is  used  than  when  the  untreated  water  is 
vaporized,  and  it  is  merely  a  question  of  whether  the  greater 
amount  of  soft  material  permits  of  more  economical  and  safer 
operation  than  does  the  smaller  quantity  of  harder  scale.  It 
is  therefore  obvious  that  the  impurities  should,  when  possible, 
be  removed  from  the  water  before  it  is  introduced  into  the 
boiler. 

(e)  There  are  some  so-called   "  boiler  compounds  "   on  the 
market  which  are  not  supposed  to  react  with  the  solids  in  the 
water  but  are  intended  to  coat  the  water  side  of  all  heating  sur- 
faces in  such  a  way  as  to  prevent  the  adherence  of  scale  and 
scale- forming   material.     Besides   the   commercial   compounds, 
kerosene  and  similar  hydrocarbon  oils  have  been  more  or  less 
successfully  used  for  this  purpose.     Oil  so  used  should  contain 


WATER  PURIFICATION  689 

no  organic  admixture  as  this  may  cause  trouble  by  saponifying 
in  the  boiler  and  it  should  contain  no  heavy  hydrocarbons 
which  will  form  tar  or  pitch  as  these  might  cause  overheating  of 
plates  to  which  they  become  attached. 

It  has  also  been  claimed  that  graphite  acts  in  a  waynsimilar  to 
kerosene  in  preventing  the  adherence  of  scale-forming  material. 


CHAPTER  XXXIX. 


POWER  PLANTS. 

326.  General,  (a)  Only  a  very  general  discussion  of  the  sub- 
ject of  power  plants  as  a  whole  can  be  attempted  in  this  book 
and  that  must  be  given  in  the  briefest  manner  possible.  Plants 
having  internal  combustion  engines  and  those  having  steam- 
operated  prime  movers  will  be  the  only  types  considered. 

(b)  The  choice  between  plants  of  these  two  types  depends  on 
many  considerations,  some  of  which  are:  (i)  kind  of  fuel  avail- 
able, (2)  fuel  economy,  (3)  first  cost  and  other  financial  con- 
siderations, (4)  reliability,  (5)  weight,  (6)  space  occupied,  (7) 
cost  of  water,  (8)  ability  to  secure  properly  trained  attendants, 
(9)  location,  and  (10)  character  of  load.  In  general,  where 
coal  is  very  expensive,  the  producer  plant  will  give  better  finan- 
cial returns  than  a  steam  plant  unless  the  power  requirements 
are  such  as  to  call  for  unusually  large  units  (say,  from  1000  to 
4000  or  5000  horse  power  for  the  plant) . 


Fuel 


327.   Internal  Combustion  Engine  Plants.     If  the  fuel  is  oil, 
or  gas,  the  plant  merely  consists  of  the  engine  with  means  of 

supplying  the  fuel  and  for 
transmitting  the  energy  de- 
veloped, and  with  provision 
for  jacket  water.  If  solid 
fuel  is  used  in  a  producer, 
the  elements  of  the  plant 


are  those  given  in  Fig.  443. 

328.  Steam  Power 
Plants,  (a)  The  location 
of  the  plant  is  selected  with 
respect  to  (i)  railroad  and 
dock  facilities  for  receiv- 
ing coal  and  disposing  of  ashes,  (2)  supply  of  water  suitable 
for  feed  and  condensing  purposes,  (3)  convenience  for  distribu- 

690 


Product 
(Electric  Energy) 


Fig.  443.  —  Elements  of  a  Producer  Gas 
Power  Plant. 


POWER  PLANTS 


691 


tion  of  its  products  (electrical  energy,  exhaust  steam  for  heating, 
belt  delivered  power,  etc.),  (4)  cost  of  real  estate,  (5)  suitability 
of  ground  for  foundations,  (6)  space  for  storage  of  fuel,  (7)  char- 
acter of  the  surrounding  neighborhood,  and  (8)  allowance  for 
increase  in  size  of  plant. 

(b)  The  building  is  generally  divided  by  a  fireproof  and  dust- 


Energy  Supply 


Outside  Source . 


••Transportation 


Fuel  Storage     I 


Coal  and  Ash 
Handling 


Forced 
Draft  Fan 

Furnaces 
and 
Boilers 

I 

- 

^* 

Indu 
Oraft 

Steam 

eader 

1 

Engines 

1 

Generators 


Product 
GSlectcic  Energy) 


fc) 


Fig.  444.— Elements  of  a  Steam  Power  Plant. 


proof  wall  into  the  boiler  room  and  the  engine  (or  turbine)  room, 
and  is  provided  with  proper  lighting  and  ventilating  facilities 
and  with  doorways  of  sufficient  size  to  admit  the  largest  pieces 
of  the  equipment.  In  large  plants  the  railroad  track  usually 
enters  the  building,  the  doors  being  large  enough  to  admit  box 
cars.  The  architecture  of  the  building  should  be  in  harmony 


692 


HEAT-POWER  ENGINEERING 


with  its  surroundings  and  the  design  should,  in  general,  permit  of 

enlargement  of  plant  to  meet  increases  in  the  demand  for  power. 

The  scheme  of  the  steam  power  plant  equipment  is  illustrated 

in  Fig.  444.     This  diagram  is  very  general  and  includes  pieces 

of  equipment  which  are 
used  only  in  special  cases; 
it  also  shows  apparatus 
which  would  not,  in  gen- 
eral, be  used  at  the  same 
time  in  ordinary  cases. 
Several  arrangements  of 
steam  power  plants  are 
shown  in  Figs.  445  to  449. 
Fig.  445.  — Small  Engine  Plant.  (c)  In  the  boiler  room, 

besides  the  boilers,  are  lo- 
cated the  feed  pumps,  fans,  feed  heaters  (generally),  economizers, 
etc.  Car  tracks  are  arranged  to  deliver  the  coal  at  such  point  as 
to  reduce  the  manual  labor  to  the  minimum.  Large  plants  usu- 


Fig.  446.— Small  Turbine  Plant. 

ally  have  overhead  bunkers,  to  which  the  coal  is  brought  by  cars 
or  by  mechanical  conveyors  of  the  bucket,  belt,  or  other  type,  and 
from  which  chutes  lead  to  the  hoppers  of  the  stokers,  or,  in  case 
of  hand  firing,  to  the  floor  in  front  of  the  boiler;  and  ash  hoppers 


POWER  PLANTS 


693 


are  generally  placed  under  the  grates  with  dumps  discharging 
to  conveyors  or  cars  below.  In  some  instances  boilers  are 
located  on  two  or  more  floors  (as  in  "double  deck"  plants)  as  in 


Atm.Relief  Valve 
B<=  Circulating  Pump 
C= Condenser 
D  =  Circ.  Water  Discharge 
E= Economizers 

—  Electric  Generator 
I  =  Circ. Water  Inlei 
T=  Turbine 


Fig.  447. — Large  Turbine  Plant. 

Fig.  448,  or  are  fired  from  both  ends  (Figs.  367  and  449),  to  re- 
duce the  ground  area  occupied.  These  special  arrangements  are 
more  often  adopted  in  turbine  plants  than  in  those  having  engines, 


694 


HEAT-POWER  ENGINEERING* 


because  the  turbine  room  is  generally  much  smaller  than  the  boiler 
room,  whereas  an  engine  room  is  ordinarily  of  about  the  same  size. 
(d)  The  larger  engine  rooms  are  usually  provided  with  over- 
head traveling  cranes  of  capacity  at  least  sufficient  to  lift  the 
heaviest  piece  of  machinery.  Surface  and  jet  condensers  and 
their  pumps  are  usually  located  below  the  engine,  in  the  base- 


Fig.  448. — Power  Plant  with  Double  Deck  Boiler  Room. 

ment;   and  barometric  and  siphon  condensers  are  often  placed 
outside  the  building. 

(e)  In  electric  plants  as  much  of  the  steam  piping  as  is  feasible 
is  located  in  the  boiler  room  to  prevent  liability  of  damage  to 
the  electrical  apparatus  by  the  steam  in  case  of  pipe  failure. 
Where  plant  shutdowns  are  of  serious  consequence,  the  ideal 
arrangement  of  piping  would  permit  (i)  of  running  any  prime 
mover  from  any  boiler,  (2)  of  any  boiler,  or  engine  unit,  being 
isolated  without  affecting  the  rest,  and  (3)  of  making  repairs 
to  any  portion  of  the  piping  without  affecting  any  unit  (or  not 
more  than  one).  This  ideal  case  is  approximated  most  closely 


POWER  PLANTS 


695 


by  the  "loop  or  ring11  system  of  piping,  a  in  Fig.  450,  and 
by  the  "double-header"  system,  as  b  in  Fig.  450.  These  systems 
call  for  an  amount  of  piping  and  a  number  of  joints  and  valves 
that  is  prohibitive  in  most  cases.  Ordinarily  the  connections 
from  the  boilers  are  merely  led  to  a  "single  header"  from  which 
other  pipes  lead  to  the  prime  movers,  as  c  in  Fig.  450.  In  large 
plants  it  is  common  practice  to  arrange  each  prime  mover  and 


D  -Circ.Water  Discharge 

C  -  Condenser' 

E  *  Economizer 

I  =Circ.  Water  Inlet 

S  *  Separators 


Fig.  449.  — Power  Plant  with  Boilers  Fired  from  Both  Ends,  and  with  Com- 
pound Steam  Engines  Exhausting  to  Low  Pressure  Turbines. 

the  boilers  which  serve  it,  as  an  independent  unit;  but  fre- 
quently cross-connections  are  provided  between  units  for  use  in 
emergencies.  There  is  almost  an  unlimited  number  of  arrange- 
ments of  piping  possible,  but  they  are  generally  modifications 
or  combinations  of  those  just  given. 

The  piping  for  the  auxiliary  apparatus  is  independent  of  the 
main  system  to  permit  that  apparatus  to  be  operated  even 
though  the  other  is  not  in  use. 


696 


HEAT-POWER  ENGINEERING 


The  steam  pipes  from  the  boiler  have  hand-operated  shut-off 
valves,  and  in  some  cases  also  include  emergency  valves  which 
will  close  if  abnormal  outflow  of  steam  occurs,  as  when  a  steam 
pipe  is  ruptured,  and  act  as  check  valves  preventing  the  inrush 


Fig.  450.  — Steam  Piping  Arrangements. 

of  steam  from  other  boilers  if  a  tube  fails.  The  engine  feeders 
also  have  shut-off  valves  near  the  cylinders  and  sometimes  there 
are  also  valves  which  will  automatically  close  if  the  engine  starts 
to  run  away.  All  steam  piping  should  be  lagged  with  non- 

•T    By-pass 


Water 
Supply 
No.,3 


By-pass 


(Hot  Well  Water 
£-*-  Water  S"PP*  No'1    I  or  Raw  Feed 

Fig.  451- 

conducting  covering;  it  must  be  properly  supported;  provision 
for  expansion  must  be  made  by  the  introduction  of  slip  or  swivel 
joints,  corrugated  sections  or  flexible  curved  portions;  and  it 
must  be  so  arranged  as  to  be  without  undrained  portions  from 
which  the  collected  water  can  be  carried  over  in  large  quan- 
tities to  the  prime  mover  with  disastrous  results.  The  piping 


POWER  PLANTS  697 

should  be  properly  drained  by  suitably  arranged  collecting 
pockets  connected  with  "traps"  or  equivalent  devices  and  at 
the  engines  there  should  be  "steam  separators."  The  traps  (by 
float  or  other  device)  automatically  discharge  the  accumulation 
of  water  from  time  to  time. 

(f)  The  boiler  feed-water  piping  is  preferably  so  arranged  that 
any  of  several  pumps  (or  injectors)  can  be  used  for  supplying 
the  feed  water,  and  also  so  that  there  are  several  sources  from 
which  this  water  can  be  obtained.     One  of  the  numerous  possible 
arrangements  of  piping  is  diagrammed  in  Fig.  451. 

(g)  Each  piece  of  auxiliary  apparatus  is  preferably  so  arranged 
that  it  can  serve  any  one  of  the  sets  of  main  units,  and  so  that 
it  can  be  isolated  if  out  of  commission  and  the  materials  which 
it  ordinarily  handles  may  be  by-passed  around  and  led  direct  to 
their  final  destinations. 


CHAPTER  XL. 

CONTINUOUS  FLOW  OF  GASES  AND  VAPORS  THROUGH  ORIFICES 

AND  NOZZLES. 

329.  Introductory,  (a)  The  thermodynamic  transformations 
previously  discussed  in  this  book  were  assumed  to  occur  in  such 
manner  that  the  change  of  kinetic  energy  (velocity  energy) 
associated  with  the  flow  of  the  working  substance  from  one  part 
of  the  system  to  another  was  zero.  In  the  usual  cases  of  flow 
of  gases  or  vapors  through  pipes  and  in  cylinders  this  same 
assumption  may  be  made  without  introducing  serious  error, 
because  of  the  relatively  low  velocities  prevailing. 

When,  however,  gases  or  vapors  flow  through  nozzles  or  ori- 
fices both  the  changes  in  velocity  and  the  corresponding  changes 
in  the  kinetic  energy  of  the  working  substance  may  be  very  large. 
In  such  instances  much  of  the  potential  energy  associated  with  the 
substance  may  be  converted  into  the  kinetic  energy  associated 
with  the  change  of  motion,  or  the  reverse  process  may  occur. 

(b)  Let  Fig.  452  represent  a  conduit  through  which  the  ma- 
terial flows  in  the  direction  of  the  arrow;    and  let  Po  and  K 
— ]  r     be  respectively  the  simultaneous  poten- 

tial and  kinetic  energies  associated  with 
a  pound  of  the  working  substance  at  any 
instant.  Then  Po\  +  K\  is  the  total 
associated  energy  per  pound  when  the 

stream  passes  section  I  in  Fig.  452  and  Po2  +  K2  is  its  value 
when  passing  section  2.  If  the  conduit  is  of  such  character  that 
energy  neither  passes  through,  nor  is  stored  by,  its  walls,  it 
follows  from  the  Law  of  Conservation  of  Energy,  and  from  the 
First  Law  of  Thermodynamics,  that 

from  which  AK  =  K2  —  KI  =  Poi  —  Po2  ....     (495) 

where  &K  is  the  Change  in  Kinetic  Energy  per  pound  of  mate- 
rial. This  equation  shows  that  the  changes  in  kinetic  and 

698 


CONTINUOUS  FLOW  OF  GASES   THROUGH  ORIFICES        699 

potential  energies  between  sections  I  and  2  are  equal  in  amounts 
but  opposite  in  direction. 

(c)  For  the  purposes  of  analytical  development  it  is  desirable 
to  examine  more  in  detail  the  character  of  the  potential  energy 
which  must  be  considered  in  connection  with  the  flow  of  gases 
and  vapors.     One  form  of  potential  energy  is  that  due  to  posi- 
tion, as  exemplified  by  the  familiar  "head"  in  hydraulics.     In 
most  engineering  problems  dealing  with  the  thermodynamics  of 
flow  of  the  materials  under  consideration  the  magnitude  of  this 
form  is  so  small  that  it  may  be  neglected  without  serious  error. 
A  second  form  is  that  due  to  a  substance's  stored  heat  energy  which 
was  expended  in  raising  the  sensible  heat  of  the  material,  or  in 
doing  internal  work,  or  in  both;    and  it  is  obviously  composed 
of  the  AS  and  A/  which  have  been  used  before.     The  only  other 
form  of  potential  energy  is  that  stored  in  the  enveloping  media 
due  to  external  work  done  upon  them  by  the  substance  sur- 
rounded.    Although  stored  in  the  surrounding  media,  it  is  con- 
venient to  consider  this  potential  energy  as  associated  with  the 
substance  that  did  the  work,  because  in  all  cases  this  energy 
would  be  returned  if  that  substance  were  brought  back  to  the 
original  conditions.     Evidently  this  stored  external  work  cor- 
responds to  the  &E  used  in  previous  discussions,  but  for  subse- 
quent purposes  it  will  be  convenient  to  obtain  a  slightly  different 
viewpoint  regarding  it. 

(d)  For  this  purpose  suppose  the  plug  a  (in  Fig.  453),  weighing 
one  pound,  and  having  a  (specific)  volume  V,  is  injected  its  full 
length  into  a  closed  vessel  b  which  is  so  large 

that  the  medium  it  contains  may  be  assumed 

to  remain  at  constant  pressure  P  pounds  per 

square  foot  during  the  process.      Then,  the 

external   work   done   by  the  plug  upon  the 

medium  is  PV  foot-pounds,  or  PV/778  B.t.u. 

This   energy   is   stored    in    the    surrounding 

medium,  but  as  it  will  be  returned  when  the 

plug  is  withdrawn,  it  may  be  considered  to 

be  associated  with  the  plug.     Obviously  all 

material,  which    is   surrounded  by  media   upon  which   it  has 

done  work  which  is  stored  as  potential  energy  of  this  form, 

may  be  considered  as  having  associated  with  it  this  returnable 

energy, 


700  HRAT-POWEk  ENGINEERING 

(e)  Now,  summing  up,  the  total  potential  energy  which  may 
be  considered  as  associated  with  a  pound  of  the  material  is 

Po  =  AS  +  A/  +  PV/778  ....  (496) 
measured  above  certain  datum  conditions  which  will  be  consid- 
ered later. 

This  value  of  the  potential  energy  may  now  be  substituted  in 
Eq.  (494)  giving,  for  the  conditions  of  flow  shown  in  Fig.  452, 

(±Si+Mi+PiVi/77*)+Ki  =  (AS2+A/2+P2V2/778)+X2,    (497) 
and  Eq.  (495)  then  becomes 


+  A/!  +  P,Vi/778)  -  (A52  +  A/2  +  P2V2/778)  .  (498) 

The  change  in  kinetic  energy  AX",  and  hence  the  change  in 
velocity,  between  sections  I  and  2  can  thus  be  computed  when 
the  intrinsic  energies  (AS  +  A/)  and  the  PV  conditions  of  the 
material  as  it  passes  these  sections  are  known. 

(f)  If  w  pounds  of  substance  are  flowing  per  second  with  a 
velocity  of  v  feet  per  second,  the  kinetic  energy  of  the  flowing 
material  is  wK  =  wvz  -5-  (2vg  X  778),  or  the  kinetic  energy  per 
pound  is  \  2 

*-  57X778  B'fcu  ......     (499) 

If  the  velocity  is  increased  from  Vi  to  V2,  the  change  in  kinetic 
energy  is,  per  pound  of  substance, 

AX  =  (Kt  -  KJ  =(~-  ^)/778  B.t.u.      .     (500) 

But  since  (K2  —  KI)  =  (Poi  —  P02)   this  equation  may  be  re- 
written        j  2   -'    2 

B.t.u.,      .     (501) 


which  may  be  used  for  determining  the  velocity  changes  when 
the  changes  in  potential  energy  are  known. 

330.  Flow  of  Saturated  Steam  in  the  Ideal  Case,  (a)  Fol- 
lowing the  general  equation  (498),  the  kinetic  energy  change 
during  flow,  in  terms  of  the  change  in  potential  energy,  is 


and  as  the  right  hand  side  of  this  equation  represents  differences 
between  the  various  heat  quantities,  it  is  immaterial  what  is 


CONTINUOUS  FWW  OF  GASES  THROUGH  ORIFICES       701 

taken  as  a  datum.  It  is  therefore  convenient  in  the  case  of  steam 
to  use  32  degrees  F.  as  such.  With  this  assumption  it  is  obvious 
that  for  saturated  steam  which  is  initially  dry  ASi  and  A52 
must  equal  qi  and  g2;  A/i  and  A/2  must  equal  pi  and  xzp^\  and 
PiVi/778  and  P2V2/778  correspond  to  (APu)i  and  (xAPu)*  if 
the  volume  of  water  be  neglected,  which  is  permissible  since  it 
is  relatively  insignificantly  small.  The  general  equation  for 
saturated  steam  may  therefore  be  written  in  the  form 

=  (q  +  P  +  APu)i  —  (q  +  xp  +  xAPu)2 


A<22, (502) 

in  which  AQi  and  A()2  are  the  total  heats  above  32  degrees  per 
pound  of  steam  at  points  I  and  2  respectively. 

While  the  foregoing  discussion  considered  only  the  case  of 
dry  saturated  steam,  it  applies  equally  as  well  to  any  initial 
condition.  Thus  in  the  ideal  case  A<2i  is  the  total  stock  of  heat 
per  pound  of  steam  entering  the  nozzle  and  AQ2  is  that  remain- 
ing when  the  lower  pressure  is  reached  by  the  process  of  ex- 
pansion. 

It  is  obvious  that  even  though  the  initial  and  final  pressures 
are  known,  Eq.  (502)  cannot  be  used  for  the  solution  of  numerical 
problems  until  some  means  is  found  for  determining  the  value 
of  xzt  or  A()2.  But  after  they  have  been  found  AK  can  be  deter- 
mined; then  from  Eq.  (501)  the  change  in  velocity  of  flow  can 
be_computed.  Methods  of  determining  the  values  of  #2  and  AQ2 
willjiow  be  considered. 

(b)  Since  the  velocity  of  steam  flowing  through  a  nozzle  or 
similar  conduit  is  very  high  there_is__yery  short  time  of  contact 
between  steam  and  walls.  And  further,  since  the  temperature 
of  the  steam  in  contact  with  any  particular  ring  in  the  wall j?f 
the  conduIF  is  always  the  same  sp_Tong  as  steady  conditions 
are  maintained,  it  follows  that  each  part  ofjjie_wall  will  acquire 
practically  the  same  temperature  as  the  steam  in  contact  with 
it.  "T^TiTresult  oFtheseTwo  facts  there  is  in  a  real  case  very 
little  transfer  of  heat  between  the  walls  and  the  steam  and 
it  [^reasonable  to  assume  no  transfer  in  anjdeal  case,  hen.ce 
theTTowlnay^be  considered  an  adiabatic  process,  or,  since  the 
pressufe^decreases  as  flow  progresses,  as  an  adiabatic  expan- 


702 


HEAT-POWER  ENGINEERING 


It  can  also  be  shown  that  for  ideal  conditions  this  adiabatic 
expansion  may"  also" "Be"  treated  without  serious  error  as  isen- 
tropic,  consequently  all  the  mechanism  previously  developed  for 
such  conditions  can  be  used  in  this  case. 

(c)  Then,  on  the  T0-diagram  in  Fig.  454,  if  the  initial  state 
point  is  i  (the  condition  being  T\,x\,  Aft),  the  ideal  expansion 

in  the  nozzle  would  be  along  the  isen- 
tropic  line  to  point  2  where  the  condi- 
tion is  Tz,  x2,  Aft.  The  heat  Aft  per 
pound  of  steam  at  the  beginning  of 
expansion  is  shown  by  the  area  sur- 
rounded by  the  heavy  line;  and  the 
heat  Aft  at  the  end  of  the  process,  by 
the  sectioned  area ;  hence  the  net  work 
&.K  done  is  Aft  — Aft  and  is  shown  by 
area  abi2.  This  area  is  seen  to  equal 
that  surrounded  by  the  lines  of  the 
p.  Clausius  cycle.  Hence,  in  the  ideal 

case   the  change  of  kinetic  energy  &K 

occurring  in  a  steam  nozzle  is  equivalent  to  the  external  work, 
AE  =  (A  ft  —  Aft),  done  with  a  Clausius  cycle  having  the  same 
expansion  line  and  using  the  same  weight  of  material. 

Thus   &K  (=  AE  =  Aft  -  Aft)   can   be  computed  by 
methods  given  in  Sect.  94  for  determining  the  work  of  the  Clausius 
cycle,  or  it  can  be  obtained  from  the 
T</>-diagram  or  from  the  M oilier  Chart. 

(d)  On  the  Mollier  Chart,  Fig.  455, 
the  ideal  (isentropic)  process  for  one 
pound  of  steam  is  represented  by  the 
line  1-2.     At  the  initial  point  the  con- 
dition of  the  steam  is  Xi,  pi,  Aft;  and  at  point  2  it  is  x2,  p2) 
Aft.     During  the  process  heat  equal  to  &K  =  (Aft  —  Aft),  as 
shown  by  the  length  1-2,  is  surrendered  for  producing  the  flow.* 

(e)  Having  found   &K  =  (Aft  -  Aft),  the   velocity   of   the 
stream  passing  point  2  is,  from  Eq.  (501), 

v*  =  vV  +  50,103  X  Ef  (Aft  -  Aft)  ft.  sec.  .  .  .  (503) 
in  which  Ef  is  the  efficiency  of  heat  conversion  as  compared 
with  the  ideal  case.  Its  value  is  unity  when  no  losses  occur. 

*  The  Ellenwood  Chart  (Appendix)  is  especially  useful  for  nozzle  problems  as 
besides  giving  &K  it  gives  values  of  xV  used  in  Eqs.  (507)  and  (508). 


/Px- 


Fig.  455- 


CONTINUOUS  FLOW  OF  GASES  THROUGH  ORIFICES        703 

If  the  acceleration  is  from  rest,  or  from  a  negligible  initial 
velocity,  which  is  ordinarily  the  case,  then  Eq.  (503)  becomes 

v  =  223.8  VE/(AQi  -  A&)  ft.  sec.,  "V_^    .     (504) 
or  v  =  223.8  VEf  X  A#  ft.  sec.       ;   >     .     .    ,     (505) 

(f)  If  the  velocity  of  the  stream  is  v  feet  per  second  at  any 
section  which  has  an  area  of  a  square  inches,  then  the  volume 
flowing  per  second  through  that  section  is  (va/i^)  cubic  feet; 
also  if  w  pounds  of  material  are  passing  the  section  per  second, 
and  if  the  specific  volume  is  V*  and  the  quality  x,  then  the 
volume  passing  per  second  is  wxV.  Hence,  at  the  given  section 

wxV  =  pa/144 (506) 

Thus,  if  a  given  weight  of  vapor,  of  known  specific  volume  and 
quality,  is  to  be  passed  with  a  given  velocity,  the  area  of  the 
passage  must  be 


a  =  —  X  144  .......     (507) 

Or  the  weight  of  the  material  passed  by  a  given  area  may  be 
computed  from  va 

=  '         '    '    '    '    "    (508) 


While  the  foregoing  discussion  was  confined  to  steam,  it,  of 
course,  applies  equally  well  to  any  other  vapor.  But  these 
equations  cannot  be  applied  indiscriminately  as  will  be  shown  in 
the  next  section. 

331.  The  Ideal  Steam  Nozzle,  (a)  Starting  with  any  initial 
state  (piXiAQi)  and  expanding  in  a  steam  nozzle  in  the  manner 
described,  it  will  be  found  that  as  the  terminal  pressure  is 
lowered  certain  peculiar  phenomena  occur  which  are  difficult 
to  understand  without  the  aid  of  curves.  These  curves  will 
now  be  constructed  : 

For  a  series  of  such  expansions,  all  for  one  pound  of  steam 
and  from  a  fixed  initial  absolute  pressure  pi  and  quality  x\t  to 

*  The  weight  of  the  steam  per  pound  of  material  is  equal  to  the  quality  x  and 
that  of  the  moisture  is  (i  —  x)  ;  the  volume  of  the  steam  is  xV  and  that  of  the 
water  is  (i  —  x)  X  volume  of  i  pound  of  water.  As  the  volume  of  one  pound  of 
water  is  about  T<&<y  that  of  the  steam  at  atmospheric  pressure  and  of  like  order  at 
other  pressures  the  volume  occupied  by  the  moisture  in  the  steam  is  negligible  and 
hence  is  not  included  in  the  discussion  given  above. 


704 


HEAT-POWER  ENGINEERING 


let  there  be  de- 


(4) 


(5) 


progressively  decreasing  absolute  pressures  p, 
rived  the  successive  values^of.^ 

(1)  The  quantities  x-at  pressures  p] 

(2)  The  heat  kK  =  Aft  —  A<2  theoretically  made  avail- 

able for  producing  flow;  and 

(3)  The  specific  volumes  V  at  pressure  p. 

Items  (i)  and  (2)  may  be  readily  obtained  from  the  Mollier  Chart 
or  they  may  be  computed  by  the  methods  given  in  Sect.  94 ;  and 
(3)  may  be  obtained  from  the  steam  tables.  Then  with  the  values 

of  A^T  as  abscissas  plot  curves,  as  in 
Fig.  456  (a) ,  to  show  by  ordinates  how  p, 
x  and  V  change  with  the  surrender  of 
heat  as  the  expansion  progresses. 

Next  compute  the  progressive  values 
of 

The  actual  volumes  (xV)  of  one 
pound  of  material ; 

The  jet  velocities  v  (by  substi- 
tuting the  different  values  of 
(Aft-A<2),inEq.(504))  ;  and 

(6)  The  areas  a  of  sections  required 
at  different  points  along  the 
nozzle  to  obtain  these  veloci- 
ties. These  areas  may  be  ob- 
tained from  Eq.  (507). 

Then  with  the  same  abscissas  as  before 
plot  curves,  as  in  Fig.  456  (b)  to  show 
-£—  ~~*l      by  ordinates  the  variation  of  xV,  v  and 

Fig'456-  a  with  AX. 

(b)  Now  referring  to  the  figure  it  will  be  seen  from  the  a-curve 
that,  as  expansion  progresses,  the  cross-sectional  area  of  the 
passage  must  at  first  contract  and  then  diverge,  if  expansion 
is  carried  far  enough,  —  thus  the  nozzle  must  have  a  neck.  Pro- 
jecting upward  from  this  neck  to  the  p-curve,  it  will  be  found 
that  the  neck  pressure  is  about  58  per  cent  of  the  initial  pressure 
and  that  the  corresponding  point  vn  on  the  p-curve  will  scale  at 
a  little  over  1400  feet  per  second.  And  it  is  important  to  note 
that  about  these  same  values  will  always  obtain  regardless  of 


CONTINUOUS  FLOW  OF  GASES  THROUGH  ORIFICES        705 

the  initial  condition  of  the  steam,*  hence  they  are  called  the 
critical  pressure  and  critical  velocity. 

(c)  Fig.  456  (c)  shows  the  longitudinal  section  of  a  nozzle  in 
which  the  amount  of  heat  surrendered  per  inch  of  length  is 
constant  from  one  end  to  the  other  and  is  equal  to  the  abscissa 
scale  used  for  the  curves  above.     This  nozzle  is  for  one  pound 
of  steam  flowing  per  second,  with  terminal  pressure  p2  pounds 
absolute  and  final  velocity  v2,  as  shown  on  the  respective  curves. 
Corresponding  to  any  other  pressure  of  exit  from  the  nozzle, 
the  end  diameter  may  be  found  by  projecting  downward  from 
the  proper  point  on  the  ^-curve  to  the  longitudinal  section  of 
the  nozzle;  —  thus  for  discharge  to  atmospheric  pressure  (14.7 
Ibs.)  the  end  diameter  is  seen  to  be  dA,  the  length  of  nozzle  is 
1AJ  and  the  terminal  velocity  is  VA;  for  discharge  to  a  pressure 
pn  =  .58^1  the  corresponding  values  would  be  dn,  ln  and  vn\ 
and  for  terminal  pressure  equal  to  ps  they  would  be  ds,  IB  and 
VB.     Evidently  a  nozzle  originally  used  with  discharge  pressure 
pz  will  be  theoretically  correct  for  a  case  where  the  pressure  is 
atmospheric,  if  its  end  is  cut  off  sufficiently  to  have  the  final 
diameter  beyond   the  neck  equal  to  dA,  and  similarly  for  the 
other  terminal  pressures.     Thus  regardless  of  the  exit  pressures, 
Fig.  456  (c)  is  the  horizontal  section  of  all  nozzles  discharging  the 
same  weight  of  steam  per  second  with  same  initial  conditions, 
the  only  difference  between  the  various  nozzles  being  in  the 
lengths  and  end  diameters,  which  are  made  to  correspond  to 
the  terminal  pressures. 

(d)  The  reason  the  neck  is  present  in  all  cases  where  the  ex- 
pansion is  to  a  pressure  below  .58  pi  can  now  be  easily  explained: 
From  Eq.  (507)  the  area  of  the  nozzle  at  any  section,  per  pound 
of  material  flowing  per  second,  is 

xV 
a  =  —  XI44- 

v 

Now  referring  to  the  curves  for  xV  and  v  in  Fig.  456  (c)  it  will 
be  seen  that  as  the  expansion  progresses  the  numerator  xV  at 
first  increases  much  slower  than  does  the  denominator  v,  and 
hence  the  nozzle  areas  (a)  must  first  diminish;  but  that  later 
the  conditions  are  reversed,  consequently  the  areas  must  then 

*  There  will  be  slight  variations  with  the  initial  conditions,  but  these  are  not 
great  and  will  not  be  discussed  in  this  elementary  treatment. 


706  HEAT-POWER  ENGINEERING 

increase.     Obviously  there  must  be  a  neck  where  the  converging 
and  diverging  portions  of  the  nozzle  join. 

(e)  It  has  been  seen  that,  corresponding  to  each  cross  section 
of  the  nozzle,  the  steam  has  a  definite  condition  and  velocity,  as 
shown  by  the  ordinates  in  Fig.  456  immediately  above  the  sec- 
tion under  consideration.     If  the  cross  sections  of  the  nozzle 
were  shifted  or  spaced  differently,  so  as  to  alter  the  longitudinal 
section  of  the  nozzle  from  that  shown,   the  ordinates  of  the 
curves  would   be  similarly   shifted   and    the   character   of   the 
curves  would  change.     This  shifting  may  be  so  done  as  to  cause 
any  one  of  the  curves  to  become  a  straight  line ;  thus  the  nozzle 
may  be  such  as  to  cause  a  uniform  drop  in  pressure  throughout 
its  length,  or  a  uniform  increase  in  velocity,  or  a  uniform  in- 
crease in  volume,  whichever  is  most  suitable  for  the  purpose  in 
hand,  or  any  line  can  be  made  to  have  any  desired  curvature. 

Usually  nozzles  are  made  with  rounded  entrance  like  that 
shown,  but  with  straight  conical  divergence,  as  in  Fig.  457,  as 
this  form  is  easiest  to  make  and  appears  to  be 
about  as  efficient  as  any.     The  stream  lines  of 
the  jet  issuing  from  such  a  nozzle  are  practically 
parallel,  which  is  important  if  the  jet  is  to  act 
Fig.  457.          on  turbine  blades.     For  such  a  nozzle  it  is  only 
necessary  to  compute  the  areas  of  the  neck  and 
discharge  end;  the  entrance   is   then   made   rounded  and  the 
diverging  portion  is  conical,  the  length  depending  on  the  angle 
of  divergence,  which  should  not  be  too  great. 

(f)  With  a  given  nozzle  (ideal  or  approximately  such)   it  is 
found  that,  accompanying  a  lowering  of  the  pressure  against 
which  it  discharges,   the  velocity  of  flow  increases  until  that 
through  the  smallest  section  (or  neck)  reaches  the  critical  value 
(the  pressure  then  being  the  critical  one)  and  that  any  further 
diminution  of  the  pressure  does  not  change  the  velocity  and 
pressure  at  that  section,  nor  does  it  increase  the  weight  of  mate- 
rial flowing  per  second  through  the  nozzle.     Hence,  if  the  ter- 
minal pressure  is  below  .58  plt  the  area  of  the  neck  and  the 
critical  velocity  will   fix  the  amount  of   material   flowing  per 
second.     If  merely  an  orifice  with  rounded  entrance  is  used  the 
discharge  velocity  will  be  the  critical  regardless  of  the  pressure 
against  which  the  jet  issues,  provided  it  is  below  the  critical. 
Alter  the  steam  has  once  passed  the  neck  it  can  further  expand 


CONTINUOUS  FLOW  OF  GASES   THROUGH  ORIFICES        707 

in  a  properly  proportioned  nozzle  and  can  acquire  in  the  diverg- 
ing portion  of  the  nozzle  an  increased  velocity  of  any  desired 
amount  (theoretically),  its  value  merely  being  dependent  on 
the  terminal  pressure. 

332.  Actual  Steam  Nozzles,  (a)  It  will  be  remembered  that 
adiabatic  conditions  are  those  under  which  the  working  sub- 
stance, while  undergoing  a  thermodynamic  change,  neither  re- 
ceives nor  surrenders  heat  as  such. 

It  has  already  been  shown  that  in  the  actual  case  of  flow 
through  nozzles  the  conditions  are  practically  adiabatic,  for  the 
time  of  contact  of  each  particle  with  the  wall  is  infinitesimal 
and,  with  continuous  flow  in  one  direction,  each  portion  of  the 
nozzle  wall  becomes  heated  to  the  temperature  of  the  contiguous 
fluid  and  remains  at  that  temperature;  hence,  neglecting  radia- 
tion and  conduction,  there  is  no  temperature  head  to  produce 
heat  transfer. 

(b)  But  although  the  conditions  are  adiabatic  the  expansion 
process   is  not  necessarily  the  equivalent  of  an  isentropic  one. 
In  fact,  it  is  possible  to  obtain  adiabatic  conditions  of  expansion, 
from  the  higher  pressure  to  the  lower  one,  under  which  none 
of  the  potential  energy  may  be  converted  into  kinetic  energy  of 
a  flowing  stream.     For  example,  if  the  expansion  is  through  a 
porous  plug  with  pressure  drop,  the  velocity  of  flow  is  negli- 
gible and,  as  has  already  been  seen,  the  total  heat  A Q2  per  pound 
of  working  substance  at  the  end  of  the  process  is  equal  to  the 
amount  AQi    it  had  at  the  beginning,  hence  AQi  —  Aft  =  o 
and  AX  =  o.     This  expansion  from  the  higher  to  lower  pressure 
is  along  the  constant  heat  lines  on  the  T^-diagram  and  on 
the  Mollier  Chart  and  is  accompanied  by  increase  in  entropy. 
This  is  a  case  of  resisted  flow,  and  it  can  be  considered  that,  for 
each  slight  pressure  drop,  some  of  the  intrinsic  energy  (65  +  dl) 
of  the  material  is  expended  in  producing  velocity  (to)  of  flow 
through  a  short  length  of  plug,  but  that  the  friction  and  eddy 
currents  reconvert  this  energy  (6X)  of  flow  back  into  heat  (5Q) 
which  is  returned  to  the  fluid  and  brings  its  stock  back  to  the 
original  value.     Throttling  of  steam  is  a  similar  process. 

(c)  Between   the   constant  heat    expansion    (with    AX  =  o) 
and  the  isentropic  one  (with  AX  =  AE)  there  may  be  an  un- 
limited number  of  processes  even  though  under  adiabatic  con- 


7o8 


HEAT-POWER  ENGINEERING 


ditions.  It  is,  of  course,  desirable  to  so  proportion  the  nozzle 
that  it  will  offer  no  resistance  to  expansion,  and  cause  no  eddying, 
also  that  it  will  deliver  the  material  in  parallel  stream  lines.  If 
this  is  effected  the  ideal  conditions  exist  and  the  expansion  is 
equivalent  to  isentropic. 

(d)  With  resisted  flow  the  velocity  of  the  steam  can  be  com- 
puted by  using  Eq.  (505)  and  introducing  the  efficiency  coeffi- 
cient £/,  the  proper  values  of  which  depend  on  the  character, 
extent  and  shape  of  the  guiding  walls,   and  on   the  velocity, 
density  and  quality,  or  superheat,  of  the  steam.      The  values  of 
Ef  range  from  .85  to  .97  in  nozzles  used  in  turbines. 

(e)  The  case  of  resisted  flow  is  shown  on  the  T^-diagram  in 
Fig.  458,  the  heat  Aft  initially  associated  with  each  pound  of 

working  substance  being  shown  by  the 
area  surrounded  by  the  heavy  line.  If 
the  expansion  were  ideal,  from  I  to  2,  the 
heat  Aft,  at  temperature  Tz,  remaining 
in  the  material  after  the  process  would  be 
shown  by  the  area  below  ab2.  However, 
with  resisted  flow  to  the  same  lower  tem- 
perature, TZ,  less  heat  than  the  ideal 
amount  is  abstracted ;  hence  more  heat  (of 
total  amount  Aft')  remains  associated 
with  the  material,  its  amount  being  shown 
The  final  state  point  is  then  at  2';  the 
as  would  be  expected,  and 


L 


Fig.  458- 


by  the  sectioned  area. 

quality  is  #2',  which  is  higher  than 

02  is  the  entropy,  which  is  greater  than  <£i. 

Evidently  the  heat  available  for  accelerating  the  jet  is 
=  (Aft  —  Aft')  which  may  be  used  under  the  radicals  in  Eqs. 
(504)  and  (505)  to  obtain  the  velocity  of  flow  for  this  case;  after 
which  Eqs.  (507)  and  (508)  may  be  used  in  the  same  manner  as 
before.  If  Ef  is  the  efficiency  of  conversion  then  &K'  =  AX"  X 
£/,  where  AJ£  is  the  energy  theoretically  available  in  the  ideal 
case.  In  the  T</>-diagram  there  is  no  one  area  representing  this 
available  energy  AK' ;  it  is  merely  shown  by  the  difference  be- 
tween the  area  surrounded  by  the  heavy  line  and  that  which  is 
hatched. 

(f)  The  Mollier  diagram  for  resisted  flow  is  shown  in  Fig. 
459.  With  ideal  expansion  from  state  point  I  to  2,  the  heat 
per  pound  of  steam  would  change  from  Aft  to  Aft,  the  heat 


|        AK=E/xAK 

•^2          ^2      - 

x* 

^v    o 

^j£ 

i*3S 

AK-AE 

•v^ 
^^ 

/h 

AQt 

A'Qg            A% 
Fig.  459- 

CONTINUOUS  FLOW  OF  GASES   THROUGH  ORIFICES        709 

surrendered  would  be  AX  =  AQi  —  A(>2,  and  the  final  quality 

would   be  #2.     With   resisted  expansion  to  the  same  terminal 

pressure,  £2,  more  heat,  A<22'  (>  A  $2),  remains  in  the  steam  than 

in  the  ideal  case  (as  less  is  abstracted)  and  the  final  state  point 

is  found  at  the  intersection  2'  of  '-  - 

the  constant  heat  line  of  AQ2' 

with  the  pressure  line  p2.     The 

final  quality  x*   (  >  x%)  and  en- 

tropy 02  (  >  0i)  are  determined 

by  I  the    quality    and    entropy 

lines  passing  through  point  2'  '. 

The  heat  converted  into  kinetic  energy  is  AX'  =  AQi  —  A(V 

(<  AX),  and  as  before  AX'  =  AXX  Ef.     This  value  of  AX' 

is  then  used  in  the  manner  described  at  the  end  of  the  preceding 

paragraph.* 

(g)  The  values  of  AX'  and  X2'  may  also  be  found  by  compu- 
tation. First  AX  for  the  ideal  case  is  determined  by  the  methods 
given  in  Sect.  94  for  the  Clausius  cycle.  Then  with  Ef  assumed, 
AX'  is  AX  X  Ef,  and  the  heat  remaining  per  pound  of  steam  at 
the  end  of  the  process  is 

Aft'  =  AQi  -  (AX  X  Ef)  .....     (509) 

Since  A^'  =  x^r*  +  £2,  it  follows  that 

x2'  =  (AQ2'  -  32)  -5-  r,,    .....     (510) 

where  g2  and  rz  correspond  to  the  known  terminal  pressure. 
The  final  entropy  is  then 


in  which  all  quantities  on  the  right-hand  side  of  the  equation 
are  either  known  or  can  be  obtained  from  the  steam  table. 

(h)  The  purpose  of  the  foregoing  discussion  is  merely  to  pre- 
sent the  fundamental  thermodynamic  theory  underlying  the 
flow  of  steam  at  high  velocities  through  nozzles  and  orifices. 
A  detailed  discussion  of  the  subject  cannot  be  attempted  in 
this  book  and  for  further  study  the  student  is  referred  to  any  of 
the  numerous  textbooks  on  Steam  Turbines. 

333.   Empirical  Formulas  for  the  Flow  of  Steam  through  Ori- 
fices.    (a)   It  is  sometimes  convenient  to  have  simple  empirical 
formulas  for  quickly  determining  the  approximate  velocity  of 
*  The  Ellenwood  Chart  can  be  used  similarly. 


7IO  HEAT-POWER  ENGINEERING 

discharge  from  a  given  orifice,  or  for  obtaining  the  area  of  orifice 
required  for  discharging  a  given  weight  of  steam  per  second, 
when  the  discharge  pressure  is  below  .58  pi.  The  following  two 
formulas  apply  to  such  cases  when  the  orifice  has  a  properly 
rounded  entrance,  and  they  also  apply  to  the  neck  of  a  diverging 
nozzle. 

(b)  Napier's  experimentally  determined  rule  gives  the  pounds 
of  steam,  initially  dry,  flowing  per  second  from  an  orifice  to  be 

w  =  (p  X  a)  +  70, (512) 

or  the  area,  in  square  inches,  is 

a  =  70  w  -5-  p, (513) 

where  p  is  the  absolute  pressure  in  pounds  per  square  inch. 

(c)  A  slightly  more  accurate  but  less  convenient  formula  is 
that  due  to  Grashof.     For  steam  initially  dry  it  is 

»~    <£p •     •     (5H) 

from  which 

60  w  ,       ^ 

a=~p,    .     .    f,  .  ,.    ,    .     (515) 

the  notation  being  the  same  as  in  (b). 

334.  Flow  of  Steam  through  Pipes,  (a)  The  law  for  the 
frictional  resistance  accompanying  the  flow  of  steam  through 
pipes  resembles  closely  that  expressed  in  Eq.  (409)  which  shows 
that  the  resistance  is  directly  proportional  to  the  length  of  pipe, 
perimeter  of  cross  section,  character  of  surface  and  square  of 
the  velocity,  and  inversely  to  the  area  of  section.  To  overcome 
this  resistance  and  the  inertia  of  the  fluid  there  must  be  a  drop 
in  pressure  from  the  entrance  to  the  pipe  to  the  discharge  end. 
As  the  resistance  varies  with  the  square  of  the  velocity,  the 
pressure  drop  increases  very  rapidly  as  the  velocity  is  made 
greater.  Hence  in  practice  the  velocities  used  in  pipes  are  very 
low,  as  compared  with  those  in  nozzles  where  the  short  length 
makes  the  loss  by  resistance  very  small  even  though  great 
velocities  are  used. 

(b)  While  the  same  treatment  that  is  used  for  nozzles  might 
be  applied  to  pipes,  the  pressure  drops  and  energy  expended  in 
producing  the  flow  are  so  small  that  it  is  convenient  to  use 


CONTINUOUS  FLOW  OF  GASES   THROUGH  ORIFICES        711 

another  method  which  disregards  altogether  the  quantity  of 
energy  expended  and  only  considers  the  pressure  drop  that  is 
involved.  This  method  makes  use  of  Eq.  (410),  which  for  round 
pipes  becomes 


If  W  pounds  of  steam  flow  per  minute,  the  volume  flowing 
per  second  is  the  product  of  the  weight  per  second  (W/6o)  and 
the  specific  volume  V,  which  is  the  reciprocal  of  the  density  5. 
If  the  diameter  of  the  pipe  in  inches  is  d,  the  velocity  of  flow 
is  obviously  v  =  (144  WV)  -f-  (60  wd2/^).  Substituting  this  in 
Eq.  (516)  and  solving  gives  the  pipe  diameter  in  inches, 

*-<\/W. (5I7) 

where 

W  =  pounds  of  steam  flowing  per  minute, 
L  =  length  of  pipe  in  feet, 
V  =  specific  volume  of  the  steam, 

AP  =  pressure  drop  throughout  the  length  of  pipe,  and 
c  =  a  constant  whose  value  is  ordinarily  .2,  but  this  may  be 
decreased  slightly  with  very  large  pipes,  as  /  seems 
to  diminish  somewhat  as  the  diameter  is  increased. 

The  longer  the  pipe  is  made  and  the  smaller  the  pressure  drop 
allowed,  the  larger  will  be  the  diameter.  But  a  larger  diameter 
means  increased  first  cost  and  greater  heat  loss  by  "radiation." 
Hence  the  diameter  selected  should  be  a  compromise  based  on 
all  these  considerations. 

(c)  If  the  allowable  velocity  (vm)  of  flow  in  feet  per  minute  and 
the  total  volume  (Vm)  of  steam  to  be  transmitted  in  the  same 
length  of  time  are  known,  then  the  area  of  pipe  in  square  inches 
immediately  follows  from 

P-XM4.  .     (5I8) 


For  steady  flow  in  high-pressure  steam  mains  vm  is  generally 
about  6000  feet  per  minute  for  saturated  steam,  while  with 
superheated  steam,  with  the  larger  sizes  of  pipe,  and  with  those 
of  short  length,  somewhat  higher  values  prevail. 

Exhaust  pipes  from  turbines  to  condensers  have  velocities  as 
great  as  24,000  feet  per  minute  and  even  higher  in  some  cases. 


712  HEAT-POWER  ENGINEERING 

(d)  Steam  engines  receive  and  exhaust  the  steam  intermit- 
tently and  the  area  of  pipes  is  commonly  obtained  by  using  Eq. 
(274)  with  v  =  6000  to  7000  feet  per  minute  for  high-pressure 
live  steam  pipes  and  v  =  3500  to  5000  for  exhaust  pipes. 

335.  Application  of  Steam  Nozzles.  The  largest  field  of 
application  for  steam  nozzles  is  in  steam  turbines,  which  have 
already  been  considered.  Another  wide  field  is  in  Steam  In- 
I  jectors,  used  for  delivering  feed  water  to  boilers,  and  for  similar 
purposes.  This  piece  of  apparatus,  in  its  simplest  form,  is 
shown  diagrammatically  in  Fig.  460.  Briefly  it  operates  as 


ivery  Check 

YaLve 


Fig.  460. 

follows:  Steam,  admitted  through  valve  V,  acquires  high  veloc- 
ity in  passing  through  the  nozzle,  is  condensed  by  the  water  in 
the  combining  tube  and  drives  the  water  through  the  delivery 
tube  and  check  valve  into  the  pipe  leading  to  the  boiler.  Thus, 
the  flow  through  the  nozzle  is  similar  to  that  in  the  ordinary 
case,  and  the  kinetic  energy  of  the  jet  is  used  for  injecting  the 
water  into  the  boiler  against  the  pressure  existing  there. 

Steam  nozzles  are  also  used  for  inducing  draft  in  the  stacks 
of  locomotives  and  traction  engines,  the  exhaust  steam  being 
used  for  the  purpose,  which  results  in  a  slight  increase  in  the 
back  pressure  on  the  engine. 

336.  Perfect  Flow  of  Ideal  Gas.  (a)  In  order  to  apply  the 
equations  of  Sect.  329  to  the  flow  of  gases,  it  is  first  necessary  to 
determine  the  intrinsic  energy,  AS  (+  A/  =  o),  per  pound  of 
material.  It  was  shown  in  Sect.  30  that  during  isen tropic  ex- 
pansion the  work  performed  per  pound  of  gas  is,  from  Eq.  (5oa), 


778  AE  =  -     *  _       ^  =  778  AS, 

which  is  done  at  the  expense  of  the  intrinsic  energy.     If  it  is 
assumed  that  this  same  law  prevails  with  expansion  continued 


CONTINUOUS  FLOW  OF  GASES  THROUGH  ORIFICES        713 

to  P2  =  o,  then  all  the  intrinsic  energy  is  converted  into  external 
work.  Thus,  upon  this  assumption,  the  total  intrinsic  energy  per 
pound  of  material  is,  in  general, 

PV 
A5  =  778-(^T)-      '    '    '    •;     (519) 

Then  from  Eq.  (496)  the  potential  energy  per  pound  is  (since 
A/  =  o), 


.     .     .     (520) 

This  is  measured  above  a  datum  of  absolute  zero  of  pressure? 
and  temperatures,  but  as  all  problems  in  flow  involve  only  differ- 
ences in  energies  this  fact  need  cause  no  inconvenience. 

(b)  Substituting  in  Eq.  (501),  for  points  i  and  2  in  Fig.  452, 
the  values  of  Po\  and  P02  in  terms  of  Eq.  (520),  gives 


(S-S=^i(PiVi-p2V2)-  •  - (52i) 

If  vi  =  o,  then  the  final  velocity  is 


P2V2),     .     .     .     (522) 

in  which  c  is  a  discharge  coefficient  with  value  equal  to  unity  in 
the  ideal  case.  Substituting  this  value  of  v  in  Eq.  (508),  with 
x  =  I ,  the  weight  discharged  per  second  is 


(523) 


All  quantities  on  the  right-hand  side  of  this  equation  are  gen- 
erally known  at  the  outset  except  V2.  This  latter  must  be  de- 
termined before  a  solution  can  be  effected.  With  isentropic 
expansion  its  value  is  found  from  the  relation  P2V2Y  =  PiVi7  to 

be  V2  = 

(c)  Substituting  the  value  of  V2  in  Eqs.  (522)  and  (523),  and 
simplifying  gives 


HEAT-POWER  ENGINEERING 


,  aXC/^2V     /„         T      p  y  1  T       /^2\         i          xv 

and   w=7^vl(pj  V  2«^TPlVT  ~  W     I" 

From  which  the  area  needed  to  discharge  a  given  weight  is 


a  = 


As  sections  I  and  2,  in  Fig.  452,  may  be  located  at  any  points 
along  the  conduit,  or  nozzle,  it  is  possible  to  use  these  formulas 
to  analyze  the  changes  occuring  between  any  two  sections,  or 
over  the  whole  length  of  passage. 

(d)  If  a  curve  is  plotted  to  show  how  v,  in  Eq.  (524),  varies  as 
(P2/Pi)  is  decreased,  it  will  be  found  that,  as  in  the  case  of  steam, 
the  nozzle  will  have  a  neck  if  P2  is  low  enough,  and  that  the 
velocity  through  this  neck  becomes  a  maximum  when  a  certain 
value  .of  Pz/Pi  is  reached.  By  differentiating  Eq.  (524)  and 
making  dv/d(P*/Pi)  =  o,  this  maximum  velocity  is  found  to 
occur  when  y 

1"          -     -     •     •     (5*7) 


the  value  of  which  is  .527  when  7  =  1.41.  Thus  in  this  case 
the  maximum  or  Critical  Velocity  at  the  neck  occurs  when  P2 
has  been  reduced  to  a  critical,  pressure  of  .527  PI. 

This  phenomenon  has  been  repeatedly  verified  experimentally. 
It  is  found,  as  with  steam,  (i)  that  at  the  neck  the  critical  pres- 
sure is,  in  the  ideal  case,  always  about  .527  PI,  provided  the 
pressure  beyond  the  neck  is  equal  to  or  less  than  this  amount; 
(2)  that  lowering  the  discharge  pressure  below  the  critical  pres- 
sure changes  neither  the  pressure  nor  the  velocity  at  the  neck; 
and  (3)  that  the  neck  velocity  and  initial  PV-condition  deter- 
mine the  maximum  amount  of  working  substance  which  can 
flow  through  a  given  orifice  or  nozzle.  Equations  (524)  and 
(525)  will  therefore  give  the  maximum  ideal  velocity  and  weight 
of  discharge  through  a  neck  of  given  cross  section  if  .527  is 
substituted  for  (P2/Pi)  ;  and  Eq.  (526)  can  be  used  to  compute 
the  neck  area  required  for  discharging  a  given  weight  of  gas,  if 
similar  substitution  is  made. 

(e)  In  Sect.  87  (f)  it  was  shown  that  when  steam  expands  isen- 
tropically,  for  an  initial  quality  greater  than  70  per  cent,  the 


CONTINUOUS  FLOW   OF  GASES   THROUGH   ORIFICES        715 

process  is  represented  quite  accurately  by  the  equation  for  the 
isentropic  expansion  of  gas,  with  an  exponent  n  equal  to  (1.035  + 
o.i  x),  in  which  x  is  the  quality  fraction.  Thus  it  follows  that 
Eqs.  (524)  to  (526)  are  applicable  to  the  flow  of  steam  through 
orifices  if  this  value  of  n  is  substituted  for  y. 

(f)  When  the  quality  is  unity,  n  =  1.135,  and  if  this  value  is 
introduced  for  7  in  Eq.  (527)  it  is  found  that  the  maximum  flow 
of  dry  saturated  steam  through  an  orifice  occurs  when  P^/P\  =  .58 
(about) .  This  is  the  value  found  by  the  method  given  in  Sect. 
331  and  its  correctness  has  been  verified  experimentally.* 

337.  Imperfect  Flow  of  Gases,  (a)  The  actual  velocity  and 
weight  of  discharge  from  an  orifice,  or  nozzle,  are  of  course  less 
than  the  theoretical.  There  are  a  number  of 
reasons  for  this :  —  The  real  gases  differ  some- 
what from  the  ideal;  friction  prevents  some  of 
the  available  heat  energy  from  becoming  con- 
verted into  kinetic  energy  of  flow ;  some  of  the 
kinetic  energy  is  wasted  in  producing  eddy 
currents;  heat  energy  is  lost  by  radiation  and 
conduction;  and,  if  an  orifice  has  improperly 
shaped  walls,  the  cross  section  of  the  jet  at  its 
neck  may  be  less  than  that  of  the  orifice,  as 
indicated  in  Fig.  461.  To  make  allowance  for 
the  contraction  of  area,  and  for  the  various 
losses,  the  discharge  coefficient  c  is  introduced  in  Eqs.  (524)  to 
(526).  The  value  of  this  coefficient  varies  from  .56  for  certain 
sharp-edged  circular  orifices  to  nearly  unity  in  the  case  of  a 
mouth  with  properly  rounded  entrance. 

*  For  superheated  steam  y  is  about  1.3  and  P2/Pi  =  .546. 


Fig.  461. 


CHAPTER  XLI. 
COMPRESSED  AIR. 

338.  Definitions,     (a)  Air  compressors  in  the  broadest  sense 
are  all  devices  used  for  raising  the  pressure  of  air,  but  technically 
the  term  is  generally  applied   only  to  apparatus  which  raises 
the  pressure  to  a  comparatively  high  value,  say  some  value 
between  25  and  several  hundred  pounds  per  square  inch.     In 
extreme  cases  the  pressure  is   increased   to   several   thousand 
pounds  per  square  inch. 

(b)  Other  devices,  such  as  fans  and  rotary  blowers,  are  really 
compressors  but  are  seldom  spoken  of  as  such,  principally  be- 
cause the  pressures  attained  are  so  small  that  the  principal  func- 
tion may  be  considered  to  be  the  propelling  of  air  rather  than 
its  compression. 

(c)  The  term  Blowing  Engines,  or  Blowers,  is  used  to  desig- 
nate certain   apparatus   used  for  compressing  air   to  pressures 
between  about  10  pounds  and  30  pounds  above  atmospheric  for 
use  in  blowing  cupolas  and  blast  furnaces.     These  are  properly 
air  compressors  but  because  of  the  low  pressures  many  of  the 
difficulties  attending  compression  to  higher  pressures  are  not 
met  in  their  design. 

339.  Elementary  Air  Compressor,     (a)  The  essential  parts  of 
an  ideal  air  compressor  of  the  simplest  kind  are  shown  semi- 

.  compressed  Air  Discharge  diagrammatically  in  Fig.  462,  A  being 

the  spring-closed  admission  or  inlet 
valve,  which  opens  inwardly,  and  B 
the  spring-closed  discharge  valve, 
opening  outwardly.  In  the  simplest 
case  there  will  be  no  clearance,  the 
piston  just  touching  the  cylinder  head 
Fig.  462.  a^  one  end  of  its  stroke. 

(b)  Imagine  the  piston  in  contact 

with  the  cylinder  head  in  the  ideal  case.     By  the  application  of 
an  external  force  to  the  piston  rod  the  piston  can  be  drawn  to  the 

716 


COMPRESSED  AIR 

right,  and  air  will  then  enter  the  cylinder  through  valve  A  at 
atmospheric  pressure  Plt  according  to  the  horizontal  line  ab  in 
Fig.  463. 

(c)  When  the  cylinder  has  been  thus  filled  with  air,  the  piston 
may  be  driven  back  to  the  left.     As  soon  as  such  motion  starts 
the  valve  A  will  be  closed  by  the  light  spring  shown,  and  the 
air  entrapped  in  the  cylinder  will  then  be       p  dPz 
compressed    according    to   some   law,   as 

shown  by  be,  the  final  volume  being  dc. 

There  are  two  limiting  conditions  which 
may  be  imagined  as  existing  during  com-         volume 
pression:  Fig.  463. 

(1)  No  heat  may  be  removed  from  the 

air  during  the  process,  in  which  case  the  compression  will  be 
adiabatic  (with  rise  in  temperature) ;  and 

(2)  All  the  heat  generated  during  compression  may  be  re- 
moved, in  which  case  the  compression  will  be  isothermal. 

All  actual  cases  generally  fall  between  these  limits  as  will  be 
seen  later. 

(d)  Imagine  the  discharge  pipe  to  be  connected  to  a  closed 
vessel,  "a  receiver."  in  which  is  maintained  a  constant  pressure, 
P2,  equal  toPc.     Assume  further  that  the  action  of  this  pressure 
upon  the  valve  B,  plus  the  action  of  the  spring  is  such  that  a 
uniform  pressure  of  Pc  pounds  per  unit  area  of  valve  face  will 
just  balance  it. 

Then  when  the  piston  has  compressed  the  air  to  the  pressure 
Pc  the  discharge  valve  will  open  (at  c)  and  the  continued  motion 
of  the  piston  will  "discharge"  the  air  at  constant  pressure,  P2. 
as  shown  by  the  line  cd.  Thus,  the  piston  will  end  its  stroke  in 
contact  with  the  cylinder  head,  having  discharged  at  pressure 
PI  all  the  air  received  at  pressure  P\. 

340.  Work  Done  in  Compressor,  (a)  In  Fig.  463,  area  abge 
shows  the  work  done  upon  the  piston  during  the  outstroke  by  the 
entering  air,  gbcde  represents  that  done  by  the  piston  on  the  air 
during  the  instroke,  and  the  net  work  is  shown  by  area  abed. 

Thus  the  area  of  the  "compressor  diagram,"  or  card,  meas- 
ures the  net  work  done  by  the  piston  upon  the  air,  just  as  the 
area  of  an  engine  diagram  measures  that  done  upon  the  piston 
by  the  working  substance. 


7l8  HEAT-POWER  ENGINEERING 

The  Compression  Line. 

(b)  In  Fig.  464  are  given  two  superposed  diagrams,  abed  and 
abc'd,  both  from  the  same  ideal  compressor  which  is  to  compress 
to  a  pressure  P2  =  Pd  the  amount  of  air  which  originally  oc- 
cupied the  volume  Vb  cubic  feet  when  at  atmospheric  pressure. 
The  compression  line  be  is  an  isothermal  and 
the  line  be'  is  an  adiabatic. 

It  is  evident  from  the  figure  that  the  dia- 
gram containing  an  adiabatic  compression 
line  encloses  more  area  than  that  having 
isothermal  compression,  and  hence  more  en- 


Fig.  464.  ergy  from  some  outside  source  will  be  re- 

quired per  cycle.  Obviously,  the  isothermal 
compression  is  the  more  desirable,  other  things  being  equal,  the 
work  saved  over  that  with  adiabatic  compression  being  shown 
on  the  diagram  by  the  area  cbc'  .  The  higher  the  compression 
pressure  the  greater  is  the  ratio  of  the  work  done  with  adiabatic 
compression  to  that  with  isothermal. 

(c)  With  isothermal  compression  the  temperature  of  the  air 
at  c  and  b  is,  of  course,  the  same,  but  during  adiabatic  compres- 
sion the  temperature  rises  according  to  Eq.  (51),  the  final  tem- 
perature being 

W.^1      ....     .     (528) 


y 
in  which  r  =  ratio  of  compression  =  ^  • 

If  the  air  with  pressure  Pcf  and  volume  Vc'  is  cooled  at  con- 
stant pressure  it  will  attain  a  volume  Vc  when  the  initial  tem- 
perature Tb  is  reached.  This  is  approximately  what  happens 
in  most  real  cases,  for  after  the  cooling  has  occurred  the  air  is 
in  the  same  condition  as  though  it  had  been  compressed  iso- 
thermally.  It  is  therefore  advisable  to  strive  for  isothermal 
compression  if  this  can  be  attained,  or  approached,  without 
entailing  greater  outlay  than  the  cost  of  the  work  area  cbc'  . 

Formulas  for  Work. 

(d)  From  the  diagrams  of  Fig.  463  and  Fig.  464,  the  work 
done  by  the  piston  per  cycle  with  isothermal  compression  and  no 
clearance  is  evidently 


COMPRESSED  AIR 

Work  =  work  on  be  +  work  on  cd  —  work  on  ab,  ft.-lbs. 

Vh 
=  Pc  Vc  loge  YC  +  pc  Vc  -  Pb  Vb,  foot-pounds.  .     .  (529) 

With  adiabatic  compression  the  work  is  (Fig.  464) 
Work  =  work  on  be'  +  work  on  c'd  —  work  on  ab 

=  ?e'Vj~f'V*  +  P<VC  ~  ft  V»,  foot-pounds.  .     (530) 

With  any  compression  curve  expressible  by  the  equation  PVn 
=  constant,  the  work  per  cycle  is 

Work  =  work  on  be"  -f  work  on  c"d  —  work  on  ab 


+  Pc"Ve"-P>Vb,  foot-pounds.      (531) 


341-  The  Effect  of  Clearance,  (a)  No  real  compressor  can 
be  operated  with  the  zero  clearance  assumed  for  the  preceding 
elementary  consideration.  There  must  always  be  a  certain 
amount  of  mechanical  clearance  between  cylinder  head  and 
piston  to  insure  safe  operation  and  there  are  always  passages 
or  ports  of  some  sort  between  the  valve  faces  and  the  inside  of 
the  cylinder. 

(b)  In  Fig.  465  is  given  an  ideal  compressor  diagram  for  a 
machine  with  clearance  volume  Vci  =  Vd-  At  the  end  of  the 
discharge,  that  is,  after  the  completion 
of  the  constant-pressure  process  cd,  the 
clearance  contains  Vci  =  Vd  cubic  feet 
of  air  at  a  pressure  P2  =  Pd-  When 
the  piston  starts  on  the  outstroke  the 
inlet  valve  will  be  held  closed  by  this 
pressure  until  the  piston  has  moved 
out  far  enough  to  allow  the  clearance 

air  to  expand  to  atmospheric  pressure  according  to  some  such 
process  as  da.  When  a  is  reached  the  inlet  valve  will  open  and 
during  the  remainder  of  the  stroke  external  air  will  enter  the  cyl- 
inder, as  in  the  previous  case.  Though  the  stroke  of  the  piston 
is  such  as  to  make  available  the  volume  Vb  —  Va'  =  F.,  the 
amount  of  air  actually  entering  the  cylinder  will  be  Vb  —  Va  =  Ve» 
and  only  a  fraction  of  the  stroke,  equal  to  V»/  V,,  has  therefore 


Volume 


720  HEAT-POWER  ENGINEERING 

been  usefully  employed.     Thus  the  volumetric  efficiency  of  this 
ideal  simple  compressor  must  be 


(532) 


Obviously  the  piston  displacement  of  the  compressor  with 
clearance  must  be  to  that  of  the  compressor  without  clearance 
in  the  proportion  Vs/  Vea  if  both  are  to  compress  the  same  quan- 
tity of  air  per  cycle,  therefore  the  existence  of  clearance  makes 
necessary  a  larger  compressor  to  handle  a  given  volume  of  air. 

Effect  of  Clearance  upon  Work. 

(c)  In  the  ideal  case  it  may  be  assumed  that  the  expansion 
of  the  clearance  air  along  da  takes  place  according  to  the  same 
law  as  the  compression  of  the  mixture  of  clearance  air  and 
cylinder  charge  along  the  curve  be.  Then,  if  the  clearance  air 
be  imagined  to  be  separated  by  a  flexible  diaphragm  from  the 
fresh  charge,  and  to  be  used  over  and  over  again,  it  is  evident 
that  it  will  deliver  just  as  much  work  when  expanding  from  d 
to  a  as  will  subsequently  be  consumed  in  compressing  it  from 
a  to  d.  Then  the  net  work  necessary  per  cycle  will  be  only  that 
required  to  compress  the  volume  Ve8  of  cylinder  charge  from 
pressure  PI  to  PZ  and  discharge  it  at  P^.  Therefore,  in  the  ideal 
case  the  presence  of  clearance  does  not  alter  the  net  work  which 
must  be  done  per  cycle. 

It  should,  however,  be  noted  that  since  the  compressor  with 
clearance  will  be  larger  than  that  without,  the  friction  losses 
and  cost  of  the  machine  will  be  greater  in  the  real  case. 

342.  Real  Single  Stage  Compressor  Diagram,  (a)  The  real 
compressor  differs  from  the  ideal  in  many  respects,  chiefly  be- 
cause the  cylinder  and  piston  cannot  be  made  of  heat-resisting 
materials,  because  the  valves  cannot  be  made  to  operate  per- 
fectly, and  because  of  the  inertia  of  the  air  being  handled. 

A  diagram  obtained  from  a  real  compressor  is  shown  in  Fig. 
466,  superposed  upon  an  ideal  one  for  the  same  machine,  the 
pressure  of  air  being  supposed  to  be  raised  from  atmospheric 
(Pi)  to  a  receiver  pressure  equal  to  P2. 

(b)  The  ideal  card  is  drawn  for  isothermal  compression  of  the 
clearance  air  and  charge  and  with  isothermal  expansion  of  the 


COMPRESSED  AIR  721 

clearance  air.  In  the  real  case  it  is  never  possible  to  obtain 
isothermal  compression  with  a  reciprocating  air  compressor; 
instead,  the  compression  line  falls  between  the  adiabatic  and  the 
isothermal  and  is  expressible  by  the  equation  PVn  =  constant, 
with  values  of  n  varying  from  about  1.2  in  extremely  favorable 
cases  to  about  1.3  under  rather  unfavorable  conditions.  To 
obtain  such  a  curve  it  is  necessary  to  cool  the  air  during  com- 
pression, by  the  methods  which  will  be 
considered  later.  For  present  purposes  PS  ' 
it  is  merely  necessary  to  note  that  the 
air,  and  therefore  the  cylinder  walls, 
will  become  heated  during  compression. 

(c)  During  expansion  of  the  clearance    J 
air,  this  material  will,  in  general,  be  in 
contact  with  walls  which  are  at  a  higher 

temperature,  hence  it  will  receive  heat  during  the  process. 
Ordinarily  the  real  expansion  line  for  this  air  lies  between 
an  adiabatic  and  an  isothermal,  but  in  the  average  case  it 
approaches  more  nearly  to  the  latter.  The  real  expansion  line 
may  then  be  assumed  to  have  a  shape  and  position  similar  to 
daf  in  the  figure. 

(d)  In  the  ideal  case  the  admission  valve  would  open  as  soon 
as  the  clearance  pressure  has  decreased  to  atmospheric,  but 
actually  the  pressure  must  drop  somewhat  lower  to  give  an 
unbalanced  pressure  great  enough  to  open  the  valve  against  its 
spring,  its  friction  and  inertia,  and  also  to  overcome  the  inertia 
of  the  air  and  the  resistance  to  flow  through  the  more  or  less 
restricted  areas  available. 

After  the  valve  is  open  and  the  air  is  in  motion  there  are  gen- 
erally several  oscillations  of  the  valve  and  the  air  column,  as 
indicated  by  the  wavy  suction  line,  after  which  the  pressure  set- 
tles down  to  an  average  value  sufficiently  below  the  atmos- 
pheric pressure  to  cause  the  inflow.  The  oscillation  of  the  valve 
is  known  as  "fluttering." 

(e)  From  the  fact  that  the  same  machine  has  been  assumed 
in  both  cases  it  is  evident  that  the  actual  volume  of  air  in  the 
cylinder  at  the  end  of  the  suction  stroke  must  be  the  same  in 
each  case.     In  the  real  case,  however,  the  air  has  a  lower  pres- 
sure than  it  has  in  the  ideal,  and,  in  general,  its  temperature  will 
also  have  been  raised  by  the  heated  walls  which  are  uncovered 


722  HEAT-POWER  ENGINEERING 

by  the  piston,  thus  the  actual  weight  present  will  be  less  than 
the  ideal.  This  effect  will  be  considered  more  in  detail  in  a 
later  section. 

(f)  Starting  at  the  point  6',  instead  of  6,  the  air  in  the  real 
case  will  be  compressed  according  to  some  law  intermediate  be- 
tween the  adiabatic  and  isothermal  and  therefore  steeper  than 
the  ideal,  as  shown  by  b'c'  in  the  figure. 

(g)  The  discharge  valve  does  not  open   until   the  pressure 
attained  is  slightly  above  that  in  the  receiver  and  it  behaves 
much  like  the  suction  valve  and  for  similar  reasons.     The  dis- 
charge line  actually  obtained  will  then  generally  look  something 
like  c'd'  instead  of  cd. 

(h)  The  discharge  valve  will  obviously  not  close  suddenly  at 
the  end  of  the  stroke,  consequently  the  corner  at  d'  may  be  more 
or  less  rounded,  the  exact  point  at  which  expansion  of  the  clear- 
ance air  starts  being  rather  difficult  to  determine. 

(i)  The  net  result  of  the  operation  of  the  real  compressor  has 
been  to  compress  a  smaller  weight  of  air  than  that  handled  by  the 
ideal  machine  and  to  require  the  expenditure  of  work  in  excess 
of  the  ideal,  as  shown  by  the  greater  area  enclosed. 

343.  Volumetric  Efficiency,  (a)  The  volumetric  efficiency  of 
the  ideal  compressor  was  shown  to  be  Ve,/V8,  the  symbols  refer- 
ring to  Fig.  465.  In  a  real  case  the  determination  of  the  volu- 
metric efficiency  is  not  as  simple  as  this  and  it  is  often  very 
difficult,  if  not  impossible,  to  obtain  its  true  value.  As  a  result 
several  incorrect  volumetric  efficiencies  easily  obtainable  from 
a  card  are  often  used  in  practice. 

True  Volumetric  Efficiency. 

(b)  An  ideal  compressor  should  receive  a  charge  equal  to  its 
total  piston  displacement  and  this  charge  should  have  atmos- 
pheric temperature  and  pressure.  The  weight  of  this  charge 
would  then  be 

w      V' 

~~v: 

in  which     V»  =  piston  displacement  in  cubic  feet,  and 

Va  =  volume   occupied  by  one  pound  of  air  under 
atmospheric  conditions. 


.  COMPRESSED  AIR  723 

If,  in  any  case,  the  weight  of  air  actually  received  per  suction 
stroke  is  W ,  the  true  volumetric  efficiency  is 


•     •    >  >  •       (533) 

V.W 

-IT —       .     .     .     .     .     (533a) 


(c)  To  evaluate  this  efficiency  it  is  necessary  to  determine  W 
and  this  is   generally   very  difficult  to  accomplish  in   any  real 
case.     It  can  be  done  by  measuring  the  air  actually  received  or 
discharged  in  a  given  time  and  then  dividing  this  by  the  number 
of  suction  strokes  occurring  during  that  time  period;  but  the 
accurate   measurement  of   large   quantities  of  air  is  generally 
difficult  and  therefore  the  true  volumetric  efficiency  is  seldom 
determined. 

Atmospheric  Volumetric  Efficiency. 

(d)  In  Fig.  467  is  given  in  exaggerated  form  a  real  compressor 
diagram  with  the  atmospheric  line  added.     If  there  is  no  change 
of  temperature  of  the  working  substance  during  charging  and 
if  the  expansion  of  the  clearance  air 

and  the  compression   of    the   mixture 
both  follow  the  same  law,  the  distance    | 
ef  must  measure  the  volume  occupied 
by  the   clearance   air,   and  fg  is  that 
occupied  by  the  charge  when  compres- 


sion has  progressed  up  to  the  point  g.  Fte  "467 

If  it  be  further  assumed  that  the 

drop  of  temperature  from  /  to  a'  and  the  rise  from  V  to  g  are 
negligible,  it  may  be  said  that  the  distance  fg  is  a  measure  of  the 
volume  occupied  by  the  charge  when  at  atmospheric  pressure 
and  temperature.  Then  the  volumetric  efficiency,  on  an  atmos- 
pheric line  basis,  would  be 

F£/a==  ^stance  /g.        .     /   .     .     .     (534) 

(e)  This  formula  will  probably  give  an  incorrect  result  in  all 
cases,  because  none  of  the  assumptions  made  in  its  derivation 
are  strictly  correct.  However,  the  error  is  generally  not  great 
in  magnitude,  hence,  because  of  the  simplicity  of  the  method, 
the  formula  is  commonly  used  in  practice. 


724  HEAT-POWER  ENGINEERING 

Suction  Line  Volumetric  Efficiency. 

(f)  A  still  less  perfect  formula  is  often  used  for  determining 
the  volumetric  efficiency  from  the  diagram.     The  point  a',  Fig. 
467,  is  first  determined  by  continuing  the  straight  part  of  the  suc- 
tion line  backward  to  intersect  the  expansion  line.     The  distance 
a'b'  is  then  taken  as  the  volume  occupied  by  the  charge  and 
the  distance  from  a'  to  the  zero  of  volumes  is  taken  as  that  of 
the  clearance  air  at  the  same  pressure  and  temperature.     Neg- 
lecting the  fact  that  the  suction  line  is  below  atmospheric  pres- 
sure the  volumetric  efficiency  on  a  suction  line  basis  is  defined  as 

T7T_       distance  a'b'  ,       . 

VEf8  = pr (535) 

(g)  This  method  contains  practically  all  the  errors  of  that 
previously  given  with  the  added  disadvantage  of  neglecting  the 
difference  of  pressure,   consequently  it  should  never  be  used 
when  the  position  of  the  atmospheric  line  can  be  obtained. 

344.  Cooling  During  Compression,  (a)  It  has  been  shown 
in  preceding  sections  that  isothermal  compression  should,  in 
general,  prove  more  economical  than  adiabatic.  It  is  practically 
impossible  to  attain  isothermal  compression  in  any  real  machine, 
but  it  can  be  more  or  less  closely  approximated  and  generally 
without  involving  excessive  cost. 

(b)  If  a  compressor  fitted  with  a  metal  cylinder  is  operated 
very  slowly,  i.e.,  one  or  two  cycles  per  minute,  the  heat  gener- 
ated by  compression  will  be  conducted  away  by  the  cylinder 
metal  almost  as  fast  as  generated   and  in  such   case  the  com- 
pression could  be  made  to  approach  an  isothermal  process  as 
closely  as  desired,  but  it  would  involve  the  use  of  enormously 
large  machines  because  of  the  slow  operation.     Some  method 
must  therefore  be  used  which  permits  of  operation  at  the  highest 
desirable  speeds. 

(c)  If  any  form  of  external  cooling,  such  as  radiation  consid- 
ered above,  is  to  be  used  the  proportions  of  the  cylinder  are 
important.     That  cylinder  which  exposes  the  greatest  surface 
to  the  external  cooling  agent,  per  cubic  foot  enclosed,  will  be 
the  best  so  far  as  cooling  is  concerned.     This  would  indicate 
the  use  of  cylinders  of  small  diameter  and  great  length,  i.e., 
"long  stroke  compressors,"  but  such  machines  are  always  more 


COMPRESSED  AIR 


725 


expensive  than  short  stroke  mechanisms,  consequently  a  com- 
mercial limit  is  set  to  cylinder  proportions  adopted. 

(d)  In  practice  a  few  types  of  compressors  are  cooled  by  radia- 
tion to  the  atmosphere,  as,  for  instance,  those  used  on  locomotives 
for  operating  the  air  brakes.  They  are  all  comparatively  small, 
are  generally  operated  in  strong  currents  of  air  and  are  at  best 
rather  inefficient.  It  is  doubtful  if  the  compression  is  appre- 
ciably better  than  adiabatic,  the  radiation  serving  simply  to 
prevent  overheating  of  the  entire  mechanism  by  storage  of  heat 
from  cycle  to  cycle. 

1  (e)  Most  commercial  machines  are  water  cooled.  There  are 
three  distinct  methods  of  applying  cooling  water,  two  or  more 
of  which  may  be,  and  generally  are,  used  on  the  same  machine. 
They  are: — (i)  Injecting  water  into  the  cylinders;  (2)  water 
jacketing  the  cylinders;  and  (3)  compressing  in  stages  and 
using  water  jacketed  vessels,  called  "intercoolers,"  between 
cylinders. 

Water  Injection. 

(f)  The  injection  of  water  into  the  compression  cylinder  has 
been  rather  extensively  used  in  Europe  but  not  in  this  country. 
If  the  water  is  introduced  as  a  solid  stream  but  little  cooling 
is  effected,  the  compression  curve  approximating  the  equation 
p 71.35  to  p 71.37  _  constant;    but  with  a  very  fine  spray  the 
cooling  effect  is  much  greater,  and  values  of  the  exponent  n  as 
low  as  1.26  to  1.28  may  be  obtained. 

(g)  The  introduction  of  water  into  the  cylinder  has  the  fol- 
lowing disadvantages:  —  It  generally  increases  the  wear  of  cyl- 
inder and  piston;    the  feeding  devices  are  an  almost  constant 
source  of  trouble;    and  the  air  leaves  the  cylinder  practically 
saturated  with  water,  some  of  which  precipitates  when  cooled 
in  the  receiver,  but  much  remains  in  the  air  and  later  may  cause 
trouble  by  freezing  when  the  air  is  expanded  in  doing  work. 

Water  Jacketing. 

(h)  Jacketing  the  compressor  cylinders  with  water  does  not 
introduce  the  difficulties  considered  above,  but  it  is  generally 
less  efficient  than  water  spraying  unless  it  is  very  perfectly 
carried  out.  Values  of  the  exponent  n  about  equal  to  1.25  to 
1.28  are  generally  attainable. 


726 


HEAT-POWER  ENGINEERING 


Multistage  Compression  and  Intercooling. 

(i)  The  raising  of  pressure  from  atmospheric  to  the  desired 
receiver  pressure  need  not  occur  entirely  in  one  cylinder.  The 
compression  may  be  divided  between  as  many  cylinders  as  desired 
without  changing  the  ideal  process  in  any  way.  This  is  shown 
in  Fig.  468  for  the  ideal  case  with  three  cylinders,  i.e.,  compres- 
sion in  three  stages.  It  can  be  seen  from  the  diagram  that  it 
is  immaterial  whether :  — 

(1)  Compression  is  carried  out  in  one  cylinder  receiving  the 
charge  Vb  and  compressing  it  isothermally  and  discharging  at  a 
pressure  P2;  or 

(2)  It  is  carried  out  in  several  cylinders,  the  first  receiving 
a  charge  Vb  at  pressure  PI,  compressing  isothermally  to  /  and 


Volume 

Fig.  468. 


Fig.  469. 


then  discharging  along  fe  to  a  second  cylinder  which,  receiving  its 
charge  along  ef,  compresses  to  g,  and  so  on  until  the  last  cylinder 
compresses  to  and  discharges  at  P2. 

(j)  This  method  has  the  practical  advantage  of  making  it 
possible  to  use  what  is  known  as  "  inter  cooling" ',  for  the  air  dis- 
charged from  one  cylinder  may  be  passed  through  a  very  effi- 
cient cooler  on  its  way  to  the  second,  and  so  on.  The  practical 
advantage  of  this  is  shown  in  Fig.  469,  which  indicates  the  com- 
pression line  which  is  thus  made  possible. 

The  line  be  represents  ideal  or  isothermal  compression,  be' 
shows  an  adiabatic,  and  the  broken  line  befghc"  the  compression 
line  which  might  be  obtained  with  a  jacketed,  or  spray  cooled, 
multistage  compressor  fitted  with  intercoolers. 

The  compression  in  the  first  cylinder  brings  the  material  to  e 


COMPRESSED  AIR 

with  a  temperature  higher  than  it  had  at  b.  An  effective  inter- 
cooler  through  which  the  air  passes  on  its  way  to  the  next  cyl- 
inder can  reduce  its  temperature  to  the  original  value,  so  that 
compression  in  the  second  cylinder  starts  under  the  same  con- 
ditions as  though  the  process  in  the  first  had  been  isothermal. 

The  work  done  in  excess  of  that  required  in  the  ideal  case  is 
evidently  measured  by  the  small  areas  chc",  hfg  and  fbe,  while 
without  intercooling  the  loss  would  probably  have  been 'some- 
thing like  that  shown  by  the  area  cbc'" . 

(k)  The  fact  that  the  cooling  water  is  often  below  the  average 
atmospheric  temperature  suggests  the  possibility  of  cooling  in  the 
intercoolers  to  a  value  lower  than  that  on 
the  isothermal.  This  would  give  a  com- 
pression line  similar  to  that  shown  in  Fig. 
470  by  befghc",  which  is  sometimes  approx- 
imated in  practice  when  very  cold  water  is 
available.  Comparing  this  with  the  iso- 
thermal be  shows  that  the  latter  may  under 
these  circumstances  be  very  closely  approx- 
imated. Some  few  machines  have  been 
operated  with  such  effective  intercooling 
that  the  sum  of  the  work  areas  under  the 

real  compression  lines  in  the  several  cylinders  was  less  than 
under  the  ideal  isothermal  between  the  initial  and  final  pres- 
sures. 

(1)  Dividing  the  compression  up  into  several  stages  and  inter- 
cooling has  a  markedly  beneficial  effect  upon  the  volumetric 
efficiency  of  a  compressor  for  two  reasons :  — 

First,  since  the  temperature  range  in  the  low-pressure  cylinder 
(ist  stage)  is  reduced,  the  air  is  heated  less  during  the  suction 
stroke,  hence  greater  actual  weight  will  enter  the  cylinder  than 
would  be  the  case  in  a  single  cylinder  operating  between  the  ex- 
treme pressure  limits. 

Second,  less  weight  of  air  remains  in  the  clearance  of  the  low- 
pressure  cylinder  because  the  discharge  pressure  from  that  cylin- 
der is  lower  than  with  a  single-stage  compressor,  which  would  be 
of  the  same  size  and  have  the  same  clearance  volume. 

This  will  be  made  clear  by  Fig.  471  in  which  the  idealized 
cards  of  a  three-stage  compressor  with  clearance  are  abed,  a'b'c'd' 
and  a"b"c"d".  It  will  be  observed  that  the  expansion  of  the 


728 


HEAT-POWER  ENGINEERING 


clearance  air  in  the  low-pressure  cylinder  theoretically  decreases 
the  charge  volume  by  the  small  amount  equal  to  Va  —  Fd;  whereas 
if  the  compression  had  all  been  carried  out  in  this  one  cylinder 
the  clearance  air  at  pressure  P2  would  have  expanded  from  a 
volume  Ve  to  a  volume  F/,  theoretically  decreasing  the  charge  by 
the  very  large  amount  F/  —  Fd.  This  serious  loss  is  one  worth 
preventing,  if  commercially  feasible. 

(m)  It  is  obvious  from  the  diagrams  and  preceding  paragraphs 
that  the  larger  the  total  pressure  range,  the  greater  in  every  way 
will  be  the  advantages  of  multistage  compression.  It  thus 
happens  in  practice  that  machines  for  compressing  to  25  or  50 
pounds  per  square  inch  are  generally  built  single  stage,  while 


Fig.  471. 


Fig.  472. 


those  intended  to  compress  to  100  or  150  pounds  are  generally 
made  two-stage.  Where  exceptional  efficiency  is  desired,  or 
where  extremely  high  pressures  are  to  be  attained,  three-,  and 
even  four-,  stage  machines  are  sometimes  used. 

(n)  The  differences  between  the  actual  cards  and  the  ideal 
ones  of  each  cylinder  of  a  multistage  compressor  are  similar  to 
those  which  have  been  discussed  for  the  single-stage  compressor. 
When  superposed  they  look  something  like  Fig.  472,  in  which 
the  atmospheric,  intercooler,  and  receiver  pressures  are  indi- 
cated by  horizontal  dash  lines.  In  each  case  the  air  is  drawn 
into  a  cylinder  at  a  pressure  below  that  at  which  it  exists  out- 
side of  the  cylinder  and  is  discharged  at  a  pressure  higher  than 
that  maintained  in  the  vessel  receiving  the  air.  This  results  in 
an  overlapping  of  the  cards  in  the  center  of  the  diagram  giving 
two  loops,  A  and  B,  which  very  evidently  represent  lost  work. 


COMPRESSED  AIR 

(o)  The  better  the  action  of  the  valves  and  the  larger  the 
passages  through  ports,  intercooler,  pipes  and  such,  the  smaller 
will  the  areas  of  these  loops  become,  the  upper  and  lower  lines 
tending  to  become  coincident.  In  very  well-designed  compres- 
sors this  lost  work  is  so  small  as  to  be  almost  if  not  quite  inde- 
terminate. 

345.  Blowing  Engines.     Blowing  engines,  or  blowers,  are  simi- 
lar to  air  compressors  in  principle,  but  they  are  generally  built  to 
handle  relatively  very  large  quantities  of  air  at  comparatively 
low  pressures,  say  10  to  20  pounds  per  square  inch  above  atmos- 
phere.    Comparatively  little  attention  need  be  given  to  cooling 
under  such  conditions  because  the  pressure  is  so  low  that  very 
little  work  can  be  saved  by  such  means.     Moreover,  the  com- 
pressed air  is  generally  heated  before  being  used,  so  that  any  cool- 
ing during  compression  would  call  for  an  expenditure  of  heat  to 
raise  the  temperature  immediately  afterward. 

Because  of  the  large  volumes  of  air  to  be  handled  considerable 
difficulty  is  generally  met  in  designing  efficient  valves,  particu- 
larly if  operated  at  high  speeds.  As  a  result  there  are  many 
different  types  of  both  inlet  and  discharge  valves  in  use,  some 
operating  automatically  under  the  action  of  springs  and  air 
pressure,  some  mechanically  operated,  and  some  partly  automati- 
cally and  partly  mechanically  operated. 

346.  Turbine   Compressors.     Since   the   successful   commer- 
cialization of  the  steam  turbine,  engineers  have  been  trying  to 
develop  satisfactory  ''Turbo  Compressors"  or  "Turbo  Blow- 
ers."    These  compressors  have  a  number  of  stages  arranged  in 
series,  each  impeller  receiving  its  supply  of  air  from  the  preced- 
ing stage  and  discharging  into  the  one  which  follows,  no  valves 
being  used.     The  stages  are  water  cooled  and  intercoolers  are  em- 
ployed.  These  machines  are  just  beginning  to  assume  prominence 
for  compressing  to  pressures  from  10  to  20  pounds  or  more  per 
square  inch,  but  as  yet  few  have  been  used  in  this  country. 

347.  Compressed-air   Engines,     (a)  Compressed  air  is  used 
commercially  in  many  different  ways  but  most  widely  in  engines 
for  the  production  of  power,  the  air  serving  as  the  working  sub- 
stance.    At   first  sight  it  seems  an   uneconomical   method  of 
producing  power  as  the  air  compressor  must  be  driven  by  an 


730  HEAT-POWER  ENGINEERING 

engine  of  some  sort  which  apparently  might  better  be  used 
directly  to  produce  the  power  desired,  rather  than  to  suffer  the 
additional  losses  incurred  during  compression  and  utilization 
of  the  compressed  air  in  a  second  engine. 

(b)  Such  reasoning  is  generally  sound  for  conditions  where  the 
desired  power  can  be  conveniently  generated  at  the  point  of  utili- 
zation by  any  of  the  prime  movers  previously  considered.    There 
are,  however,  many  cases  where  this  cannot  be  done.     Where  a 
number  of  small  engines  are  to  be  operated  at  widely  scattered 
points  and  where  electrical  transmission  is  not  suitable,  com- 
pressed air  engines  find  a  field  to  which  they  are  admirably  suited. 
Compressed  air  can  be  transmitted  for  great  distances  without 
appreciable  loss,  and,  as  will  be  shown  later,  any  loss  can  be  more 
than  made  good  at  the  point  of  consumption.     Steam,  on  the 
other  hand,  cannot  be  efficiently  transmitted  over  great  distance 
because  of  the  resulting  condensation ;  and  more  than  this,  steam 
engines  of  small  size  are  very  inefficient  and  the  high  temper- 
ature at  which  they  operate  renders  them  unsuitable  when  han- 
dling is  required.     The  working  substance  of  internal  combustion 
engines  can  be  transmitted  as  easily,  if  not  more  easily,  than 
compressed  air,  but  the  complicated  valve  and  ignition  mecha- 
nisms, the  high  temperature  and  the  hot  noxious  exhaust  gases 
make  them  less  desirable  than  compressed  air  engines  for  a  num- 
ber of  purposes. 

(c)  Thus  compressed  air  engines  are  widely  used  in  mining 
and  quarrying  operations  and  for  the  driving  of  small  portable 
tools  in  shops  and  such.     In  Paris  there  is  installed  a  central 
compressor  station  which  distributes  compressed  air,  much  as 
gas  is  distributed  in  this  country,  and  air  is  used  by  the  con- 
sumers for  operating  small  plants  much  as  electricity  is  used 
here. 

348.  Compressed  Air  Engine  Cycles,  (a)  Compressed  air  is 
sometimes  used  in  engines  without  expansion,  that  is,  according 
to  the  rectangular  cycle.  The  work  done  per  cycle  in  an  engine 
without  clearance  is  obviously 

work=  76(P2-Pi), (536) 

in  which  F&  is  the  volume  displaced  per  stroke,  P%  is  the  upper 
pressure,  and  PI  that  of  discharge. 


COMPRESSED  AIR  731 

Such  use  of  compressed  air  is  very  uneconomical  as  no  use  is 
made  of  its  associated  heat  and,  as  a  result,  better  methods  of 
utilization  have  been  devised. 

(b)  A  cycle  similar  to  the  Clausius  described  under  vapor 
cycles  is  generally  considered   to   represent  the  ideaP  cycle  for 
air.     As  shown  in  Fig.  463,  it  consists  of  two  constant  pressure 
lines,  dc  and  ba,  a  constant  volume  line  ad,  and  an  adiabatic 
expansion  line  cb.     The  theoretical  work  made  available  by  such 
a  cycle  can  easily  be  determined  from  the  formulas  previously 
given. 

(c)  In  practice  the  air  generally  enters  an  engine  at  about 
atmospheric  temperature  and  during  the  approximately  adiabatic 
expansion  it  becomes  cooled,  in  some  cases  to  such  an  extent  that 
the  moisture  in  it  freezes  and  leads  to  difficulties.     The  theoreti- 
cal temperature  decrease  can  never  be  attained  in  any  real  engine 
because  heat  will  be  supplied  to  the  engine  cylinder  from  the  sur- 
rounding atmosphere  and  will  tend  to  make  the  expansion  more 
nearly  isothermal.     If  the  engine  were  operated  very  slowly  the 
expansion  would  very  closely  approach  a  true  isothermal. 

(d)  This   approach    toward   isothermal   expansion   is   advan- 
tageous for  the  following  reasons: 

(1)  It  tends  to  prevent  the  deposition,  in  the  form  of  ice,  of 
the  moisture  accompanying  the  air,  thus  tending  to  prevent  the 
resultant  troubles  with  lubrication  and  stoppage  of  valves  and 
passages. 

(2)  It  increases  the  work  made  available,  as  the  area  under 
an  isothermal  is  greater  than  that  under  the  steeper  adiabatic 
between  the  same  two  pressures. 

(3)  It  lessens  the  range  of  temperature  within  the  cylinder  so 
that  there  is  less  tendency  to  cool  down  the  entering  air.     Such 
cooling  would  result  in  a  decrease  of  volume  and  therefore  an 
increase  in  the  weight  required  per  cycle. 

(e)  It  is  interesting  to  note  that  from  the  theoretical  view- 
point isothermal  operation  is  not  as  advantageous  as  adiabatic. 
The  object  of  using  expansion  is  to  make  use  of  some  of  the  heat 
associated  with  the  working  substance  as  it  enters  the  engine. 
If  the  expansion  is  isothermal  no  work  can  be  done  at  the  expense 
of  such  associated  heat;    on  the  contrary,  heat  equivalent  in 
quantity  to  the  work  done  must  be  supplied  from  an  external 
source.     With  an  adiabatic  expansion,  however,  all  work  would 


73  2 


HEAT-POWER  ENGINEERING 


be  done  at  the  expense  of  heat  already  associated  with  the  gas 
as  it  enters  the  cylinder. 

The  discrepancy  between  theory  and  practice  is  due  to  the 
fact  that  in  the  assumed  case  heat  supplied  from  the  atmosphere 
during  the  isothermal  expansion  costs  nothing  and  may  there- 
fore be  freely  used  without  decreasing  the  commercial  efficiency 
of  the  process. 

(f)  It  was  shown  that  it  was  uneconomical  to  use  complete 
expansion  in  a  reciprocating  steam  engine.     The  same  thing  is 
true  in  the  case  of  a  reciprocating  compressed  air  engine,  and  as 
a  result  the  toe  of  the  card  is  cut  off  in  practice. 

(g)  Real  engines  are  further  found  to  operate  more  quietly, 
and  therefore  more  satisfactorily,  when  the  exhaust  valve  closes 
before  the  end  of  the  stroke  trapping  some  air  which  is  then 
compressed  into  the  clearance.     Such  operation  causes  a  loss  of 
diagram  area  and  therefore  a  loss  of  work  from  a  given  size  of 
cylinder  running  at  a  given  speed.     It  may,  however,  result  in  a 
saving  in  the  amount  of  air  used  per  horse  power  in  two  ways: 

(1)  When  compression  is  not  used  the  air  admitted  must  first 
be  mixed  with  that  in  the  clearance  until  the  full  admission  pres- 
sure is  attained ;  after  that  the  entering  air  becomes  available  for 
driving  out  the  piston,  and 

(2)  Compression  tends  to  raise  the  temperature  of  the  walls, 
cylinder  head  and  piston  and  thus  to  decrease  the  cooling  effect 
upon  the  incoming  air. 

349.  Preheating,  (a)  In  practical  use,  compressed  air  en- 
gines and  the  compressors  supplying  the  working  fluid  are  gen- 
erally widely  separated.  It  has  already  been  shown  that  so  far 
as  the  compressor  is  concerned  the  cooler  the  air  the  better.  A 
cool  supply  means  larger  capacity  for  a  given  machine  and 
efficient  cooling  during  operation  means  a  smaller  amount  of 
work  required.  The  same  thing  is  true  for  the  "receiver"  or 
storage  tank,  and  for  the  pipe  line  carrying  the  air  to  the  engine, 
for  the  cooler  the  air  the  smaller  can  these  parts  be  for  a  given 
quantity  of  air. 

(b)  Conditions  are,  however,  quite  different  so  far  as  the 
engine  is  concerned.  The  warmer  the  air,  within  reason,  the 
better. 

If  the  compressed  air  could  be  heated  at  constant  pressure 


COMPRESSED  AIR 


733 


before  entering  the  engine,  it  would  expand  according  to  Charles' 
law.  A  given  volume  of  heated  air  admitted  to  the  engine  would 
represent  a  smaller  actual  weight  but  would  be  able  to  deliver 
the  same  amount  of  work  as  a  larger  weight  of  colder  air,  and 
there  would  be  the  added  advantage  that  there  would  be  less 
danger  of  the  moisture  freezing  at  the  end  of  expansion. 

(c)  Such  heating  of  the  air  is  known  as  "  preheating  "  and 
the  devices  in  which  it  is  effected  are  called  "preheaters."  It 
is  actually  used  in  places  where  the  transmission  piping  is  of 
great  length  and  also  where  the  engine  units  are  few  and  of  large 
size.  It  is  found  in  practice  that  the  running  expense  for  the 
fuel  supplied  for  preheating  is  less  than  the  extra  charges  against 
the  larger  compressor  and  pipe  line  which  would  otherwise  be 
used. 


CHAPTER  XLII. 
REFRIGERATION. 

350.  Definition,     (a)  By  refrigeration  is  generally  meant  the 
removal  of  heat  from  a  body,  or  substance,  to  such  an  extent  as 
to  leave  it,  or  maintain  it,  at  a  lower  temperature  than  that  of 
its  surroundings.     This  may  be  done  commercially  in  moderate 
climates  by  the  use  of  ice ;  it  may  be  accomplished  in  the  labora- 
tory by  the  use  of  liquefied  gases;  it  may  be  done  in  very  hot 
climates  by  the  naturally  rapid  evaporation  of  water. 

(b)  In  the  ordinary  engineering  application  of  the  term,  how- 
ever, it  is  taken  to  mean  the  removal  of  heat  by  mechanisms, 
or  systems,  which  will  be  described  in  later  sections  and  which 
are  grouped  under  the  title  of  Mechanical  Refrigeration. 

351.  Thermodynamics  of  Refrigeration,     (a)  It  was  shown 
in  Sect.  49  (h)  that  by  the  expenditure  of  energy  (AE)  a  reversed 

heat  engine  would  remove  heat  from  a  body 
at  low  temperature  and  would  discharge  to 
another  body,  at  higher  temperature,  that 
heat  plus  the  heat  equivalent  to  the  energy 
expended  in  the  operation.  That  is,  a  re- 
versed heat  engine  shown  diagrammatically 
as  R  in  Fig.  473  can  receive  a  stream  of  heat 
A<22  from  the  low  temperature  body  T2  and 
discharge  the  larger  stream  A@i,  made  up  of 
A<22  and  AE,  to  the  high  temperature  body  T\. 
(b)  This  is  a  process  of  refrigeration  because 
heat  can  be  removed  from  the  low  temperature  body  even  if  its 
temperature  be  far  below  that  of  its  surroundings.  It  thus 
appears  that  the  reversed  heat  engine,  which  has  been  called 
a  heat  pump,  is  what  may  now  be  called  a  refrigerator,  or 
refrigerating  machine. 

(c)  Imagine  the  Carnot  cycle,  shown  in  Figs.  18  and  21  to 
PV-  and  T0-coordinates,  to  be  carried  through  in  the  direction 

734 


REFRIGERATION  735 

dcba  for  purposes  of  refrigeration.  Heat  will  be  absorbed  along 
the  line  dc  at  temperature  T2,  and  in  quantity  as  shown  on  the 
T0-diagram  by  the  area  dcef.  The  work  expended  in  driving  the 
machine  will  be  shown  by  the  area  abed  on  the  PV-diagram,  if 
measured  in  foot-pounds,  or  by  the  similarly  lettered  area  on  the 
T</>-diagram,  if  measured  in  thermal  units.  Heat  will  be  dis- 
charged along  the  line  ba  at  temperature  7\  and  its  quantity 
will  be  the  area  feba  on  the  T$-diagram,  equal  to  the  sum  of  two 
areas  previously  considered. 

(d)  The  expenditure  made  in  order  to  abstract  the  heat  Aft, 
shown  in  Fig.  21  by  area  dcef,  is  obviously  the  energy  AE  used 
in  driving  the  machine  as  shown  by  the  area  abed.     If  the  heat 
removed,  Aft,  be  taken  as  the  result  obtained,  the  efficiency  of 

the  process  is  »    .,  n.  A  ^ 

Ej  _       Result       _  Aft 

Expenditure       AE 

(e)  It  is  obvious  from  the  T0-diagram  of  Fig.  21  that  for  the 
case  for  which  this  figure  was  drawn  Aft  is  considerably  greater 
than  AE,  hence  the  ratio  which  has  just  been  given  as  the  effi- 
ciency will   be  greater   than   unity.     This  is   a  very  common 
property  of  refrigerating  processes.     Since  engineers  are  not  ac- 
customed to  speak  or  think  of  efficiencies  greater  than  unity  it 
is  common  practice  to  call  this  ratio  the  Coefficient  of  Performance 
(C.o.P.),  or  the  Figure  of  Merit,  rather  than  the  efficiency  of  the 
process.     Then  the 

C.O.P.  =|f (537) 

for  refrigerating  machinery  of  this  kind. 

(f)  The  apparently  remarkable  attainment  of  an  efficiency 
greater  than  unity  is  meaningless.     The  work  expended  and 
the  heat  removed  from  the  cold  body  are  really  not  connected 
in  any  such  way  as  are  heat  supplied  and  work  done  in  the  case 
of  an  engine.     This  can  best  be  seen  from  the  T<£-diagram  of 
Fig.  21.     Assume  the  line  dc  to  be  moved  upward  while  the 
line  ab  maintains  its  position.     Then  the  heat  removed  (Aft) 
will  obviously  increase  while  the  area  of  the  cycle,  representing 
AE,  will  decrease,  that  is,  it  takes  less  work  to  remove  larger 
amounts  of  heat. 

(g)  That  this  should  be  so  can  easily  be  seen  by  carrying  the 


736  HEAT-POWER  ENGINEERING 

assumptions  to  the  limit.  If  dc  rises  above  ab  the  previously 
cold  body  has  attained  a  temperature  greater  than  the  previ- 
ously hotter  one  and  work  can  actually  be  obtained  by  allowing 
heat  to  flow  from  it  to  the  latter.  Obviously  the  coincidence  of 
the  lines  dc  and  ab  would  indicate  that  the  two  bodies  are  at 
the  same  temperature,  that  no  work  is  attainable  by  heat  flow, 
and  that  no  work  is  necessary  to  cause  heat  flow. 

Requirements  for  Maximum  Coefficient  of  Performance. 

(h)  Inspection  of  the  T<£-diagram  will  show  that  anything 
which  brings  the  two  lines  ab  and  dc,  that  is,  the  temperatures 
7\  and  T%,  closer  together  will  increase  the  value  of  the  coeffi- 
cient of  performance.  This  can  be  done  by  dropping  T\  or  by 
raising  TV  Dropping  T\  will  decrease  AE  but  will  not  change 
Aft.  Raising  T2  will  decrease  AE  and  increase  Aft  by  the 
same  amount.  It  is  therefore  evident  that  raising  the  lower 
temperature  is  more  effective  for  attaining  a  high  coefficient 
than  lowering  the  upper  temperature;  but  this  results  in  a 
higher  temperature  in  the  cold  body  and  hence  may  not  be 
desirable. 

Obviously  with  given  upper  temperature  TI,  the  lower  the  tem- 
perature (T2)  of  the  cold  body  is  maintained  the  smaller  will  be 
the  C.o.P. ;  and,  with  given  lower  temperature  (jT2),  the  lower 
the  temperature  of  the  hot  body  receiving  the  heat,  the  larger 
will  be  the  value  of  the  C.o.P. 

Theoretical  Values  of  Coefficient  of  Performance. 

(i)  For  purposes  of  comparison  with  real  refrigerating  ma- 
chinery the  ideal  reversible  refrigerator  already  described  is 
very  useful  although  its  theoretical  performance  can  never  be 
even  closely  approximated  by  a  real  machine.  The  case  is 
very  similar  to  that  of  engines  where  the  perfect  Carnot 
engine  is  used  as  a  measure  of  perfection  although  practically 
unattainable. 

(j)  In  order  that  numerical  comparisons  may  be  made  later, 
several  values  of  the  coefficient  of  performance  will  now  be 
obtained  for  a  Carnot  cycle  refrigerator.  The  formula  pre- 
viously given  can  be  put  in  more  convenient  form  for  this  pur- 


REFRIGERATION 


737 


pose  in  the  following  way.     It  was  shown  on  page  82  that  for  a 
Carnot  engine  the  net  work  is 

AE  =  RTt  loge  r  -  RT2  log,  r 


and  that  AQ2  = 

Then,  for  this  case, 


C.o.P.  = 


loge  r. 


RT2\oger 


AE 


•      (538) 


Values  of  the  C.o.P.  can  be  easily  obtained  by  substitution  of 
assumed  temperatures  in  the  last  term. 

A  very  common  case  would  be  a  machine  which  theoretically 
withdrew  heat  from  a  cold  body  at  18°  F.  and  discharged  it  to 


10  20  30 

Temperature,  T2  in  Fab.  Degrees. 
Fig.  474- 


a  hot  body  (cooling  water)  at  a  temperature  of,  say,  50°  F.     The 
coefficient  of  performance  in  this  case  would  be 


Tl  _ 


(50  +  460)  -  (18  +  460) 


I5,approx. 


(k)  The  results  obtained  by  varying  the  two  temperatures 
are  shown  by  the  curves  in  Fig.  474,  in  which  each  curve  is 
drawn  for  a  certain  upper  temperature  7\  and  shows  by^  its 
rise  toward  the  right  the  increase  in  the  value  of  the  coefficient 
of  performance  with  rise  of  the  temperature  T2. 


HEAT-POWER  ENGINEERING 


Air  Cooler 


Cold.  Water 


352.  The  Air  Refrigerating  Machine,  (a)  Any  gas,  not  lique- 
fiable  at  ordinary  temperatures,  may  be  used  as  the  working 
substance,  or  refrigerant,  in  commercial  refrigerating  machines, 
but  air  is  the  gas  most  commonly  used.  This  material  has  the 
advantages  of  being  readily  procurable,  non-poisonous  and  can 
be  brought  into  actual  contact  with  food  stuffs  and  such,  which 
are  to  be  cooled  or  kept  cool  without  detriment  to  the  latter. 

(b)  In  the  ideal  machine  the  same  charge  of  air  would  be  used 
continuously  and  the  entire  operation  would  be  carried  out  in 
a  single  cylinder.  In  practice  it  is  found  more  convenient  to 

use  separate  organs  to  perform 
different  functions  during  the 
cycle  and  it  is  generally  found 
best  to  discharge  the  air  used 
in  each  cycle  and  to  draw  in  a 
fresh  supply  for  the  next.  It 
will  be  noted  that  this  parallels 
the  conditions  met  with  in  most 
real  engines. 

(c)  An  idealized  refrigerating 
machine  using  a  unit  weight  of 
air  as  a  working  substance  is 
shown  diagrammatically  in  Fig.  475,  the  apparatus  consisting  of 
a  compression  cylinder,  an  air  cooler  and  an  expansion  cylinder. 
The  compression  cylinder  (without  clearance)  draws  cold  air 
from  the  cold-storage  room  at  atmospheric  pressure  and  at 
a  constant  temperature  T2,  according  to 
the  constant  pressure  line  ab  in  Fig.  476. 
The  air  is  then  compressed  adiabatically,  p 
as  shown  by  be,  and  discharged  at  the 
higher  pressure  PI  with  a  temperature  7\, 
higher  than  T2,  and  specific  volume  dc. 
If  the  delivery  pressure  is  sufficiently 
high,  the  temperature  attained  may  be 
greater  than  that  of  available  cooling 
water  so  that  the  air  may  be  cooled  by 
discharging  it  into  the  cooler  through  which  this  water  is  circu- 
lated. By  assuming  the  volume  of  the  cooler  to  be  very  large, 
the  reduction  of  temperature  may  be  assumed,  without  sensible 
error,  to  take  place  at  constant  pressure;  hence,  the  delivery  to 


Fig.  475- 


Fig.  476. 


REFRIGERATION  739 

the  cooler  is  shown  by  the  line  cd  in  the  figure,  but  when  cooled 
the  volume  of  the  air  is  de  at  this  same  pressure. 

Continued  operation  of  the  compressor  cylinder  would  result 
in  continued  duplication  of  the  cycle  abed. 

(d)  The  expansion  cylinder  running  at  the  same  speed  as  the 
compressor  can  be  imagined  as  receiving  from  the  cooler  exactly 
the  same  weight  of  air  per  cycle  as  is  delivered  by  the  com- 
pressor.    This  air  will  be  admitted  according  to  the  constant- 
pressure  line  de,  in  Fig.  476,  and  its  adiabatic  expansion  will  be 
according  to  line  ef,  bringing  the  material  back  to  the  initial 
pressure  P2  but  with  a  temperature  lower  than  the  original 
temperature  T"2,  for,  according  to  Charles'  law, 

Tf/Tb  =  Tf/T*  =  Vf/Vb, 

from  which  Tf  =  T2(Vf/Vb) (539) 

This  cooled  air  at  temperature  Tf  can  then  be  discharged  to 
the  cold-storage  room  to  balance  heat  leaking  into  it  through 
the  walls  or  brought  in  by  fresh  produce.  It  is  only  necessary 
to  properly  regulate  the  quantity  of  air  handled  and  the  tem- 
perature at  which  it  is  returned,  to  maintain  any  desired  tem- 
perature (within  limits)  in  the  cold-storage  room. 

Power  Required. 

(e)  The  work  consumed  by  the  compressor  is  obviously  shown 
by  the  area  abed  and   that  made  available  in  the  expansion 
cylinder  is  similarly  shown  by  the  area  defa.     The  net  work 
required  per  cycle  is  then  only  fbce  if  the  expansion  and  com- 
pressor pistons  be  connected  together.     This  work  can  be  ex- 
pressed in  terms  of  temperatures,  pressures  and  volumes  by  the 
equations  given  in  Chap.  VIII. 

Refrigerating  Effect  and  Coefficient  of  Performance. 

(f)  The  net  refrigerating  effect,  that  is,  the  heat  Aft  removed 
from  the  cold  room  per  cycle,  is  obviously  the  difference  between 
the  heat  in  the  air  as  it  leaves  and  that  in  the  same  air  when  it 
returns.     That  is,     &Q2  =  WCp(Tb  -  Tf),    .     .     .     .     •     (54°) 
in  which  _       .  ,       .    .  CyCle 

Cp  =  specific  heat  of  air  at  constant  pressure, 
Tb  =  temperature  of  air  leaving  cold  room,  and 
Tf  =  temperature  of  air  returning  to  cold  room. 


740  HEAT-POWER  ENGINEERING 

(g)  In  a  similar  way  the  heat  rejected  to  the  water  must  be 

Aft  =  WCP  (Te  -  Te) (541) 

Since  AE  =  Aft  -  Aft,  it  follows  that 

AE  =  WCP  (Tc  -  Te)  -  WCP  (Tb  -  7»,      .     (542) 
and  from  these  values 

r     P       Aft_  WCp(Tb-Tf) 

U'ar-  ~  AE       WCP  (Tc  -  Te)  -  WCP  (Tb  -  Tf)    . 


(Tc  -  Te)  -  (Tb  -  Tf) (543) 

This  value  may  be  further  simplified  as  follows:    Inverting 
both  sides  of  the  equation  gives 

1  (Te   -    Te)    _ 

C.o.P.        Tb-Tf   ' 
and  since  from  the  adiabatic  relation 

_  —  _  —     c  —     e 
Yb~Tf~Tb-T/ 

1  Tc  -  Tb      Te-  Tf 


C.o.P.  Tb  Tf 

and 

C.O.P.  =  — ^y  =       T<       .    .    .    .    (544) 

I  c  —   lb          1  e  —   1  f 

Comparison  with  the  Reversed  Carnot  Cycle. 

(h)  A  Carnot  cycle  refrigeration  would  work  between  the 
temperatures  Tb,  which  is  the  highest  temperature  of  the  cool 
material,  and  Te,  which  is  the  lowest  temperature  of  the  warm 
material.  Its  coefficient  of  performance  would  therefore  be 


C.o.P.  = 


Tb 


e-  Tb 

Since  (Te  -  Tb)  is  less  than  (Tc  -  Tb)  in  Eq.  (544),  it  follows 
that  even  in  the  ideal  case  the  real  refrigerating  machine  de- 
scribed must  have  a  lower  coefficient  of  performance  than  that 
obtained  with  the  reversed  Carnot  cycle. 

The  difference  is  due  to  the  use  of  two  irreversible,  variable- 
temperature;  constant-pressure  processes  which  in  the  real  case 
increase  the  temperature  range.  The  temperature  of  the  air 


REFRIGERATION  741 

discharged  to  the  cooler  must  be  so  high  that  the  water  used 
can  remove  heat  from  it,  finally  bringing  the  air  down  to  a  value 
approaching  that  which  it  had  when  entering  the  compressor 
cylinder. 

Similarly,  the  air  is  cooled  during  expansion  to  a  temperature 
considerably  lower  than  that  of  the  cold  room,  and  when  intro- 
duced into  that  room  it  is  heated  irreversibly  until  it  finally 
attains  the  temperature  existing  there. 

Practical  Modifications. 

(i)  In  a  real  machine  operating  on  the  cycle  just  discussed, 
there  will  be  clearance  and  valve  losses  in  both  cylinders,  fric- 
tion throughout  the  mechanism,  and  heat  losses  to  and  from  the 
working  substance  as  it  passes  through  the  apparatus  with 
temperatures  different  from  those  of  surrounding  bodies.  These 
will  all  increase  the  size  of  machine  and  the  amount  of  work 
necessary  to  produce  a  given  amount  of  refrigeration. 

(j)  In  practice  it  is  customary  to  water  jacket  the  compressor. 
This  makes  the  compression  line  less  steep,  i.e.,  intermediate 
between  the  adiabatic  and  the  isothermal,  and  proportionally 
reduces  the  amount  of  work  required.  It  also  leaves  less  heat 
to  be  removed  in  the  cooler  and  makes  possible  the  use  of  a 
smaller  vessel  for  that  purpose.  It  is  therefore  decidedly  ad- 
vantageous. 

Actual  Coefficient  of  Performance. 

(k)  Both  in  the  ideal  and  actual  cases,  the  coefficient  of  per- 
formance of  air  refrigerating  machines  is  very  poor  in  compari- 
son with  machines  using  vapors  such  as  ammonia.  The  use  of 
air  machines  is  therefore  dictated  by  convenience  rather  than  by 
economy  of  power. 

For  average  cold-storage  conditions,  in  temperate  climates 
for  instance,  the  coefficient  of  performance  of  a  Carnot  cycle 
refrigerator  is  about  9  to  10.  The  coefficient  of  the  ideal  air 
machine  (Eq.  (544))  is  only  about  1 .5  to  2 ;  and  in  the  real  machine 
it  is  generally,  if  not  always,  below  0.75,  as  determined  by  test. 

353-  Vapor  Compression  Process  of  Refrigeration,  (a)  It 
was  shown  in  the  previous  section  that  the  air  machine  there 
described  was  considerably  handicapped  by  the  cycle  on  which 


742  HEAT-POWER  ENGINEERING 

it  operated,  its  theoretical  coefficient  of  performance  being 
necessarily  much  lower  than  that  of  the  ideal  Carnot  cycle 
refrigerator  because  the  constant  pressure  reception  and  rejec- 
tion of  the  heat  are  not  reversible  processes  with  gases. 

(b)  By  using  a  liquid  and  its  vapor  as  the  working  substance, 
instead  of  a  gas,  a  much  better  performance  can  be  obtained 
because  the   constant-pressure   processes   for  saturated  vapors 
and  their  liquids  are  reversible  isothermal  ones.     It  therefore 
follows  that  with  such  working  substances  the  same   sort  of 
machine  as  that  just  described  would  in  the  ideal  case  operate 
on  a   Carnot   cycle   which   would   give   the   best   performance 
possible. 

(c)  Fig.  477  can  be  used  for  the  purpose  of  developing  this 
cycle  by  assuming  the  discharge  pipe  of  the  expansion  cylinder 

and  the  inlet  pipe  of  the  compressor  con- 
nected by  a  coil,  as  shown  dotted  by  C 
in  Fig.  475,  so  that  the  entire  system  is 
"closed."  This  coil  may  be  regarded  as 
immersed  in  the  material  to  be  cooled. 

Imagine  the  ideal  compression  cylinder 
to  draw  in  a  charge  of  mixed   saturated 
vapor  and  its  liquid,  at  temperature  jT2 
pjg    77  from  this  coil,  as  shown  by  the  line  ab 

in  Fig.  477.     The  return   stroke  of  the 

piston  will  result  in  adiabatic  compression  to  the  point  c,  and, 
with  a  properly  chosen  quality  at  b,  the  material  can  be  brought 
to  the  condition  of  dry  saturation  at  c. 

From  c  to  d  the  working  substance  is  driven  into  the  cooler 
which  now  acts  as  a  condenser  reducing  all  of  the  vapor  to  the 
liquid  form  with  volume  de.  The  liquid  may  then  be  admitted 
to  the  expansion  cylinder,  as  shown  by  the  line  de,  expanded 
adiabatically  to  /  and  discharged  along  the  line  fa  into  the 
assumed  coil  C,  where  it  may  be  vaporized  wholly,  or  partly, 
at  temperature  T2,  at  the  expense  of  heat  in  the  material 
surrounding  the  coil.  After  this  it  may  be  readmitted  to  the 
compressor  and  the  cycle  repeated. 

(d)  So  far  as  cycle  is  concerned  the  operations  outlined  have 
resulted  in  the  generation  of  the  reversed    Carnot   cycle  fbce. 
So  far  as  heat  is  concerned  they  have  resulted  in  the  removal  of 
heat  A()2  from  the  cooler  substance  during  vaporization  at  tem- 


REFRIGERATION  743 

perature  T2  and  in  the  surrender  of  a  larger  amount  of  heat  Aft 
to  the  warmer  substance  (condensing  water)  at  the  tempera- 
ture TV 

T<|>-Diagram  of  Vapor  Process. 

(e)  The  T</>-changes  of  ammonia  vapor  and  its  liquid,  in  an 
ideal  case,  are  shown  in  Fig.  478  in  which  points  are  lettered  to 
correspond  with  those  of  Fig.  477.  The  liquid  line  and  the 
saturation  line  have  been  added  to  the  diagram. 

From  this  diagram  it  can  be  seen  that 
the  heat  absorbed  from  the  cooler  body 


/  f 


\ 
A 


is  r2  (xb  —  Xf)  and  that  discharged  to  the 
warmer  body  is  r\.  The  work  required  in 
B.t.u.  per  pound  of  substance  is  therefore 

AE  =  rl-r2(xb-Xf).  .     (545) 

Fig.  478. 

The   mixture    of   liquid  and  vapor  is 

cooled  during  the  expansion  ef  by  the  giving  up  of  heat  to  cause 
partial  vaporization  as  indicated. 

Practical  Modifications  of  Vapor  Compression  Process. 

(f)  In  any  real  case  the  expansion  cylinder  would  be  very 
small   in    comparison  with   the   compression  cylinder,  and   the 
work  done  by  it  would  be  practically  negligible.     It  has  come 
to  be  regarded  as  more  of  an  incumbrance  than  a  benefit  and  is 
commonly  omitted  in   real   machines.     In   its   place  is  substi- 
tuted an  "  expansion  valve,"  as  X  in  Fig.  479.     This  is  merely  a 
throttle  valve  through  which  the  working  substance  can  flow 
from  the  high  pressure  of  the  condenser  to  the  low  pressure  of 
the  coil. 

(g)  This  flow  is  an  adiabiatic  process  but  is  not  reversible  and 
hence  is  not  isen tropic.     It  is  not  represented  by  the  line  ef  of 
Fig.  478,  but  by  some  line  starting  at  e  and  terminating  on  the 
line  fb  at  some  point  /'  to  the  right  of  /.     The  entropy  increases 
and  the  possible  refrigeration  effect  decreases  because  the  energy 
which  would  have  been  given  up  as  external  work  during  isen- 
tropic  expansion  here  remains  associated  with  the  substance  giv- 
ing it  the  higher  quality  */,  instead  of  */.     The  heat  which  can 
be  absorbed  from  the  body  to  be  cooled  is  then  only  r2  (*&-*/) 
instead  of  TZ  (xb  —  Xf). 


744 


HEAT-POWER  ENGINEERING 


In  real  cases  the  difference  is  so  small  that  it  is  negligible  in 
comparison  with  the  increase  in  mechanical  efficiency  and  ease 


Fig.  479- 

of  operation,  and  with  the  decrease  in  first  cost  and  operating 
expense. 

Actual  Coefficient  of  Performance. 

(h)  The  great  majority  of  vapor  compression  machines  oper- 
ate with  ammonia  vapor  for  their  working  substance.  Such 
machines  give  a  coefficient  of  performance  of  from  5  to  7  under 
conditions  which  give  a  coefficient  of  9  to  10  for  the  ideal  Carnot 
cycle.  In  comparison  with  the  values  given  for  air  machines 
these  performances  are  very  much  higher  and  it  is  doubtful  if 
the  ammonia  machines  can  be  greatly  improved. 

354.  Relative  Advantages  of  Different  Vapors,  (a)  While 
most  vapor  refrigerating  machines  use  ammonia  this  material 
is  not  the  only  one  available.  For  plants  used  aboard  ship 
carbon  dioxide  is  often  preferred  and  many  stationary  machines 
have  been  operated  with  this  substance  and  with  sulphur  di- 
oxide. Other  materials,  including  water,  have  been  used. 

(b)  The  choice  of  ammonia  as  the  common  working  substance 
is  decided  largely  by  practical  considerations,  though  it  so  hap- 
pens that  certain  ihermodynamic  properties  would  lead  to  the 
same  choice.  The  most  important  considerations  are  probably 
those  of  volume  and  pressure, 


REFRIGERATION  745 

(c)  The  actual  volume  of  working  substance  required  to  cause 
a  given  amount  of  refrigeration  determines  the  size  of  machine 
required.      The   larger   the   machine,   the    greater  the  friction 
losses  if  other  things  are  equal.     Since  all  friction  must  even- 
tually result  in  the  generation  of  heat  the  refrigerating  effect 
will  be  diminished  thereby.     Bulk  is  therefore  undesirable  be- 
cause of  cost  of  machines,  cost  of  power  to  operate  and  loss  of 
refrigerating  effect  by  friction. 

The  pressure  is  important  in  two  ways.  Some  available 
substances  have  vapor  pressures  below  atmospheric  when  at  the 
temperatures  common  in  refrigeration.  Their  use  would  mean 
the  maintenance  of  a  vacuum  within  the  refrigerating  machine 
which  is  by  no  means  a  simple  matter  because  of  difficulty  with 
air  leakage.  Other  substances  have  vapor  pressures  so  high 
that  they  can  be  used  only  with  great  difficulty. 

(d)  Ammonia  is  quite  satisfactory  both  as  regards  bulk  and 
pressure.     More  than  twice  the  bulk  of  sulphur  dioxide  is  re- 
quired for  the  same  refrigerating  effect,  and  between  300  and 
400  times  the  bulk  of  water  vapor.     Carbon  dioxide  requires 
only  about  one-quarter  the  bulk  of  ammonia  vapor  but,  as  will 
be  seen,  is  handicapped  by  enormously  high  pressures. 

The  pressure  of  water  vapor  is  entirely  below  atmospheric 
at  refrigerating  temperatures,  while  that  of  sulphur  dioxide  is 
below  for  the  lowest  temperatures  and  only  slightly  above  for 
the  highest  temperatures. 

The  pressure  of  ammonia  vapor  varies  from  about  20  or  25 
pounds  to  something  below  200  pounds,  while  that  of  carbon 
dioxide  varies  from  about  300  to  1000  pounds  per  square  inch. 

It  is  obvious  that  the  best  commercial  balance  is  struck  when 
ammonia  is  adopted,  excepting  in  cases  where  an  ammonia  leak 
might  cause  very  serious  difficulties. 

(e)  In  the  case  of  real  machines  there  is  also  another  point  which 
must  be  considered  and  which  is  more  of  a  thermodynamic  nature. 
Where  an  expansion  valve  is  substituted  for  the  expansion  cylin- 
der, the  working  substance  brings  into  the  refrigerating  coil  heat 
which  in  the  ideal  case  would  have  been  converted  into  work  and 
used  in  driving  the  machine.     Obviously  any  heat  brought  into 
the  coil  by  the  working  substance  itself  means  just  so  much  less 
heat  to  be  abstracted  from  the  surroundings  to  cause  evapor- 
ation, hence  there  will  be  an  equal  reduction  in  the  refrigeration. 


746  HEAT-POWER  ENGINEERING 

That  material  which  brings  in  relatively  the  smallest  amount 
of  heat  in  this  way  will  be  the  most  desirable  if  other  things 
are  equal. 

The  amount  of  heat  under  consideration  is  that  in  the  liquid 
at  the  end  of  the  liquefaction  process,  that  is,  it  is  the  quantity 
when  the  working  substance  is  at  the  higher  temperature  TI 
which  is  above  that  in  the  same  liquid  at  the  lower  temperature 
TV  It  is  therefore  equal  to  C  (Ti  —  T2)  in  which  C  is  the  specific 
heat  of  the  liquid.  The  larger  this  value  in  proportion  to  the 
latent  heat  of  vaporization  at  the  temperature  T2,  the  poorer  the 
material  for  use  in  a  vapor  compression  machine  having  an  ex- 
pansion valve. 

From  this  point  of  view,  water  is  the  best  of  the  materials 
cited  as  possibilities  and  ammonia  comes  next,  carbon  dioxide 
being  the  worst  of  all ;  thus,  ammonia  forms  a  good  commercial 
compromise. 

355.  The  Ammonia  Absorption  Process,  (a)  The  vapor 
compression  machine  operates  (i.e.,  refrigerates)  because  the 
process  of  vaporization  requires  a  supply  of  heat  from  external 
sources  and  the  process  of  liquefaction  yields  heat  to  external 
media.  Any  device  or  machine  which  can  bring  about  such  alter- 
nate liquefaction  and  vaporization  can  be  used  as  a  refrigerating 
machine. 

(b)  The   so-called    absorption    refrigerating   machine    carries 
through  these  two  processes  in  a  manner  analogous  to  that  of  the 
compression  machine  but  by  entirely  different  means.     It  is  illus- 
trated diagrammatically  in  Fig.  480  and  operates  in  the  following 
way: 

(c)  The  generator  contains  a  strong  solution  of  ammonia  in 
water,  and  the  ammonia  is  driven  off  from  this  solution  at  high 
temperature  and  pressure,  by  the  heat  supplied  by  the  steam 
coils  shown  at  5.     The  vapor,  under  this  pressure,  enters  the 
condenser  K  in  which  it  is  liquefied,  as  in  the  previous  case.     It 
then  passes  through  the  expansion  valve  X  and  evaporates  in 
the  refrigerating  coils  C  as  before. 

Leaving  the  refrigerating  coils  as  vapor,  it  enters  the  absorber 
A  at  low  pressure  and  low  temperature  and  is  absorbed  by  water 
to  form  a  strong  solution  which,  by  a  pump  P,  is  delivered  to 
the  generator  to  displace  that  which  has  given  up  ammonia 


REFRIGERATION  »,» 

vapor  under  the  action  of  heat,  and  which  is  then  returned  to 
the  absorber. 

(d)  The  absorber,  pump  and  generator  together  correspond 
to  the  compressor  of  the  previous  type.     The  action  in  the  ab- 


Fig.  480. 

sorber  corresponds  to  the  charging  operation  of  the  compressor; 
the  action  of  pump  and  generator  corresponds  to  the  compression 
and  discharge. 

Coefficient  of  Performance  of  Absorption  Machines. 

(e)  No  mechanical  power,  except  the  small  amount  for  pump 
P,  is  supplied  such  a  machine,  the  absorption  of  heat  at  a  low 
temperature  following  from  the  supply  of  heat  at  a  high  tem- 
perature.    The  coefficient  of  performance  cannot  therefore  be 
obtained  as  in  previous  cases.     If,  however,  it  is  considered  as 
the  quotient  found  by  dividing  the  heat  absorbed  by  heat  sup- 
plied to  cause  that  absorption,  a  ratio  is  obtained  which  may 
be  used  in   the  same  way  as  the  coefficient  of  performance. 
Comparing  such  ratios  with  those  for  ideal  refrigeration  oper- 
ating on  a  reversed  Carnot  cycle  it  is  found  that  the  absorption 
machine  has  a  coefficient  of  performance  of  about  one-eighth  to 
one-tenth  that  of  the  ideal. 

(f)  It  was  shown  in  Sect.  353  (h)  that  for  the  compression 
process  the  coefficient  is  about  seven-tenths  of  the  ideal  and  it 
would  seem  from  this  that  the  absorption  machine  should  give 
a  very  poor  commercial  result,     It  should,  however,  be  observed 


748  HEAT-POWER  ENGINEERING 

that  the  coefficient  for  the  compression  machine  was  based  upon 
the  energy  supplied  the  compressor  and  not  upon  the  heat 
supplied  the  plant  which  generated  that  energy. 

To  make  the  two  results  comparable  the  value  of  0.7  for  the 
compression  machine  must  be  multiplied  by  the  thermal  effi- 
ciency of  the  plant  on  the  basis  of  developed  horse  power. 
When  this  is  done  the  two  types  are  more  nearly  on  an  equal 
footing,  with  the  absorption  machine  giving  the  better  perform- 
ance for  wide  temperature  ranges,  excepting  when  a  very  efficient 
plant  is  used  to  drive  the  compression  machine. 

356.  Rating  of  Refrigerating  Machines,  (a)  Refrigerating 
machines  are  generally  used  in  practice  for  the  purpose  of  main- 
taining a  cold  atmosphere  in  "cold-storage  rooms"  or  for  the 
making  of  ice.  The  ammonia  machines  generally  achieve  both 
results  indirectly  by  cooling  brine  and  pumping  the  brine  to  the 
point  at  which  heat  is  to  be  absorbed. 

(b)  No  matter  what  use  is  made  of  the  refrigerating  machine 
or  how  it  operates,  it  is  rated  on  ice-melting  capacity  in  pounds, 
or  tons,  per  unit  of  time.  To  melt  one  pound  of  ice  at  32°  F.  to 
water  at  the  same  temperature  requires  approximately  144  B.t.u. 

A  machine  which  could  absorb  from  the  cold  body  a  quantity 
of  heat  equal  to  144  B.t.u.  per  hour  would  have  an  ice-melting 
capacity  of  one  pound  per  hour.  The  capacity  is  generally  ex- 
pressed in  tons  per  twenty-four  hours,  thus  this  machine  would 
have  an  ice-melting  capacity  of  (i  X  24)  -f-  2000  =  0.012  ton, 
approximately. 

Ice-melting  capacity  has  no  direct  connection  with  ice-making 
capacity.  When  making  ice  the  water  from  which  it  is  made 
must  first  be  cooled  to  freezing  temperature,  the  ice  then  formed, 
and  generally  reduced  to  a  temperature  considerably  below  32°  F. 
As  a  result,  the  ice-making  capacity  of  a  machine  is  generally 
only  about  one-half  of  its  ice-melting  capacity. 


PROBLEMS. 


CHAPTER  H. 

1.  Assuming  the  specific  heat  of  water  constant  and  equal  to  unity,  how 
many  B.t.u.  are  required  to  raise  the  temperature  of  I  Ib.  of  water  from 
32°  F.  to  212°  F.? 

2.  Under  the  same  assumptions  as  above,  how  many  B.t.u.  must  be  ab- 
stracted to  lower  the  temperature  of  20  Ibs.  of  water  from  212°  F.  to  32°  F.? 

3.  If  33,000  ft. -Ibs.  of  mechanical  energy  are  completely  converted  into 
heat  energy,  how  many  B.t.u.  result? 

4.  If  mechanical  energy  is  made  available  at  the  rate  of  33,000  ft. -Ibs.  per 
minute  for  I  hour  it  is  said  that  i  horse-power  hour  has  been  made  available. 
What  is  the  energy  equivalent  of  I  horse-power  hour  in  thermal  units? 

5.  Find  the  weight  of  water  (specific  heat  =  i)  which  will  have  its -tem- 
perature doubled  by  the  addition  of  180  B.t.u.,  the  final  temperature  being 
120°  F. 

6.  Find  the  change  of  temperature  of  12  oz.  of  lead  (specific  heat  =  0.0314) 
when  4  B.t.u.  are  added. 

7.  Assuming  no  loss  by  radiation,  how  much  electrical  energy  in  terms  of 
thermal  units  would  be  required  to  raise  the  temperature  of  a  copper  wire 
one  mile  long  and  weighing  0.3  Ib.  per  foot  through  a  range  of  10  degrees? 
The  specific  heat  of  copper  is  0.095. 

8.  If  130  B.t.u.  raise  the  temperature  of  10  Ibs.  of  cast  iron  100  degrees,  what 
must  be  the  specific  heat  of  this  material? 

9.  Assume  the  specific  heat  of  wrought  iron  as  0.113,  the  specific  heat  of 
water  as  i.o  and  the  weight  of  water  as  62.5  Ibs.  per  cu.  ft.     Find  the  increase 
in  temperature  of  2  cu.  ft.  of  water  when  a  common  temperature  of  45°  re- 
sults from  putting  into  the  water  a  piece  of  iron  weighing  10  Ibs.  and  at  a 
temperature  of  1000°  F. 

10.  A  winch  is  used  in  lowering  a  load  of  two  tons  a  vertical  distance  of 
50  ft.     The  load  is  lowered  by  means  of  a  friction  brake  which  prevents  the 
attainment  of  too  high  a  speed  and  which  brings  the  load  to  rest  just  as  it 
reaches  the  end  of  the  50-1 1.  drop.      It  takes  one  minute  to  lower  the  load. 
Neglecting  friction  of  bearings  and  similar  losses,  how  much  heat  must  be 
radiated  by  the  mechanism  of  the  brake  and  winch?     How  many  horse  power 
must  be  absorbed  by  the  brake? 

11.  An  electric  motor  receives  electrical  energy,  converts  part  of  it  into 
heat  within  itself  and  delivers  the  remainder  at  the  pulley  as  available  me- 
chanical energy.     A  certain  motor  delivers,  in  this  way,  20  horse  power  (i  h.p. 
=  33,000  ft.-lbs.  per  min.)  and  converts  into  heat  15  per  cent  of  all  the  energy 
supplied  it.     How  much  heat  must  this  motor  dissipate  per  hour?     How  many 
ft.-lbs.  of  energy  must  be  supplied  it  per  minute? 

12.  Assume  yourself  called  upon  to  investigate  the  claims  made  for  a  piece 
of  mechanism  with  the  following  characteristics.     It  receives  no  energy  of 
any  kind  excepting  that  given  it  by  a  driving  belt  which  supplies  250,000  ft.- 
lbs.  per  minute.     It  is  claimed  that  the  mechanism  gives  out  or  makes  avail- 
able 400  B.t.u.  per  minute.     Would  you  make  the  investigation?     Why? 

13.  What  is  the  largest  amount  of  heat  energy  which  the  mechanism  oper- 
ating as  in  problem   12  could  make  available  per  minute  in  an  ideal  case? 
Could  it  do  this  in  practice?    Why? 

749  . 


750  HEAT-POWER  ENGINEERING 

14.  Assume  yourself  called  upon  to  investigate  the  claims  made  for  a  piece 
of  mechanism  with  the  following  characteristics.     It  is  supposed  to  receive 
no  energy  of  any  kind  excepting  300  B.t.u.  per  minute  and  is  supposed  to 
make  available  240,000  ft.-lbs.  of  mechanical  energy  in  the  same  time.     Would 
you  make  the  investigation?    Why? 

15.  Assume  that  the  mechanism  in  problem  14  above  is  supposed  to  receive 
only  300  B.t.u.  as  before  and  that  in  the  ideal  case  (neglecting  friction,  radia- 
tion, conduction  and  similar  losses)  it  is  supposed  to  deliver  233,400  ft.-lbs. 
in  the  same  time.     Would  you  make  the  investigation?     Why? 

1 6.  Assume  that  the  value  of  the  variable  specific  heat  C  of  a  subtance  is 
given  for  temperature  t  by  the  equation 

C  =  0.5  +  0.02  /. 

Find  the  total  heat  required  to  raise  the  temperature  of  12  Ibs.  of  the  material 
from  50°  to  1 00°  F. 

17.  An  engine  receiving  300  B.t.u.  per  minute  and  no  other  energy  of  any 
kind  rejects  to  a  cold  body  an   amount  of  energy  equal  to  150  B.t.u.  per 
minute.     If  there  are  no  friction  or  similar  losses,  what  would  be  the  amount 
of  mechanical  energy  in  ft.-lbs.  made  available  per  minute? 

18.  If  the  engine  operating  as  in  the  first  part  of  prob.  17  above  loses  in 
friction  and  radiation  10  per  cent  of  the  energy  which  would  otherwise  be 
made  available,  what  will  be  the  amount  of  mechanical   energy  in  ft.-lbs. 
made  available  per  minute? 

19.  A  factory  building  is  being  designed.     Calculations  from  the  radiating 
surface  of  the  building,  character  of  that  surface,  location,  direction  of 'winds, 
etc.,  indicate  that  about  400,000  B.t.u.  per  hour  must  be  liberated  within  the 
building  to  keep  the  temperature  up  to  65°  F.     The  heating  engineer  desires 
to  keep  the  cost  of  the  heating  equipment  down  to  a  low  figure  and  believes 
that  he  can  do  so  by  allowing  for  heat  generated  by  friction  of  the  moving 
mechanisms  within  the  factory.     He  discovers  that  100  horse  power  (i  h.p. 
=  33>°°°  ft.-lbs./min.)  are  to  be  continuously  supplied  the  factory  by  means 
of  an  electric  motor  and  that  all  of  this  power  will  be  consumed  within  the 
factory.     The  motor  has  an  efficiency  of  85  per  cent.     What  allowance  can 
the  heating  engineer  make  on  theoretical  grounds? 

20.  In  the  manufacture  of  a  certain  chemical  compound  it  is  necessary  to 
stir  and  mix  a  rather  heavy  liquid  in  a  large  vat.     If  the  temperature  of  the 
liquid  rises  above  a  certain  value  it  is  apt  to  cause  a  violent  explosion.     The 
formation  of  the  compound  causes  the  absorption  of  20,000  B.t.u.  per  hour 
and  the  vat  is  so  arranged  that  25,000  B.t.u.  can  be  carried  away  per  hour 
under  all  conditions  by  means  of  a  water  jacket  and  loss  to  the  surrounding 
atmosphere.     How  many  foot-pounds  of  energy  could  be  supplied  the  stirring 
apparatus  per  hour  without  causing  a  dangerous  rise  of  temperature? 

CHAPTER  IV. 

1.  An  ideal  gas  occupies  a  volume  of  17  cu.  ft.  at  a  pressure  of  1500  Ibs.  per 
sq.  ft.  and  a  temperature  T.     What  will  be  its  volume  at  a  pressure  of  2000 
Ibs.  per  sq.  ft.  and  at  the  same  temperature? 

2.  A  gas  has  its  volume  halved  by  an  increase  of  pressure  at  constant  tem- 
perature.    The  initial  pressure  was  3000  Ibs.  per  sq.  ft.;    what  is  the  final 
pressure? 

3.  A  gas  with  an  initial  pressure  of  4500  Ibs.  per  sq.  ft.  is  contained  in  a 
water-jacketed  cylinder,  the  jacket  being  so  connected  with  a  water  system 
that  the  temperature  within  it  is  always  60°  F.     The  cylinder  is  fitted  with  a 
fnctionless  piston  which  can  be  moved  in  or  out  as  desired.     The  piston  is 
moved  very  slowly  so  that  the  gas  is  maintained  at  the  same  temperature  as 
the  water  jacket.     At  the  end  of  a  certain  time  the  pressure  of  the  gas  within 
the  cylinder  is  found  to  be  14.7  Ibs.  per  sq.  in.     Was  the  piston  moved  in  qr 
out?     What,  is  the  ratio  of  the  final  volume  to  the  initial? 


PROBLEMS 


751 


4.  A  balloon  is  filled  with  hydrogen  gas  at  atmospheric  pressure  (14.7  Ibs. 
per  sq.  in.)  and  at  atmospheric  temperature.     The  balloon  then  ascends  to  a 
point  where  the  atmospheric  pressure  is  only  12.7  Ibs.  per  sq.  in.  but  the 
temperature  is  the  same  as  at  the  lower  level.     If  the  balloon  is  made  of  non- 
extensible  material,  what  will  be  the  pressure  of  the  hydrogen  gas  within  it? 
If  the  balloon  is  made  of  perfectly  stretchable  material  (stretching  with  appli- 
cation of  only  infinitesimal  forces),  what  will  be  the  pressure  within  it?     In 
the  latter  case  what  expansion  of  volume  must  have  occurred? 

5.  The  inner  tube  of  a  certain  tire  has  a  capacity  of  854  cubic  inches.     How 
many  pounds  of  air  will  it  contain  when  filled  with  air  at  a  pressure  of  70  Ibs. 
per  sq.  in.  and  a  temperature  of  32°  F.?     (One  cubic  foot  of  air  at  14.7  Ibs. 
pressure  and  32°  F.  weighs  0.0807  Ibs.) 

6.  What  will  be  the  increase  of  pressure  of  air  in  problem  5  if  the  tempera- 
ture rises  to  70°  F.  and  the  tire  does  not  stretch  during  the  process? 

7.  A  closed  metal  tank  is  designed  to  be  safe  when  subjected  to  an  internal 
pressure  of  100  Ibs.  per  sq.  in.     It  is  used  to  hold  compressed  air  and  is  filled 
with  this  material  at  a  temperature  of  60°  F.  and  a  pressure  of  80  Ibs.  per  sq. 
in.     The  tank  stands  in  the  sun  and  its  contents  may  attain  a  temperature  of 
125°  F.     Assuming  that  the  tank  does  not  expand  with  temperature  and 
pressure  changes,  will  the  designed  pressure  be  exceeded?     What  temperature 
would  have  to  be  attained  to  raise  the  pressure  of  the  air  to  the  100  Ibs.  for 
which  the  tank  was  designed? 

8.  A  submarine  boat  is  closed  at  the  surface,  with  air  content  at  a  tempera- 
ture of  80°  F.  and  a  pressure  of  14.5  Ibs.  per  sq.  in.     After  sinking  beneath 
the  surface  the  temperature  of  the  air  drops  to  40°  F.     If  the  hull  has  not 
changed  size  during  the  temperature  change  what  must  be  the  pressure  of  the 
air  under  the  submerged  conditions? 

9.  Assuming  that  the  men  and  machinery  in  the  boat  of  problem  8  radiate 
enough  heat  to  maintain  a  temperature  of  60°  within  the  boat  what  will  the 
air  pressure  be? 

10.  A  quantity  of  gas  occupies  a  volume  of  10  cu.  ft.  at  a  pressure  of  5000 
Ibs.  per  sq.  ft.  and  a  temperature  of  70°  F.     What  will  its  volume  be  at  a 
pressure  of  7000  Ibs.  per  sq.  ft.  and  a  temperature  of  100°  F.? 

11.  A  quantity  of  gas  occupies  a  volume  of  15  cu.  ft.  at  a  pressure  of  40 
Ibs.  per  sq.  ft.  and  a  temperature  of  60°  F.     What  will  be  its  volume  at  a 
temperature  of  70°  F.  and  a  pressure  of  30  Ibs.  per  sq.  ft.? 

12.  A  quantity  of  gas  occupies  a  volume  of  10  cu.  in.  at  a  pressure  of  7000 
Ibs.  per  sq.  ft.  and  a  temperature  of  50°  F.     What  will  be  its  volume  at  at- 
mospheric pressure  (14.7  Ibs.  per  sq.  in.)  and  a  temperature  of  70°  F.?    • 

13.  The  value  of  R  for  a  certain  gas  is  55.     One  pound  of  this  gas  occupies 
a  volume  of  12.8  cu.  ft.  at  a  pressure  of  14.7  Ibs.  per  sq.  in.     What  is  the  tem- 
perature of  the  gas?     What  will  be  the  volume  of  two  pounds  of  this  gas  if 
pressure  and  temperature  (ordinary  Fahrenheit  scale)  are  doubled? 

14.  Three  pounds  of  air  are  enclosed  in  a  nonexpansible  vessel.     The  pres- 
sure is  20  Ibs.  per  sq.  in.  and  the  temperature  is  80°  F.     The  value  of  R  is  53-34- 
What  is  the  volume  content  of  the  vessel?     What  will  be  the  pressure  of  the 
air  if  its  temperature  is  increased  to  180°  F.? 

15.  One-half  pound  of  nitrogen  gas  is  contained  in  a  cylinder  fitted  with  a 
piston.     The  temperature  of  the  gas  is  80°  F.  and  its  pressure  is 5  40 >   bs.  per 
sq.  in.     The  piston  moves  out  until  the  volume  of  the  gas  has  doubled  and 
it  is  then  found  that  its  pressure  is  20  Ibs.  per  sq.  in.     What  must  the  tempera- 
ture have  become?     (R  for  nitrogen  =  55.16.)  . 

16.  A  certain  gas  is  collected  over  mercury  and  measured.     It  is  found  to 
have  a  volume  of  10  cu.  in.  at  a  pressure  of  14.6  Ibs.  per  sq.  in.  and  a  tem- 
perature of  60°  F.     The  gas  is  then  passed  through  a  reagent  which  absorbs 
part  of  it  and  the  remainder  is  collected  over  mercury  and  measured.     11 
measures  6  cu.  in.  at  the  same  pressure  as  before  but  the  temperature  has 
changed  to  70°  F.  between  the  two  measurements.     What  percentage  c 
original  volume  was  absorbed  by  the  reagent? 

17.  The  products  of  combustion  from  a  boiler  reach  the  base  of  the  stack 


752 


HEAT-POWER  ENGINEERING 


at  a  temperature  of  500°  F.  At  the  top  of  the  stack  their  temperature  is  only 
200°  F.  Neglecting  the  slight  pressure  change  which  would  occur  during  the 
ascension,  determine  the  relative  values  of  the  cross-sectional  areas  at  top  and 
bottom  of  the  stack  to  give  equal  gas  velocities  at  the  two  points. 

1 8.  An  air  compressor  draws  into  its  cylinder  a  charge  of  air  at  a  pressure 
of  13.5  Ibs.  per  sq.  in.  and  a  temperature  of  60°  F.     It  compresses  this  air  to  a 
volume  equal  to  one-quarter  of  its  original  value  and  the  pressure  attained  is 
60  Ibs.     What  must  be  the  final  temperature  of  the  air? 

19.  A  diving  bell  is  to  be  used  for  executing  certain  work  under  water.     It  is 
made  in  the  form  of  a  flat-ended  cylinder  open  at  the  bottom.    The  inside  diam- 
eter is  12  ft.  and  the  inside  height  is  14  ft.     The  men  and  tools  accommodated 
within  the  bell  occupy  a  cubical  content  of  120  cu.  ft.     If  the  bell  is  lowered 
into  the  water  when  atmospheric  pressure  is  14.7  Ibs.  per  sq.  in.  and  tempera- 
ture is  60°  F.,  how  far  below  the  surface  can  the  bottom  of  the  bell  be  lowered 
if  the  water  has  a  temperature  of  40°  F.,  weighs  62.5  Ibs.  per  cu.  ft.,  and  is  not 
to  rise  to  a  height  of  more  than  4  ft.  from  the  bottom  of  the  bell?     Assume  that 
men  and  tools  remain  entirely  within  the  air  space,  that  they  do  not  change 
volume  with  pressure  change;    that  the  air  within  the  bell  acquires  the  same 
temperature  as  the  surrounding  water. 

20.  A  quantity  of  heat  equal  to  1000  B.t.u.  (=  A0  is  given  to  an  ideal 
gas  maintained  at  constant  volume.     What  are  the  numerical  values  of  the 
several  terms  in  the  equation  AQ  =  AS  +  A/  +  AE? 

21.  Two  pounds  of  a  gas  with  Cv  =  0.1662  and  Cp  =  0.2317  are  heated  at 
constant  volume  from  a  temperature  of  60°  F.  to  a  temperature  of  80°  F.,  and 
then  at  constant  pressure  to  a  final  temperature  of  100°  F. 

(a)  How  much  heat  is  supplied  to  the  gas? 

(b)  What  is  the  value  of  AS  for  each  part  of  the  process? 

(c)  What  is  the  value  of  AE  for  each  part  of  the  process? 

22.  The  true  specific  heat  of  a  certain  gas  is  0.1733  in  thermal  units.     The 
value  of  R  is  55.16,  what  is  the  value  of  Cp  for  this  gas? 

23.  Three  pounds  of  an  ideal  gas  are  heated  until  200  B.t.u.  per  Ib.  have 
been  supplied  it.     During  the  process  the  gas  expands  and  133,038  ft. -Ibs  of 
work  are  done  by  it.     Find  the  value  of  AS. 

24.  A  balloon  is  filled  with  hydrogen  gas  at  a  pressure  of  14.7  Ibs.  per  sq.  in 
and  a  temperature  of  60°  F.     The  balloon  is  spherical  in  shape  and  has  an 
internal  diameter  of  25  ft.     At  a  later  time  it  is  found  that  the  pressure  of  the 
gas  within  the  balloon  is  only  0.95  of  the  original  value  but  that  the  tempera- 
ture is  the  same  as  before.     What  fraction  of  the  original  weight  of  gas  must 
have  escaped  if  the  dimensions  of  the  balloon  have  not  changed?     How  much 
heat  would  have  had  to  be  removed  to  cause  the  pressure  to  fall  to  the  same 
extent  if  no  leakage  occurred?     (i  Ib.  of  hydrogen  at  32°  F.  and  14.7  Ibs./sq.  in. 
occupied  a  volume  of  178  cu.  ft.     R  =  766.5;    CP  =  3.41.)     What  would  be 
the  final  temperature? 

25.  Ten  pounds  of  air  (specific  volume  at  32°  and  14.7  Ibs.  =  12.387  cu.  ft.) 
are  contained  in  a  receiver  at  a  temperature  of  55°  F.  and  a  pressure  of  100 
Ibs.  per  sq.  in.     Air  leaks  out  until  at  a  later  time  the  pressure  in  the  receiver 
is  found  to  be  only  40  Ibs.  per  sq.  in.  with  a  temperature  of  50°  F.     What 
weight  has  leaked  out? 

26.  An  air  receiver  has  a  factor  of  safety  of  5  when  filled  with  air  at  a  pres- 
sure of  200  Ibs.  per  sq.  in.  and  a  temperature  of  100°  F.     What  amount  of 
heat  would  have  to  be  supplied  the  air  to  reduce  the  factor  of  safety  to  2.5  on 
the  assumption  that  the  cubical  content  of  the  receiver  remains  constant  with 
changing  temperatures.    (Cp  =  0.2374;  7  =  i-4°37-)    Assume  vol.  =  20  cu.  ft. 

27.  The  value  of  R  for  a  certain  gas  is  34.9.     How  much  external  work 
vill  be  done  by  five  pounds  of  this  gas  if  its  temperature  is  raised  from  50°  F. 
to  150°  F.  at  constant  pressure? 

28.  The  value  of  Cp  for  a  certain  gas  is  0.23  and  the  value  of  7  is  1.39. 
What  volume  must  this  gas  occupy  when  at  a  temperature  of  60°  F.  and  sub- 
jected to  a  pressure  of  150  Ibs.  per  sq.  in.?     Assume  5  Ibs.  of  gas. 

29.  A  certain  gas  with  molecular  weight  equal  to  28  occupies  a  volume  of 


PROBLEMS 


753 


12.8  cu.  ft.  per  Ib.     What  volume  will  another  gas  with  molecular  weight  of 
32  theoretically  occupy  when  at  the  same  temperature  and  pressure? 

30.  A  certain  gas  with  molecular  weight  of  44  weighs  0.1224  Ibs.  per  cu.  ft. 
at  standard  conditions.     Another  gas  has  a  molecular  weight  of  26.     What 
is  its   theoretical   density   under   the  same  conditions  of    temperature  and 
pressure? 

31.  A  water  pump  running  at  50  strokes  per  minute  delivers  I  cu.  ft.  of 
water  per  stroke.     An  air  chamber  is  to  be  fitted  to  this  pump  of  such  size 
that  the  discharge  pressure  on  the  pump  shall  vary  from  100  Ibs.  per  sq.  in. 
at  the  beginning  of  the  stroke  to  150  Ibs.  per  sq.  in.  at  the  end  of  the  stroke 
if  all  the  water  delivered  during  one  stroke  must  be  accommodated  in  the  air 
chamber.     The  temperature  of  the  water  and  of  the  air  in  the  chamber  re- 
main constant  at  60°  F.  and  no  air  is  absorbed  by  the  water,     (a)  What  must 
be  the  volume  of  the  air  chamber  if  R  for  air  is  equal  to  53.3?     (b)  Would 
there  be  any  economic  advantage  in  using  a  gas  with  R  =  96? 

32.  Assume  that  gas  is  to  be  used  for  the  doing  of  external  work  by  being 
heated  at  constant  pressure  through  a  certain  temperature  range.     If  a  large 
number  of  gases  are  available  but  only  one  pound  of  any  one  gas  can  be  used, 
would  you  select  the  gas  having  the  lowest  or  highest  value  of  R  if  maximum 
amount  of  work  was  a  consideration?     Why?     What  other  property  of  the 
gases  would  you  consider  if  size  of  machine  was  also  of  importance?     Why? 
Assuming  that  it  is  desired  to  determine  the  gas  which  would  give  the  maxi- 
mum amount  of  work  with  the  smallest  machine,  how  would  you  proceed? 


CHAPTER  V. 

1 .  (a)  How  much  work  can  be  done  by  two  pounds  of  air  expanding  at  a 
constant  pressure  of  50  Ibs.  per  sq.  in.  to  twice  the  original  volume  if  the  initial 
temperature  is  50°  F.?     (b)  What  will  be  the  final  temperature?     (c)  How 
much  heat  will  have  to  be  supplied  the  gas?     (Cp  =  0.2374.) 

2.  One-half  pound  of  nitrogen  is  inclosed  in  a  cylinder  fitted  with  a  fric- 
tionless  piston.     When  the  gas  has  a  temperature  of  100°  F.  the  pressure  upon 
the  piston  is  25  Ibs.  per  sq.  in.     It  is  desired  to  abstract  20  B.t.u.  from  the  gas 
without  changing  its  pressure.     What  will  be  the  temperature  drop  and  how 
much  must  the  volume  be  decreased?     (Cp  =  0.2438.) 

3.  A  vessel  with  a  capacity  of  5  cu.  ft.  is  filled  with  air  at  a  pressure  of  125 
Ibs.  per  sq.  in.  when  at  a  temperature  of  60°  F.     It  is  desirable  to  lower  the 
pressure  to  50  Ibs  per  sq.  in.     What  amount  of  heat  will  have  to  be  abstracted 
and  what  will  be  the  final  temperature  of  the  gas,  assuming  that  the  vessel 
does  not  change  in  size  with  change  of  temperature?     (R  =  53-34J  7  =  i-4°37-) 

4.  A  cylinder  permanently  closed  at  one  end  is  fitted  with  a  frictionless 
piston  and  stands  vertical  upon  its  closed  end  in  a  vacuum.     It  holds  a  volume 
of  I  cu.  ft.  of  gas  at  a  temperature  of  75°  F.,  and  a  pressure  of  20  Ibs.  per  sq.  in., 
the  pressure  being  maintained  by  the  weight  of  the  piston  and  superposed 
discs  of  metal.     The  temperature  is  raised  to  150°  F.  and  the  piston  is  pre- 
vented  from   rising  by  additional  weights  placed  upon  it.     (a)  What  per- 
centage of  the  original  weight  of  piston  and  discs  must  be  added?     (b)   If  no 
additional  weights  had  been  added  how  much  external  work  would  have  been 
done  by  the  expanding  gas? 

5.  How  much  work  must  be  done  to  compress  100  Ibs.  of  air  isothermally 
from  a  pressure  of  13  Ibs.  per  sq.  in.  at  a  temperature  of  70°  F.  to  a  pressure 
of  no  Ibs.  per  sq.  in.?     (Spec.  vol.  at  32°  F.  and  14.7  Ibs.  =  12.387.) 

6.  How  much  heat  must  be  absorbed  during  the  process  assumed  in  prob- 
lem 5  above?  i    L •   j     r  •    •     i 

7.  One  pound  of  air  expands  isothermally  in  a  cylinder  behind  a  tnctionless 
piston.     The  initial  pressure  is  100  Ibs.  per  sq.  in    the  initial  temperature  is 
50°  F.,  the  ratio  of  expansion  is  5.     (Spec.  vol.  at  32   F.  and  14.7  Ibs.  =  12.387.) 
(a)  What  amount  of  work  will  the  gas  do  upon  the  piston?     (b)  How  much 
heat  will  have  to  be  supplied  the  gas  during  the  expansion  f 


I 


754 


HEAT-POWER  ENGINEERING 


8.  Find  the  work  done  by  0.5  Ib.  of  carbon  dioxide  expanding  isothermally 
at  100°  F.  from  an  initial  pressure  of  100  Ibs.  per  sq.  in.  to  a  final  volume  of  10 
cu.  ft.     (Spec.  vol.  at  32°  and  14.7  Ibs.  =  8.1  cu.  ft.) 

9.  Air  is  compressed  at  constant  temperature  from  a  volume  of  60  cu.  ft. 
and  a  pressure  of  14.7  Ibs.  per  sq.  in.  to  a  volume  of  12  cu.  ft.     Find  (a)  final 
pressure,  (b)  heat  removed,  and  (c)  work  done  upon  the  gas. 

10.  Find  the  work  done  by  4  Ibs.  of  air  expanding  isothermally  from  a 
pressure  of  100  Ibs.  per  sq.  in.  to  20  Ibs.  per  sq.  in.,  the  final  volume  being 
80  cu.  ft. 

11.  Five  pounds  of  air  expand  isothermally  from  a  pressure  of  120  Ibs.  per 
sq.  in.  to  a  final  pressure  of  20  Ibs.  per  sq.  in.,  the  work  done  being  248,500  ft.- 
Ibs.     (R  =  53.3.)     Find  (a)  initial  volume,  (6)  final  volume,  (c)  initial  tem- 
perature, and  (d)  heat  supplied. 

12.  The  volume  of  I  Ib.  of  air  at  32°  F.  and  14.7  Ibs.  per  sq.  in.  =  12.387 
cu.  ft.      (a)  Find  work  done  during  the  isothermal  expansion  of  one  pound  of 
air  from  100  Ibs.  per  sq.  in.  to  20  Ibs.  per  sq.  in.  at  100°  F.  (loge  5  =  1.61.) 
(b)  Find  initial  and  final  volumes.   ^  (c)  Find  value  of  R. 

13.  A  given  weight  of  gas  occupies  3.09  cu.  ft.  and  is  under  a  pressure  of 
200  Ibs.  per  sq.  in.     It  expands  isothermally,  the  ratio  of  expansion  being  3. 
Find  (a)  final  volume,  (b)  ft. -Ibs.  of  work  done,  and  (c}  B.t.u.  necessary  to  do 
this  work. 

14.  Atmospheric  pressure  at  sea  level  on  a  certain  day  is  14.7  Ibs.  per  sq.  in. 
and  on  a  certain  mountain  it  is  12.5  Ibs.  per  sq.  in.     An  air  compressor  at 
each  place  compresses  isothermally  100  cu.  ft.  of  air  per  minute  (measured  at 
existing  atmospheric  pressure  and  same  temperature  in  each  case)  to  a  pres- 
sure of  80  Ibs.  per  sq.  in.     How  much  work  is  done  upon  the  gas  in  each  case? 
What  is  the  difference,  and  what  per  cent  of  the  smaller  quantity  is  used  in 
excess  in  the  less  favorable  location? 

15.  If,  in  the  preceding  problem,  each  compressor  had  raised  the  pressure 
to  five  times  atmospheric  pressure  at  its  own  location,  how  would  the  quantities 
of  work  compare? 

1 6.  A  gas  with  7  =  1.4  expands  adiabatically  from  an  initial  volume  of  10 
cu.  ft.  and  an  initial  pressure  of  100  Ibs.  per  sq.  in.  to  a  terminal  pressure  of 
15  Ibs.  per  sq.  in.     What  is  the  final  volume? 

17.  A  gas  with  j  =  1.35  expands  adiabatically  from  an  initial  volume  of 
0.4  cu.  ft.  and  an  initial  pressure  of  80  Ibs.  per  sq.  in.  to  a  final  volume  of  4 
cu.  ft.     What  is  the  final  pressure? 

1 8.  A  gas  with  7  =  1.41  is  compressed  adiabatically  from  an  initial  volume 
of  5  cu.  ft.  and  an  initial  pressure  of  15  Ibs.  per  sq.  in.  to  a  final  volume  of 
I  cu.  ft.     What  is  the  final  pressure? 

19.  A  gas  with  7  =  1.33  is  compressed  adiabatically  from  an  initial  volume 
of  2  cu.  ft.  and  an  initial  pressure  of  15  Ibs.  per  sq.  in.  to  a  final  pressure  of 
85  Ibs.  per  sq.  in.     What  is  the  final  volume? 

20.  One  pound  of  air  expands  adiabatically  in  a  cylinder  fitted  with  a 
frictionless  piston.     The  initial  pressure  is  100  Ibs.  per  sq.  in.;    the  initial 
temperature  is  50°  F.;  the  ratio  of  expansion  is  5.     (Spec.  vol.  at  32°  and  14.7 
Ibs.  =  12.387;   7  =  1.4037.)      (a)  What  amount  of  work  will  the  gas  do  upon 
the  piston?     (b)  How  much  heat  will  have  to  be  supplied  the  gas  during  the 
expansion?     (c)  Compare  with  results  of  problem  7. 

21.  Five  pounds  of  gas  with  7  =  1.4  expand  adiabatically  from  a  volume 
of  0.2  cu.  ft.  and  a  pressure  of  90  Ibs.  per  sq.  in.  to  a  final  pressure  of  18  Ibs. 
per  sq.  in.     (a)  What  is  the  final  volume?     (&)  How  much  external  work  is 
done  by  the  gas? 

22.  How  much  work  must  be  done  upon  two  pounds  of  gas  to  compress 
them  adiabatically  from  a  volume  of  2  cu.  ft.  and  a  pressure  of  14  Ibs.  per  sq. 
in.  to  a  final  pressure  of  80  Ibs.  per  sq.  in.?     The  value  of  7  is  1.4. 

23.  What  will  be  the  difference  in  the  amounts  of  work  required  to  com- 
press 5  cu.  ft.  of  free  air  (air  at  60°  F.  and  14.7  Ibs.  per  sq.  in.)  to  a  pressure  of 
90  Ibs.  per  sq.  in.  when  the  compression  is  adiabatic  and  when  it  is  isothermal? 
(7  =  14037.) 


PROBLEMS 

24.  Assume  that  an  air  compressor  can  be  so  arranged  as  to  compress  air 
either  isothermally  or  adiabatically.     It  receives  air  at  a  pressure  of  14  Ibs. 
per  sq.  in.  and  compresses  to  a  pressure  of  75  Ibs.  per  sq.  in.    (7  =  1.41.)     (a) 
How  much  work  would  be  done  in  compressing  an  initial  volume  of  I  cu.  ft. 
of  air  by  each  method?     (b)  What  would  be  the  percentage  of  saving  when 
using  the  more  economical  method? 

25.  Five  pounds  of  gas  have  an  initial  pressure  of  300  Ibs.  per  sg.  in.  and 
occupy  an  initial  volume  of  20  cu.  ft.     (Cp  =  0.238;  R  =  53.3.)     (a)  Find 
Cv  and  T\.     (b}  If  this  gas  is  expanded  adiabatically  to  a  pressure  of  150  Ibs. 
per  sq.  in.,  what  will  be  the  numerical  value  of  V2,  T2  and  work  done? 

26.  One-quarter  of  a  pound  of  gas  with  Cp  =  0.238  and  Cv  =  0.169  is  ex- 
panded adiabatically  from  V\  =  0.2  cu.  ft.  and  pi  =  300  Ibs.  per  sq.  in.  to 
p-i  =  150  Ibs.  per  sq.  in.     (a)  What  are  the  numerical  values  of  R,  T,  V2,  T2? 
(b)  What  is  the  numerical  value  of  work  done? 

27.  One-quarter  of  a  pound  of  air  is  compressed  adiabatically  from  13  Ibs. 
per  sq.  in.  and  60°  F.  to  a  pressure  of  100  Ibs.  per  sq.  in.     After  compression  its 
temperature  is  decreased  to  60°  F.  while  the  volume  is  maintained  constant. 
(a)  How  much  heat  will  have  to  be  abstracted  to  bring  this  about?     (b)  What 
will  be  the  final  pressure?     (c)  If  the  gas  is  now  allowed  to  expand  adiabati- 
cally to  a  pressure  of  13  Ibs.,  how  much  work  can  it  do  and  how  does  this 
compare  with  that  required  in  the  original  compression?     (d)  What  will  be 
the  volume  and  temperature  at  end  of  expansion  as  in  (c)  above?     (Spec.  vol. 
at  32°  and  14.7  Ibs.  =  12.387;   y  =  1.4037;    Cp  =0.2374.) 

28.  Using  logarithmic  cross-section  paper  determine  the  pressure  exerted  by 
a  gas  for  each  cubic  foot  of  volume  increase  when  expanding  according  to  the 
law  P71-35  =  constant,  from  an  initial  pressure  of  100  Ibs.  per  sq.  in.  and  an  ini- 
tial  volume  of  one  and  one-half  cu.  ft.  to  a  terminal  pressure  of  15  Ibs.  per  sq.  in. 

29.  Air  is  drawn  into  an  air  compressor  at  a  temperature  of  61°  F.  and  at 
atmospheric  pressure  (14.7  Ibs.  per  sq.  in.).     The  flash  point  of  the  oil  used 
to  lubricate  the  compressor  piston  is  350°  F.     If  compression  is  adiabatic, 
what  pressure  could  be  attained  in  the  compressor  if  the  maximum  allowable 
temperature  is  50  degrees  below  the  flash  point  of  the  oil?     (Assume  y  =  1.41.) 

30.  An  air  compressor  compresses  adiabatically  ipo  cu.  ft.  of  air  per  min- 
ute measured  at  initial  conditions  of  15  Ibs.  per  sq.  in.  and  60°  F.     The  final 
pressure  is  90  Ibs.  per  sq.  in.     (a)  Find  work  done  on  air  per  minute,     (b)  Find 
final   temperature,     (c)  Find  weight  of  air  compressed   per  minute.     (Spec, 
vol.  =  12.387  at32°F.  and  14.7  Ibs.;  R  =  53.3;  and  7  =  M1-) 

31.  The  initial  conditions  of  two  pounds  of  gas  are  pi  =  100  Ibs.  per  sq.  in. 
and  /i  =  60°  F.     (R  for  this  gas  is  53.3  and  y  =  1.41.)     (a)  How  much  work 
will  be  done  by  the  gas  if  it  expands  isothermally  to  a  final  pressure  of  15  Ibs. 
pcrsq.  in.?     (6)  If  the  expansion  is  adiabatic?     (c)  What  is  the  percentage 
gain  by  the  former  method?     (d)  How  is  this  gain  purchased?     (e)  How  do 
the  final  temperatures  compare? 

32.  Power  is  obtained  by  expanding  air  adiabatically  m  an  engine  cylinder. 
It  is  found  that  when  the  temperature  of  the  air  drops  below  32    F-  the  mois- 
ture which  is  carried  by  the  air  freezes  and  impairs  the  action  ot  the  engine. 
Air  is  received  by  the  engine  at  a  temperature  of  60°  F.  and  a  pressure  ot  IOG 
Ibs.  per  sq.  in.      (Assume  y  =  1.41  and  assume  further  that  the  quantity  o 
moisture  present  in  the  air  is  so  small  as  to  have  no  thermodynamic  effect 
i.e.,  all  formulas  may  be  used  as  though  dry  air  only  were  present.)     (a)  What 
is  the  lowest  pressure  to  which  the  air  can  expand  if  its  temperature  is  not  t< 
drop  below  32°  F.?     (b)  To  what  initial  temperature  would  it  be  necessary  to 
heat  the  air  in  order  that  it  may  be  possible  to  expand  to  15  Ibs.  per  sq.  in. 
without  dropping  below  the  minimum  allowable  temperature?  f 

33.  Air  is  available  for  use  in  a  compressed  air  *&!^  **£*"% 
65°  F.  and  at  a  pressure  of  125  Ibs.  per  sq.  m.     It  is  desired  to  preheat 
constant  pressure  to  such  a  temperature  that  it  will  not  drop  ^£a  *"£g*: 

WiSSS^^ 

if  CP  =  0.237? 


756  HEAT-POWER  ENGINEERING 

34.  How  much  work  will  be  required  to  compress  two  pounds  of  gas  from 
Vl  =  25  cu.  ft.  and  pi  =  13.5  Ibs.  per  sq.  in.  to  p2  =  75  Ibs.  per  sq.  in.  accord- 
ing to  the  equation  PF1-35  =  const.?  What  will  be  the  final  temperature  if 
the  initial  temperature  is  55°  F.? 

CHAPTER  VI. 

1.  Is  the  following  process  thermodynamically  reversible?     Why?     Gas  in 
contact  with  a  hot  body  with  the  same  temperature  as  the  gas,  receives  heat 
from  that  hot  body  while  expanding  isothermally  and  doing  work. 

2.  Is  the  following   process  thermodynamically  reversible?     Why?     Gas 
expands  isothermally  and  does  a  certain  amount  of  work  at  the  expense  of 
heat  received  from  a  hot  body  at  temperature  10  degrees  higher  than  that  of 
the  gas. 

3.  Is  the  following  process  thermodynamically  reversible?     Why?     A  gas  is 
made  to  expand  at  constant  pressure  by  being  brought  into  contact  with  a 
hot  body. 

4.  Is  the  following  process  thermodynamically  reversible?     Why?     A  gas 
maintained  at  constant  volume  has  its  pressure  decreased  by  being  brought 
into  contact  with  a  cold  body. 

5.  Is  the  following  process  thermodynamically  reversible?     Why?     Gas  is 
compressed  adiabal  ically  in  a  nonconducting  cylinder. 

6.  Is  the  following  process  thermodynamically  reversible?     Why?     Gas  is 
compressed  in  a  cylinder  with  metallic  walls. 

7.  Is    the    following    process    thermodynamically    reversible?     Why?     A 
blacksmith  strikes  his  anvil  forcibly  with  his  hammer. 

8.  Is  the  following  process  thermodynamically  reversible?     Why?     The 
hot  gases  resulting  from  the  combustion  of  fuel  within  a  boiler  furnace  flow 
up  a  smoke  stack  because  their  density  is  less  than  that  of  the  atmosphere 
surrounding  the  stack.     Is  the  process  going  on  in  the  stack  reversible? 

9.  Is  the  following  process  thermodynamically  reversible?     Why?     A  car- 
penter bores  a  hole  in  a  piece  of  wood  by  means  of  a  brace  and  bit. 

10.  Is    the    following    process   thermodynamically    reversible?     Why?     A 
machinist  cuts  a  thread  upon  a  bar  of  metal  which  is  rotated  in  a  lathe.     The 
bar  and  cutting  tool  are  kept  cool  by  a  stream  of  soap  solution.     Outline  the 
energy  changes  occurring  and  tell  whether  the  process  is  reversible  so  far  as 
these  energy  changes  are  concerned. 

11.  Assume  two  vessels  of  equal  cubical  content  arranged  as  in  Sect.  35  (b), 
one  containing  one  pound  of  air  at  a  temperature  of  60°  F.  and  a  pressure  of 
100  Ibs.  per  sq.  in.,  the  other  absolutely  void.     (Spec,  volume  of  air  at  32°  F. 
and  14.7  Ibs.  =  12.387).     Assume  that  it  is  possible  to  open  the  cock  between 
the  two  suddenly,  to  allow  gas  to  flow  from  the  high-pressure  to  the.  low-pres- 
sure vessel  until  both  have  the  same  pressure  of  gas,  and  then  to  close  the 
cock  suddenly  so  as  to  isolate  the  two  bodies  of  gas.     Assume  further  that 
the  material  "of  which  the  two  vessels  and  fittings  are  made  is  absolutely 
impervious  to  heat,     (a)  At  the  end  of  the  process  what  will  be  the  tempera- 
ture of  the  gas  contained  in  the  vessel  originally  charged  with  high-pressure 
gas?     (b)  At  the  end  of  the  process  what  will  be  the  temperature  of  the  gas 
contained  in  the  vessel  originally  void? 

CHAPTER  VII. 

1.  Find  the  change  of  entropy  of  4  Ibs.  of  a  gas  heated  at  constant  pressure 
from  a  temperature  of  60°  F.   to  a  temperature  of   1000°  F.     (Cv  =  0.192; 

R  =  45-3-) 

2.  If  6  Ibs.  of  air  are  cooled  at  constant  volume  until  the  final  pressure  is 
one-fourth  of  the  initial,  find  the  change  of  entropy.     (Cv  =  0.169.) 

3.  If  10  Ibs.  of  air  are  heated  at  constant  pressure  until  (2  =  2/1,  thereby 
adding  1185  B.t.u,  to  the  gas,  find  the  change  of  entropy,     (CP  =  0.237.) 


PROBLEMS 


757 


4.  Find  the  entropy  change  of  gas  which  is  compressed  isothermally  from 
a  pressure  of  14.7  Ibs.  per  sq.  in.  and  a  volume  of  60  cu.  ft.  to  a  volume  of  12 
cu.  ft.     The  gas  is  maintained  at  a  temperature  of  80°  F. 

5.  If  25  Ibs.  of  carbon  dioxide,  having  R  =  35.1,  are  compressed  from  a 
volume  of  50  cu.  ft.  to  a  volume  of  10  cu.  ft.,  the  pressure  remaining  constant, 
find  the  change  in  entropy.     (Cp  =  0.2008.) 

6.  If  5  Ibs.  of  air  expand  isothermally  from  a  pressure  of  100  Ibs.  per  sq.  in. 
to  a  pressure  of  20  Ibs.  per  sq.  in.  and  a  temperature  of  60°  F.,  find  the  change 
in  entropy.     (R  =  53.3.) 

7.  If  £  Ib.  of  air  is  allowed  to  expand  isothermally  at  a  temperature  of  70°  F. 
until  its  final  volume  is  4  times  its  initial  one,  find  its  change  in  entroov 
(R  =  53-3-) 

8.  Find  the  entropy  change  of  5  Ibs.  of  a  gas  which  expands  isothermally 
at  60°  F.  until  the  ratio  of  its  final  volume  to  initial  volume  is  14.8.     (Cp  = 
0.2008;  Cv  =  0.1548.) 

9.  Find  how  much  heat  would  be  required  to  heat  4  Ibs.  of  air  at  constant 
volume  so  that  it  would  experience  an  entropy  change  of  0.468,  its  initial 
temperature  being  60°  F.     (Cv  =  0.169.) 

10.  3  Ibs.  of  air  are  compressed  isothermally  from  a  volume  of  36  cu.  ft. 
and  pressure  of  15  Ibs.  per  sq.  in.  to  a  volume  of  9  cu.  ft.     Find  the  change 
in  entropy.     (R  =  53.3.) 

11.  At  the  end  of  the  compression  stroke  in  a  gas  engine  cylinder,  the  tem- 
perature is  found  to  be  970°  abs.  and  the  entropy  change  from  32°  F.,  and  same 
volume  as  at  end  of  compression,  is  0.55.     After  combustion  at  constant  vol- 
ume (pressure  rise  at  const,  vol.)  the  entropy  has  increased  to  0.96.    (Cv  =  0.16.) 

(1)  What  is  the  final  temperature  at  the  end  of  combustion? 

(2)  How  much  heat  has  been  added? 

12.  Imagine  0.4  Ib.  of  an  ideal  gas  to  expand  in  a  cylinder  which  prevents 
any  heat  flow  to  or  from  the  gas,  initial  pressure  being  100  Ibs.  per  sq.  in.  and 
initial  volume  |  cu.  ft.,  find  the  work  done  when  its  volume  has  become  3  cu.  ft. 
Find  change  in  temperature.      Find  the  change  in'  entropy.      (Cp  =  0.124. 
Cv  =  0.093.) 

CHAPTER  VIII. 

1.  A  Carnot  cycle  is  performed  with  gas  as  a  working  substance.      The 
temperature  of  the  hot  body  is  1000°  F.  and  that  of  the  cold  body  is  60°  F. 
How  much  work  is  done  per  cycle  if  the  heat  supplied  per  cycle  is  10  B.t.u.? 

2.  In  the  case  of  the  Carnot   cycle  as   above  with  higher  temperature 
1000°  F.  and  lower  temperature  60°  F.,  how  much  work  would  be  done  per 
cycle  if  the  heat  rejected  per  cycle  equals  10  B.t.u.? 

3.  A  Carnot  cycle  with  gas  as  working  substance  is  used  for  the  develop- 
ment of  power.     It  is  desired  to  obtain  100  ft.-lbs.  of  work  per  cycle.     The 
heat  supplied  per  cycle  equals  0.3  B.t.u.  and  the  temperature  of  the  hot  body 
is  500°  F.     What  must  be  the  temperature  of  the  cold  body? 

4.  A  Carnot  engine  is  to  be  used  as  a  heat  pump  to  remove  10  B.t.u.  per 
cycle  from  a  body  at  a  temperature  of  32°  F.  and  discharge  to  a  body  at  a 
temperature  of  100°  F.     (a)  How  much  energy  will  be  required  per  cycle  to 
operate  this  heat  pump?     (6)  How  much  will  be  required  if  the  upper  tem- 
perature is  200°  F.?     (c)  How  much  heat  will  be  discharged  to  the  hot  body 
in  each  case?  .  , 

5.  An  engine  using  air  as  a  working  substance,  receiving  heat  from  a  hot 
body  at  temperature  1000°  F.  and  rejecting  at  temperature  100   F.,  operates 
on  a  cycle  composed  of  an  isothermal  expansion,  an  adiabatic  expansion   an 
isothermal  compression,  and  an  isovolumic.     Is  this  a  reversible  cycle?     Why? 

6.  Draw  cycle  described  in  5  above  and  determine: 

(1)  Heat  supply  (positive  or  negative)  during  each  process. 

(2)  Work  done  (positive  or  negative)  during  each  process. 

(3)  Efficiency  of  cycle.  p  _ 

(4)  Carnot  efficiency  with  same  temperature  limits;  y  =  1.41;  A  -  53.3, 
W  =  %  Ib.;  r  =  2  for  the  isothermal  expansion. 


758  HEAT-POWER  ENGINEERING 

7.  One-half  of  a  pound  of  air  is  enclosed  in  a  cylinder  fitted  with  a  move- 
able   piston.     It   occupies  a  volume   of   3  cu.  ft.,  exerts  a   pressure  of    100 
Ibs.  per  sq.  in.,  and  the  area  of  the  piston  is  I  sq.  ft.     The  gas  is  expanded  at 
constant  pressure  to  a  volume  of  6  cu.  ft.;    the  pressure  is  then  dropped  at 
constant  volume  to  a  value  of  15  Ibs.  per  sq.  in.;   the  gas  is  then  compressed 
at  constant  pressure  to  a  volume  of  3  cu.  ft.;    lastly  the  pressure  is  raised  to 
100  Ibs.  per  sq.  in.  at  constant  volume. 

(a)  Draw  the  cycle  to  PV  coordinates  and  indicate  values  of  pressure,  vol- 
ume and  temperature  at  the  four  corners. 

(b)  Find  the  net  work  done  by  the  gas  during  one  cycle. 

(c)  Find  the  heat  supplied  or  rejected  during  each  process  and  the  net  heat 
change. 

(d)  Find  the  efficiency  of  the  cycle. 

(e)  Assuming  the  use  of  one  hot  and  one  cold  body  is  this  cycle  reversible? 
Why? 

8.  (a)  Draw  the  Carnot  cycle  to  PV  and  T<£  coordinates  for  the  following  con- 
ditions.    Two  pounds  of  nitrogen  are  used  as  working  substance.     The  maxi- 
mum temperature  is  1500°  F.  and  the  maximum  pressure  is  200  Ibs.  per  sq.  in. 
The  ratio  of  isothermal  expansion  is  2.     The  minimum  temperature  is  50°  F. 

(b)  Find  the  heat  supplied,  the  heat  rejected  and  the  work  done. 

(c)  Find  the  efficiency  of  the  cycle,  or  of  an  engine  using  the  cycle. 

9.  (a)  Determine   the   efficiencies   of  Carnot  cycle  engines  using  gaseous 
working  substances  when  the  hot  body  and  the  cold  body  have  the  following 
temperatures  respectively: 

.     Hot  Body  Temperature  Cold  Body  Temperature 

(1)  3000°  F.  500°  F. 

(2)  i500°F.  .  o°F. 
fo)  isoo°F.                               500°  F. 

\b)  Which  is  the  more  effective  method  of  increasing  the  efficiency,  raising 
TI  or  lowering  TV     Why? 

10.  If  the  maximum  and  minimum  temperatures  and  pressures  are  both 
given,  what  must  be  the  ratio  of  isothermal  expansion  in  a  Carnot  cycle  engine 
using  gas  as  a  working  substance? 

11.  An  engine  operating  on  the  Joule  cycle  has  the  following  conditions  at 
the  end  of  compression  Va  =  0.5  cu.  ft.;  pa  =  70  Ibs.  per  sq.  in.;   Ta  =  1800° 
abs.     After  constant  pressure  expansion  the  volume  is  0.75  cu.  ft.     For  the 
gas  used  Cp  =  0.26  and  Cv  —  0.19.     Temperature  at  end  of  expansion  is  900° 
abs.  and  at  the  beginning  of  compression  is  600°  abs.     Find 

(1)  Net  work  of  cycle. 

(2)  Efficiency  of  cycle. 

12.  A  gas  engine  operating  on  the  Otto  cycle  uses  0.15  Ib.  of  gas  per  cycle 
having  Cp  =  0.2056,  and  Cv  =  0.1457.     The  pressure  at  end  of  compression 
is  75  Ib.  per  sq.  in.  and  the  temperature  is  1000°  abs.     At  end  of  explosion 
line  the  temperature  has  risen  to  2500°  abs.;    at  the  end  of  expansion  the 
temperature  is  1800°  abs.  and  at  the  beginning  of  compression  it  is  720°  abs. 
Find: 

(1)  Work  during  expansion  and  compression. 

(2)  The  heat  sent  into,  and  the  heat  sent  out  of,  the  system. 

(3)  The  efficiency  of  the  cycle. 

13.  A  gas  engine  operating  on  the  Diesel  cycle  uses  an  oil,  the  products  of 
combustion  of  which  have  a  gamma  value  of  1.41.     The  weight  of  gas  used  is 
0.15  Ibs.     The  temperature  at  end  of  compression  is  1800°  abs.  and  at  end 
of  constant  pressure  expansion  is  2000°  abs.     The  clearance  is  8  per  cent  and 
the  piston  displacement  is  2  cu.  ft.  (Cp  =  0.2056,     Cv  =  0.1457.)     Find: 

(a)  Heat  added. 

(b)  Heat  rejected. 

(c)  The  pressure  obtained  at  beginning  and  end  of  each  process. 

(d)  The  entropy  changes  for  each  line. 


PROBLEMS  759 

14.  A  Rider  hot  air  engine,  operating  on  the  Stirling  cycle,  uses  0.066  Ibs. 
of  air.  The  temperature  of  the  hot  body  is  2000°  abs.  and  that  of  the  cold 
body  is  600°  abs.,  the  initial  volume  being  0.8  cu.  ft.  and  the  final  volume 
being  i  cu.  ft.  (Cp  =  0.237,  Cv  =  0.169.)  Lowest  pressure  in  cycle  =  14.7 
Ibs.  per  sq.  in.  Find: 

(a)  The  pressures  at  the  beginning  and  end  of  expansion,  and  at  the  end  of 
compression. 

(&)  Net  work  of  cycle,     (c)  Efficiency  of  cycle. 

15.  A  Diesel  gas  engine  operates  with  a  gas  haying  Cp  =  0.22  and  Cv  = 
0.156.  The  pressure  at  the  end  of  the  compression  is  550  Ibs.  per  sq.  in.;  t he- 
volume  is  o.i  cu.  ft.  and  the  temperature  2000°  abs.  At  the  beginning  of  the 
adiabatic  expansion  the  temperature  is  2400°  abs.  and  at  the  end  of  same  it 
is  1200°  abs.  Find  all  necessary  temperatures,  pressures  and  volumes  to 
determine: 

(a)  The  work  done  during  the  constant  pressure  and  adiabatic  expansions. 

(6)  Work  during  adiabatic  compression. 

(c)  Efficiency  of  cycle. 

1 6.  A  gas  engine  working  on  the  Otto  cycle  has  a  pressure  at  the  beginning 
of  compression  =  13  Ibs.  per  sq.    in.     Find   the   clearance   to  give  a  com- 
pression of  91  Ibs.  per  sq.  in.,  assuming  the  exponent  for  compression  to  be 
1.22.     If  the  initial  temperature  is  60°  F.  find  the  temperature  at  the  end  of 
compression. 

17.  Suppose  a  gas  engine  is  working  on  the  Otto  cycle,  under  the  following 
conditions:    Compression  pressure  =  80  Ibs.  per  sq.  in.;    pressure  after  ex- 
plosion =  240  Ibs.  per  sq.  in.     The  volume  at  the  beginning  of  compression  is 
6  cu.  ft.,  and  at  the  end  of  compression  it  is  2  cu.  ft.     (7  =  1.41.)     Find  work 
done  for  each  step  of  cycle  and  the  net  work  done. 

18.  With  the  same  data  as  in  the  previous  problem,  find  the  efficiency  of 
the  cycle,  the  heat  supplied  per  cycle  and  the  heat  rejected. 

19.  If  a  gas  engine  working  on  the  Otto  cycle  has  25  per  cent  clearance,  find 
the  efficiency  of  the  cycle.     (7  =  1.41.) 

20.  Find  the  horse  power  of  a  gas  engine  making  100  cycles  per  minute, 
each  cycle  transforming  50  B.t.u.  into  work. 

21.  How  many  B.t.u.  per  minute  will  be  required  to  develop  100  H.P.  in  a 
single-acting  4-stroke  cycle  gas  engine  running  200  R.P.M.  if  the  efficiency  of 
the  cycle  is  30  per  cent?     What  would  be  the  heat  input  per  cycle? 

CHAPTER  IX. 

1.  If  liquid  with  a  constant  specific  heat  equal  to  0.5  vaporizes  at  a  tem- 
perature of  150°  F.  when  the  pressure  is  atmospheric  and  solidifies  at  2   F.; 
(a)  What  is  the  value  of  q  for  atmospheric  pressure  figured  above  the  tempera- 
ture of  fusion?     (&)  What  is  the  value  of  q  figured  above  32°  F.  as  a  datum? 

2.  A  certain  liquid  has  a  variable  specific  heat  given  by  the  following  equa- 
tion,  Cp  =  0.7  +  0.003  t  -  o.oooi  t2  in   which   t  stands  for  temperature  m 
Fahrenheit  degrees.     It  vaporizes  at  a  temperature  of  100°  F.  under  atmos- 
pheric pressure  and  solidifies  at  -  35°  F.     What  is  the  numerical  value  of 
the  heat  of  the  liquid  figured  above  temperature  of  fusion  as  a  datum? 

3.  When  one   pound   of  a  certain   liquid  vaporizes  under  a  pressure  of 
35  Ibs.  per  sq.  in. ,  there  is  a  volume  change  of  50  cu.  ft.     The  total  amount  ot 
heat  added  to  cause  vaporization  of  liquid  already  at  vaporizing  temperature 
is  900  B  t  u.     (a)  What  is  the  numerical  value  of  the  latent  heat  of  vapor- 
ization?    (b)  What   is  the  numerical  value  of  the  external  latent  heat  of 
vaporization?     (c)  What  is  the  numerical  value  of  the  internal  latei 
vaporization?  .        vj-/- 

4.  A  certain  liquid  has  a  constant  specific  heat  of  0.85;    it  solidifies  at 
-  25°  F.  and  vaporizes  under  a  pressure  of  50  Ibs.  per  sq.  in.  at  a  temperatu   :  ot 
175°  F      The  total  heat  required  to  raise  the  temperature  of  one  pound  of 
material  from  60°  F.  and  so  cause  total  vaporization  at  a  pressure  of  50  Ibs  per 
sq.  in.  is  equal  to  1250  B.t.u.     (a)  What  is  the  numerical  value  of  q  for  these 


760 


HEAT-POWER  ENGINEERING 


conditions,  figured  above  fusion  temperature  as  a  datum?  (b)  What  is  the 
numerical  value  of  r  for  these  conditions?  (c)  What  is  the  numerical  value 
of  X  for  these  conditions? 

5.  The  pressure  of  a  certain  saturated  vapor  at  a  temperature  of  250°  F. 
is  75  Ibs.  per  sq.  in.     What  will  be  the  temperature  of  vaporization  of  this 
material  under  a  pressure  of  75  Ibs.  per  sq.  in.? 

6.  The  latent  heat  of  vaporization  of  a  certain  material  under  certain  con- 
ditions is  525  B.t.u.  and  the  heat  of  the  liquid  is  210  B.t.u.     What  will  be  the 
heat  above  the  chosen  datum  associated  with  5  pounds  of  the  vapor  of  this 
material  when  it  has  a  quality  of  85  per  cent? 

7.  Three-quarters  of  a  pound  of  liquid  and  one-quarter  of  a  pound  of  the 
vapor  of  that  liquid  have  been  standing  in  a  closed  vessel  for  a  considerable 
length  of  time.     The  temperature  of  the  liquid  is  75°  F.      (a)  What  is  the  con- 
dition of  the  vapor?    Why?     (b)  What  is  the  temperature  of  the  vapor?    Why? 

8.  The  average  constant  pressure  specific  heat  of  a  certain  vapor  over  a 
temperature  range  of  100  degrees  starting  at  the  temperature  of  vaporization  at 
a  pressure  of  100  Ibs.  per  sq.  in.  is  0.4.     The  internal  latent  heat  of  vaporization 
at  this  pressure  is  700  B.t.u.     The  external  work  done  during  vaporization  is 
46,600  ft. -Ibs.     The  specific  heat  of  the  liquid  is  constant  and  equal  to  0.9 
over  the  temperature  range  of  200  degrees  between  datum  temperature  and 
the  temperature  of  vaporization  under  the  pressure  given  above.     What  is 
the  total  heat  associated  with  10  Ibs.  of  this  superheated  vapor  at  a  temper- 
ature of  100  degrees  higher  than  its  temperature  of  vaporization  at  the  assumed 
pressure? 

9.  A  certain  material  has  a  latent  heat  of  vaporization  of  700  B.t.u.  at 
atmospheric   pressure.     The   constant   pressure   specific   heat   of   its   super- 
heated vapor  at  atmospheric  pressure  is  0.5.     If  7  Ibs.  of  100°  superheated 
vapor  are  brought  into  intimate  contact  with  5  Ibs.  of  75  per  cent  vapor  of  the 
same  material  and  the  combination  is  maintained  at  atmospheric  pressure, 
what  will  be  the  ultimate  condition  of  the  resulting  product? 

10.  A  gas  occupying  a  vessel  with  internal  volume  of  I  cu.  ft.  exerts  a 
pressure  of  10  Ibs.  per  sq.  in.     Another  gas  in  a  similar  vessel  exerts  a  pressure 
of  15  Ibs.  per  sq.  in.     What  will  be  the  pressure  on  the  walls  if  both  gases 
simultaneously  occupy  one  of  the  vessels? 

n.  A  certain  space  is  saturated  with  a  vapor  at  a  temperature  of  250°  F. 
which  exerts  a  pressure  of  17  Ibs.  per  sq.  in.  Air  at  the  same  temperature  as 
the  vapor  is  pumped  into  the  same  space  until  the  pressure  has  risen  to  25  Ibs. 
sq.  in.  What  weight  of  air  occupies  each  cubic  foot  of  the  space  if  the  spe- 
cific volume  of  air  at  32°  F.  and  14.7  Ibs.  per  sq.  in.  is  12.387? 

12.  A  certain  liquid  is  vaporized  in  a  closed  vessel  from  which  the  vapor  is 
allowed  to  escape  as  fast  as  generated.  The  pressure  of  the  vapor  in  question 
at  the  temperature  within  the  vessel  should  be  100  Ibs.  per  sq.  in.  but  a  pres- 
sure gauge  indicates  a  pressure  of  102  Ibs.  per  sq.  in.  The  excess  is  supposed 
to  be  due  to  air  mixed  with  the  vapor.  The  value  of  R  for  air  is  53.34.  How 
much  air  must  be  present  per  cubic  foot  of  space?  Assume  temperature  of 
100°. 

CHAPTER  X. 

1.  By  means  of  the  steam  table  find  the  temperature,  total  heat,  heat  of 
the  liquid,  internal  latent  heat,  and  external  latent  heat  for  one  pound  of  dry 
saturated  steam  having  the  following  absolute  pressures  in  Ibs.  per  sq.  in.: 
I5»  50.  80,  125,  175  and  300. 

2.  Determine  from  the  steam  table  the  space  filled  by  10  Ibs.  of  dry  satu- 
rated steam  under  an  absolute  pressure  of  200,  175,  135,  100,  80  and  10  Ibs. 
per  sq.  in. 

3-  By  means  of  the  steam  table  determine  the  number  of  pounds  of  steam 
that  will  be  required  to  fill  10  cu.  ft.  when  under  an  absolute  pressure  of  200, 
115,  40  and  5  Ibs.  per  sq.  in.:  (a)  If  the  quality  is  100  per  cent;  (b)  If  the 
quality  is  80  per  cent. 

4,   Determine  by  means  of  the  steam  table  the  entropy  of  the  liquid,  and 


PROBLEMS  761 

the  entropy  of  vaporization  for  I  Ib.  of  steam  under  the  following  absolute 
pressures:  15,  50,  80,  125,  175,  and  300  Ibs.  per  sq.  in.  (a)  If  the  quality  is 
100  per  cent,  (b)  If  the  quality  is  90  per  cent. 

5.  Assuming  the  specific  heat  of  water  to  be  unity,  compute  the  entropy  of 
the  liquid  for  a  pound  of  water  heated  to  the  point  of  vaporization  for  an  abso- 
lute pressure  of  100  Ibs.  per  sq.  in.     Find  the  per  cent  error  by  comparison 
with  steam  table  values. 

6.  Compute  the  entropy  of  vaporization  for  a  pound  of  steam  having  the 
following  temperatures:   400,  300  and  200°  F.,  the  corresponding  latent  heats 
being  827.2,  909.5  and  977.8  B.t.u. 

7.  (a)  Determine  from  the  steam  tables  the  amount  of  heat  required  to 
make  a  pound  of  steam,  having  a  pressure  of  100  Ibs.  per  sq.  in.  abs.,  by  heat- 
ing the  water  to  the  temperature  of  vaporization  from  a  temperature  of  100°  F., 
and  then  vaporizing  until  the  quality  is  80,  90  and  100  per  cent. 

(b)  Draw  the  T<£-diagram  for  (a). 

8.  With  the  same  data  as  in  (7)  find: 

(a)  The  amount  of  heat  required  to  superheat  the  steam  100°,  200°.     Take 
Cp  =  0.50.     (6)   Draw  the  T<£-chart  for  (a). 

9.  Determine  by  means  of  the  steam  table  the  quality  of  steam  containing 
1029  B.t.u.  of  intrinsic  heat  and  having  a  pressure  of  125  Ibs.  per  sq.  in.  abs. 

10.  Determine  by  means  of  the  steam  table  the  intrinsic  heat  added  to 
I  Ib.  of  water  in  heating  it  from  90°  F.  to  444°  F.,  if  the  pressure  is  keot  con- 
stant at  1 20  Ibs.  per  sq.  in.  abs. 

11.  Heat  is. added  to  I  Ib.  of  steam  at  a  constant  pressure  of  80  Ibs.  per  sq. 
in.  abs.,  thereby  increasing  the  quality  from  0.4  to  0.9.     Find  by  means  of 
steam  tables:    (a)  How  much  heat  is  added,     (b)  How  much  internal  heat  is 
added.      (c)   How  much  external  heat  is  added,      (d)  How  much  work  in  ft.- 
Ibs.  is  done,     (e)   How  much  the  volume  of  the  steam  is  increased. 

12.  Find  by  means  of  the  steam  table  the  heat  required  to  evaporate  50  Ibs. 
of  water  having  a  temperature  of  102°  F.  when  pumped  into  a  boiler,  the  steam 
pressure  in  which  is  125  Ibs.  per  sq.  in.  abs. 

13.  If  the  temperature  of  the  feed  water  is  200°,  find  by  means  of  the 
stearn  table  the  amount  of  heat  required  to  make  100  Ibs.  of  steam  having  a 
quality  of  95  per  cent,  the  pressure  being  constant  at  175  Ibs.  per  sq.  in.  abs. 

14.  By  means  of  the  steam  table  determine  the  volume  occupied  by  the 
steam  in  the  previous  problem. 

15.  Compute  the  external  work  performed  in  vaporizing  4  Ibs.  of  water 
into  dry  steam  under  a  constant  pressure  of  100  Ibs.  per  sq.  in.  abs.     Com- 
pare with  tabular  value. 

1 6.  Find  the  pressure  equivalent  to  the  internal  force  which  must  be 
overcome  in  vaporizing  I  Ib.  of  water  under  a  pressure  of  100  Ibs.  per  sq.  in.  abs. 

17.  Steam  in  a  boiler  is  under  an  absolute  pressure  of  100  Ibs.  per  sq.  in., 
and  is  superheated  150.6°. 

(a)  Find  by  Tumlirz  equation  the  specific  volume  of  this  steam. 

(b)  Find  the  total  heat  of  this  steam  if  its  specific  heat  is  0.51. 

(c)  Show  part  (b)  on  a  T<£-chart. 

1 8.  Find  the  heat  of  superheat,  and  the  total  intrinsic  heat  energy  for  the 
steam  in  the  previous  problem. 

19.  Sketch  on  a  T0-chart  the  water  curve  and  saturation  curve  for  a  pound 
of  water  vapor  between  the  pressure  limits  of  2  and  200  Ibs.  per  sq.  m.  abs. 
showing  the  intermediate  values  for  the  following  pressures,  10   50  and  loo. 

(a)  Mark  on  the  sketch  the  value  of  the  temperature  and  the  entropy  for 
each  point,  estimating  the  distances  as  closely  as  possible. 

(b)  Give  the  numerical  values  for,  and  show  what  areas  represent,  the  heat 
of  the  liquid,  and  the  latent  heat  for  the  two  limiting  pressures  given  above. 

(c)  If  you  had  drawn  the  above  sketch  to  the  following  scale:    I     =  100   of 
temperature  and  i"  =  £  unit  of  entropy,  how  many  sq.  in.  would  represent:  the 
total  heat  of  the  steam  for  the  pressure  of  200  Ibs.  per  sq.  m.  abs.?     Indicate 
this  area  on  your  sketch.  r 

20.  Find  the  volume  of  a  boiler  containing  1000  Ibs,  of  water  and  o  IDS.  of 


762  HEAT-POWER  ENGINEERING 

dry  saturated  steam  under  a  pressure  of  135  Ibs.  per  sq.  in.  abs.  What  per 
cent  of  this  volume  is  occupied  by  each?  What  per  cent  of  the  total  heat 
energy  above  32°  is  contained  in  each? 

21.  How  much  water  having  a  temperature  of  60°  F.  will  be  required  to 
condense  3000  Ibs.  of  steam  per  hour,  the  quality  of  the  steam  being  90  per 
cent  and  the  pressure  within  the  condenser  being  I  Ib.  per  sq.  in.  abs.?     How 
much,  if  the  condenser  pressure  is  5  Ibs.  per  sq.  in.?     Assume  the  cold  water  to 
be  thoroughly  mixed  with  the  steam. 

22.  Four  pounds  of  steam  having  an  absolute  pressure  of  125  Ibs.  per  sq. 
in.  are  condensed  by  flowing  into  200  Ibs.  of  water,  the  temperature  of  which 
is  thereby  raised  from  60  to  80°  F.     Find  the  initial  quality  of  the  steam. 

23.  Find  the  total  heat  necessary  to  change  500  Ibs.  of  water  from  a  feed 
pump  temperature  of  80°  F.  into  superheated  steam  having  a  temperature 
of  1000°  F.,  the  boiler  pressure  remaining  constant  at  125  Ibs.  per  sq.  in.  abs. 
Take  the  specific  heat  of  superheated  steam  for  this  range  to  be  0.50. 

24..  One  pound  of  water  at  a  temperature  of  60°  F.  enters  a  boiler  and  is 
vaporized  under  a  pressure  of  115  Ibs.  per  sq.  in.  abs.  until  it  becomes  dry  and 
saturated  steam.  How  many  pounds  of  water  might  have  been  vaporized  if 
the  same  amount  of  heat  had  been  added  to  the  water  at  a  temperature  of 
212°  and  changed  into  dry  steam  at  this  temperature? 

25.  How  much  steam  with  a  quality  of  90  per  cent  and  an  absolute  pressure 
of  3.00  Ibs.  per  sq.  in.  is  condensed  in  a  surface  condenser  using  14,500  Ibs.  of 
circulating  (or  condensing)  water  per  hour,  the  water  entering  the  condenser 
at  55°  F.  and  leaving  it  at  115°  F.? 

26.  An  engine  develops  15  horse  power  using  28  Ibs.  of  steam  per  horse- 
power hour.     If  the  engine  exhausts  its  steam  with  a  quality  of  85  per  cent  and 
pressure  of  15  Ibs.  per  sq.  in.  abs.  to  the  atmosphere,  find  the  amount  above 
32°  F.  discharged  per  minute.     What  would  be  the  maximum  amount  of  heat 
that  could  be  abstracted  per  minute  from  this  exhaust  steam  by  means  of 
water  which  is  to  attain  a  temperature  of  200°? 

27.  For  each  pound  of  coal  having  a  heating  value  of  14,300  B.t.u.,  a  certain 
boiler  evaporated  10  Ibs.  of  water  into  steam,  with  quality  of  95  per  cent,  the 
pressure  being  constant  at  145  Ibs.  per  sq.  in.  abs.,  and  the  temperature  of 
the  feed  water  being  188°  F. 

Suppose  that  another  boiler,  using  this  same  kind  of  coal,  evaporated  9  Ibs. 
of  water  into  dry  steam,  under  constant  pressure  of  125  Ibs.  per  sq.  in.,  from 
a  feed  water  temperature  of  121°  F. 

Find  the  heat  given  water  and  steam  by  each  boiler,  and  the  boiler  efficiencies 
(efficiency  =  heat  supplied  water  and  steam  -r-  heat  supplied  boiler). 

28.  Determine  by  means  of  the  T0-diagram  the  pressure  at  which  steam 
will  become  dry  and  saturated  by  expanding  reversibly  and  adiabatically 
from  a  pressure  of  100  Ibs.  per  sq.  in.  and  a  superheat  of  50°  F. 

29.  Determine  by  means  of  the  T$-diagram  the  final  condition  of  steam 
which  expands  reversibly  and  adiabatically  from  an  initial  superheat  of  150°  F. 
at  a  pressure  of  150  Ibs.  per  sq.  in.  to  a  final  pressure  of  15  Ibs.  per  sq.  in. 

30.  Determine  by  means  of  the  T0-diagram  the  volume  of  10  Ibs.  of  80 
per  cent  steam  at  a  pressure  of  75  Ibs.  per  sq.  in. 

31.  By  means  of  the  values  given  in  the  steam  table  draw  a  T</>-diagram 
for  steam  to  such  a  scale  as  to  show  the  extreme  upper  parts  of  the  water  and 
saturation  lines.     Explain  the  shape  produced. 

32.  Draw  by  means  of  values  given  in  the  steam  tables  a  physical  equil- 
ibrium diagram  for  liquid  water  and  water  vapor  between  the  critical  tempera- 
ture and  100°  F.  similar  to  part  of  Fig.  34.       (Use  care  in  choosing  scales  so 
that  entire  diagram  can  be  drawn  on  sheet  chosen.) 

33.  Determine  by  means  of  the  Mollier  Chart  the  final  conditions  of  steam 
expanding  reversibly  and  adiabatically  from  an  initial  superheat  of  400  degrees 
at  a  pressure  of  100  Ibs.  per  sq.  in.  to  a  final  pressure  of  10  Ibs.  per  sq.  in. 

34.  Find  from  the  Mollier  Chart  the  heat  which  must  be  supplied  to  change 
10  Ibs.  of  95  per  cent  steam  at  20  Ibs.  per  sq.  in.  to  steam  superheated  200 
degrees  F.  at  the  same  pressure.* 

*  The  Ellenwood  Chart  may  be  used  instead  of  the  Mollier  in  this  and 
subsequent  problems. 


PROBLEMS 


CHAPTER   XI. 


763 


1.  One  pound  of  dry  saturated  steam  at  an  absolute  pressure  of  100  Ibs  oer 
sq.  in.  is  expanded  along  a  reversible  adiabatic  until  its  pressure  is  so  Ibs'  per 
sq.  in.  abs.     Find  its  new  quality,  volume  and  the  work  done 

2.  Find  the  same  quantities  with  the  same  data  as  in  the  previous  problem 
except  the  second  pressure,  which  is  15  Ibs.  per  sq.  in. 

3.  Steam  is  formed  in  a  boiler  at  a  constant  pressure  of  loolb.  pfcrsq.  in  abs 
and  with  such  a  quality  that  a  pound  occupies  only  3.54  cu.  ft.     Heat  is  added 
at  constant  pressure  until  the  steam  is  superheated  150  degrees       (a)  Deter 
mine  the  quality  at  the  beginning  of  the  superheating  process,     (b)  Find  the 
total  heat  added  and  the  heat  of  superheat,     (c)  Show  on  T</>-chart 

4.  How  much  external  work  was  done  in  the  previous  problem  during  the 
period  of  superheating?     What  is  the  total  intrinsic  heat  energy  at  the  point 
of  maximum  superheat? 

5.  Steam  is  contained  in  a  cylinder,  at  an  absolute  pressure  of  125  lb«  per 
sq.  in.  and  a  quality  of  80  per  cent.     It  expands  isentropically  to  25  Ibs.  per 
sq.  m.  abs.     (a)  Find  volume  occupied  by  steam  before  expansion      (b)  Find 
quality  at  end  of  expansion,     (c)  Find  work  done  in  ft.-lbs.  during  adiabatic 
expansion. 

6.  For  previous  problem  find  the  total  heat  of  steam  at  the  beginning  and 
at  the  end  of  expansion;   also  the  intrinsic  heat  energy  used  UD  in  exoandine- 
adiabatically. 

7.  Steam  with  a  superheat  of  200  degrees  and  an  absolute  pressure  of  125 
Ibs.  per  sq.  in.  expands  at  constant  entropy  in  a  cylinder,  until  its  pressure 
has  been  reduced  80  per  cent.     How  much  work  has  been  accomplished? 

(a)  What  is  the  total  heat  of  the  steam  at  point  of  maximum  superheat? 

(b)  Show  on  PV-  and  T0-charts. 

8.  If  the  steam  of  previous  problem  expands  further  to  15  Ibs.  per  sq.  in., 
find  quality  and  intrinsic  heat  at  end  of  the  expansion. 

9.  Steam  in  a  cylinder  at  a  pressure  of  25  Ibs.  per  sq.  in.  abs.  and  a  quality 
of  90  per  cent  is  compressed  along  a  reversible  adiabatic  until  just  dry  and 
saturated. 

(a)  What  are  the  temperature,  pressure,  and  specific  volume  at  end  of  com- 
pression? 

x  ip.  Steam  at  an  absolute  pressure  of  175  Ibs.  per  sq.  in.  is  confined  in  a 
metal  cylinder.  Heat  is  abstracted  at  constant  volume  until  its  temperature 
pecomes  240°  F.  The  steam  is  initially  dry  and  saturated. 

(a)  Find  the  quality  at  the  end  of  change. 

(b)  Find  the  amount  of  heat  abstracted  during  the  process. 

(c)  Show  on  PV-  and  T<£-fields. 

11.  Superheated  steam  exists  in  a  cylinder  at  a  pressure  of  25  Ibs.  per  sq. 
in.  abs.  and  a  temperature  of  366°  F. 

(a)  Determine  volume  of  steam  at  this  point. 

(b)  Isothermal  compression  occurs  until  the  steam  is  just  dry  and  saturated; 
how  much  heat  has  been  abstracted?     Show  on  T<£-chart. 

12.  Steam  at  a  pressure  of  125  Ibs.  per  sq.  in.  abs,  and  a  quality  of  80.4 
per  cent  has  heat  abstracted  at  constant  volume  until  the  pressure  becomes 
15  Ibs.  per  sq.  in.  abs. 

(a)  Find  quality  at  end  of  the  process. 

(b)  Find  volume  at  beginning  and  end  of  process. 

(c)  Find  intrinsic  heat  change  during  process. 

13.  One  pound  of  steam  under  a  pressure  of  120  Ibs.  per  sq.  in.  abs.  expands 
isentropically  until  its  pressure  is  reduced  50  per  cent;    find  its  new  quality, 
if  its  initial  quality  was  0.2,  0.4,  0.6,  0.8,  i.o.     Show  each  of  the  above  expan- 
sions on  T0-chart.     Tabulate  results. 

14.  If  a  pound  of  dry  saturated  steam  under  a  pressure  of  150  Ibs.  per  sq.  in. 
abs.  is  cooled  at  constant  volume  to  a  temperature  of  59°  F.,  find  its  new 
quality,  pressure  and  the  heat  removed.     Show  on  T#-chart. 

15.  Steam  with  70  per  cent  quality  is  heated  at  a  constant  pressure  of  125 


764  BEAT-POWER  ENGINEERING 

Ibs.  per  sq.  in.  abs.  until  it  becomes  just  dry  and  saturated.     More  heat  is  then 
added  isothermally  until  a  pressure  of  25  Ibs.  per  sq.  in.  abs.  is  reached. 

(a)  Find  heat  added  during  both  processes. 

(b)  Find  intrinsic  heat  gained  during  each  operation. 

16.  If  a  pound  of  steam  with  quality  of  70  per  cent  and  pressure  of  20  Ibs.  per 
sq.  in.  abs.  has  heat  removed  from  it  while  maintained  at  constant  volume, 
thereby  reducing  its  pressure  to  15  Ibs.  per  sq.  in.  abs.,  find  its  final  quality 
and  the  heat  removed. 

17.  Dry  saturated  steam  having  a  pressure  of  165  Ibs.  per  sq.  in.  abs.  has  heat 
abstracted  from  it  while  maintained  at  constant  volume  until  its  pressure 
becomes  25  Ibs.  per  sq.  in  abs. 

(a)  Find  the  heat  abstracted. 

(b)  Find  the  final  quality  of  the  steam. 

(c)  Find  intrinsic  heat  change  during  process. 

18.  Fifteen  pounds  of  dry  saturated  steam  under  a  pressure  of  no  Ibs./sq. 
in.  abs.  are  enclosed  in  a  metallic  tank,  and  this  tank  is  then  immersed  in 
looo  Ibs.  of  water  at  a  temperature  of  60°  F.    If  the  tank  is  left  in  the  cold  water 
until  the  pressure  within  has  reached  atmospheric  (14  7),  find  the  temperature 
of  the  cold  water  and  the  quality  of  the  steam.     (Assume  the  tank  to  be  a 
perfect  conductor  and  that  there  are  no  heat  losses.) 

19.  Given  a  pound  of  steam  with  a  quality  of  80  per  cent  and  a  pressure  of 
loo  Ibs.  per  sq.  in.  abs.     Find  the  heat  required  and  the  work  done  to  double 
its  volume  at  constant  pressure. 

20.  Suppose  a  pound  of  dry  saturated  steam  having  an  absolute  pressure  of 
150  Ibs.  per  sq.  in.  expands  isothermally  until  its  volume  is  doubled;  find  the 
work  done,  heat  supplied  and  final  pressure. 

21.  Work  previous  problem,  starting  with  the  steam  having  a  quality  of 
45  per  cent . 

22.  Find  the  work  done  in  ft. -Ibs.  in  superheating  one  pound  of  steam 
100  degrees  at  a  constant  pressure  of  68  Ibs.  per  sq.  in.  abs.     Find  the  change 
in  the  intrinsic  energy  of  the  steam.     Find  the  change  in  volume  and  the  exter- 
nal work. 

23.  Suppose  one  pound  of  steam  under  an  abs.  pressure  of  100  Ibs.  I  sq.  in. 
and  a  quality  of  90  per  cent  expands  along  reversible  adiabatic  to  a  pressure 
of  2  Ibs./sq.  in.  abs.     Find  its  new  quality,  volume  and  the  work  done. 

24.  Suppose  the  steam  in  the  previous  problem  to  have  been  superheated 
200  degrees;   find  the  same  quantities. 

25.  Given  a  pound  of  steam  under  a  pressure  of  15  Ibs./sq.  in.  abs.  and 
quality  of  50  per  cent.     If  heat  is  added  while  it  is  maintained  at  constant 
volume  until  its  quality  is  unity,  find  the  heat  required,  the  final  temperature 
and  the  pressure. 

CHAPTER   XII. 

1.  An  engine  using  water  vapor  and  operating  on  the  Carnot  cycle,  as  in 
Sect.  91.  between  the  pressure  limits  of  185  Ibs.  and  25  Ibs.  per  sq.  in.  begins 
adiabatic  expansion  at  80  per  cent  quality. 

(a)  Find  the  qualities  at  end  of  expansion  and  at  beginning  of  adiabatic 
compression. 

(b)  Find  the  work  accomplished  in  ft. -Ibs. 

(c)  Find  the  efficiency  of  the  cycle  by  two  methods. 

(d)  Show  the  cycle  on  both  PV-  and  T>-fields. 

2.  With  the  same  initial  temperature  and  the  same  back  pressure  as  in 
previous  problem,  suppose  adiabatic  expansion  to  start  from  a  point  in  the 
superheated  region  where  the  pressure  is  60  Ibs.  per  sq.  in.     Cp  =  0.53. 

(a)  Determine  conditions  of  the  steam  at  the  end  of  the  adiabatic  expansion. 
(6)  Find  the  work  accomplished  in  ft. -Ibs. 

(c)  Find  the  efficiency  of  the  cycle. 

(d)  Show  the  cycle  on  both  PV-  and  T<£-fields. 

3.  Given  the  initial  pressure  of  a  Carnot  Cycle  with  steam  as  working  sub- 
stance at  135  Ibs.  per  sq.  in.  and  the  final  pressure  25  Ibs.  per  sq.  in.     The 


PROBLEMS 


isothermal  expansion    starts  with  water  and  the  steam  at  the  beginning  of 
adiabatic  expansion  is  just  dry  and  saturated. 
(a)  Find  the  heat  added  and  the  heat  rejected 

' 


c  de  Find  the  intrinsic  Cnergy  at  the  banning'  and  end  of  each  line  of  the 

(c)  Find  the  efficiency  of  the  cycle. 

(d)  Show  on  T0-chart. 

4.  What  is  the  efficiency  of  the  Carnot  cycle  for  a  steam  engine  receiving 
dry  saturated  steam  at  a  pressure  of  150  Ibs.  per  sq.  in.  abs.  and  exhausting  it 
at  a  pressure  of  15  Ibs.  per  sq.  in.  abs. 

Show  on  the  PV-  and  T0-charts. 

5.  If  the  exhaust  pressure  in  the  previous  problem  had  been  2  Ibs  per  sq 
in.  abs.  what  would  have  been  the  efficiency? 

Show  on  PV-  and  T</>-charts. 

6.  If  the  engine  in  problem  4  exhausts  8000  B.t.u.  per  min.,  what  is  its 
power? 

7.  If  the  engine  in  problem  5  exhausts  8000  B.t.u.  per  min.,  what  is  its 
power? 

8.  The  adiabatic  expansion  of  a  Carnot  cycle  which  starts  with  liquid 
at  the  temperature  of  vaporization  begins  with  a  steam  pressure  of  25  Ibs.  per 
sq.  in.  abs.  and  a  temperature  of  344.4°  F. 

This  expansion  ends  when  a  temperature  of  213°  F.  has  been  reached. 
Find  the  heat  supplied,  heat  rejected  and  the  efficiency  of  the  cycle.  Check 
the  efficiency  by  a  second  method. 

Show  on  T</>-chart. 

9.  If  the  cycle  of  the  previous  problem  were  reversed,  and  we  were  to  use 
some  suitable  working  substance,  what  would  be  the  coefficient  of  perform- 
ance for  a  cooling  machine?     For  a  warming  machine? 

(Coef.  of  perf.  =  result  -5-  expenditure.) 
Show  on  the  T$-chart. 

10.  An  engine    working  on   the   Carnot    cycle  transforms     113.94   B-t.u. 
into  work  per  cycle.     If  the  temperature  of  the  steam  initially  is  358.5°  F. 
and    finally   250.3°  F.,  find   the   initial   state  of  the  steam.      Show  on   the 
T<£-chart. 

n.  If  a  steam  engine,  working  on  the  Carnot  cycle  with  an  efficiency  of 
20  per  cent  requires  3000  Ibs.  of  dry  saturated  steam  per  hour  the  pressure 
being  100  Ibs.  per  sq.  in.  abs.,  find  the  exhaust  pressure.  How  much  heat  does 
the  condenser  remove  per  hour?  What  is  the  horse  power  of  this  ideal  engine? 
Show  on  the  T<£-chart. 

12.  If  a  boiler  supplies  dry  saturated  steam  with  a  pressure  of  150  Ibs.  per 
sq.  in.  abs.  to  an  engine  operating  on  the  Carnot  cycle,  in  which  the  back 
pressure  is  5  Ibs.  per  sq.  in.  abs.,  find  the  work  done,  the  heat  flow  for  each 
path,  the  net  work  of  the  cycle,  and  its  efficiency.      Show  on  T<£-  and  PV- 
charts.     Check  your  net  work  by  another  method. 

13.  Solve  previous  problem  starting  with  a  quality  of  90  per  cent. 

14.  An  engine  operates  on  the  Clausius  cycle  between  the  pressure  limits 
of  185  Ibs.  per  sq.  in.  and  25  Ibs.  per  sq.  in.     Adiabatic  expansion  occurs  from 
a  temperature  of  575°  F.     Cp  =  0.54.     (a)  Determine  the  total  heat  added 
A<2i.     (b)   Determine  the  total  heat  rejected  AQ2.     (c)  Determine  the  work 
accomplished  during  adiabatic  expansion,     (d)  Find  the  efficiency  of  the  cycle. 

15.  Suppose  the  engine  of  the  previous  problem  to  operate  on  the  Rankine 
cycle  with  release  at  25  Ibs.  per  sq.  in.  and  a  back  pressure  of  5  Ibs.  per  sq.  in. 
abs.     (a)  Determine  the  efficiency  of  this  cycle,     (b)  What   would   be  the 
efficiency  of  a  Carnot  cycle  operating  between  the  same  temp,  limits. 

16.  Find  the  difference  in  the  heat  supplied,  heat  rejected,  work  done  and 
the  efficiency  of  a  Carnot  and  Clausius  cycle  when  each  engine  receives  dry 
saturated  steam  having  an  abs.  pressure  of  no  Ibs.  per  sq.  in.,  the  back  pres- 
sure being  20  Ibs.  per  sq.  in.  abs. 

Show  on  the  PV-  and  T0-charts. 


766 


HEAT-POWER  ENGINEERING 


17.  Find  the  heat  supplied,  heat  rejected,  work  done  and  the  efficiency  of 
an  engine  working  on  the  Clausius  cycle  receiving  steam  with  a  pressure  of 
140  Ibs.  per  sq.  in.  abs.  and  150°  of  superheat,  if  the  exhaust  pressure  is  15  Ibs. 
per  sq.  in.  abs. 

Show  the  PV-  and  T<£-charts. 

18.  Find  the  heat  supplied,  heat  rejected,  work  done  and  efficiency  of  an 
engine  working  on  the  Rankine  cycle  in  which  the.  initial  ste.  m  pressure  is 
130  Ibs.  per  sq.  in.  abs.  with  150°  of  superheat;  and  the  temperature  at  the  end 
of  adiabatic  expansion  is  240.1°  F.  while  the  exhaust  pressure  is  15  Ibs.  per  sq. 
in.  abs. 

Show  on  PV-  and  T<£-charts.* 

19.  Given  a  feed  pump  cycle  (rectangular  PV-diagram)  working  between 
the  pressure  limits  of  135  Ibs.  per  sq.  in.  and  15  Ibs.  per  sq.  in.     The  steam 
is  superheated  100°  F.     (Cp  =  0.55.)      (a)  Find  the  volume  of  the  cylinder  re- 
quired,    (b)  Find  the  efficiency  of  the  cycle,     (c)  Show  on  PV-  and  T<£-charts. 

20.  *  Find  the  heat  supplied,  heat  rejected  and  work  done  per  pound  and 
the  efficiency  of  a  feed  pump  cycle  in  which  the  heat  abstraction  begins  when 
the  steam  has  a  pressure  of  140  Ibs.  per  sq.  in.  abs.,  and  50°  of  superheat.     The 
constant  volume  change  ends  when  a  temperature  of  213-°  F.  has  been  reached. 

21.  Suppose  an  engine  working  on  the  Rankine  cycle  receives  dry  satu- 
rated steam  having  a  pressure  of  200  Ibs.  per  sq.  in.  abs.,  then  expands  it  until 
its  pressure  drops  90  per  cent.     The  condenser  pressure  is  4  Ibs.  per  sq.  in.  abs. 

(a)  Find  the  efficiency  of  the  cycle. 

(b)  If  the  engine  requires  j  of  a  pound  of  steam  per  cycle  find  the  volume 
of  the  cylinder  necessary  for  this  ideal  cycle. 

(c)  With  the  same  data  as  in  (b)  find  the  horse  power  if  the  engine  runs  300 
cycles  per  min. 

(d)  Plot  the  PV-  and  T<£-charts  for  this  cycle  estimating  distances  as  closely 
as  possible. 

(e)  What  is  the  horse  power  per  cu.  ft.  of  piston  displacement? 

22.  With  the  same  initial  steam  and  the  same  back  pressure  as  in  previous 
problem,  find  the  same  quantities  for  the  Clausius  cycle. 

23.  With    the  same   initial    steam  and   the  same  back   pressure  as   in  21 
find  the  same  quantities  for  the  cycle  in  which  there  is  no  expansion  of  the 
steam. 

CHAPTER  XHI. 

1.  How  much  heat  is  transformed  into  work  by  an  engine  delivering  100 
h.p.  for  24  hrs.? 

2.  Find  the  i.h.p.  of  a  JO-in.  by  12-in.  engine,  double  acting,  running  200 
rev.  per  min.  when  the  m.e.p.  from  the  indicator  diagram  is  30  Ibs.  per  sq.  in. 

3.  Suppose  the  engine  of  the  previous  problem  had  given  an  indicator 
diagram,  having  an  area  of  2.7  sq.  in.,  and  a  length  of  3  in.     If  the  scale  of 
the  spring  used  in  the  indicator  had  been  50  Ibs.  per  in.,  find  the  i.h.p. 

4.  An  engine  18  in.  by  24  in.,  double  acting,  running  150  rev.  per  min. 
delivers  100  b.h.p.     If  the  indicator  diagram  gives  a  m.e.p.  of  25  Ibs.  per  sq. 
in.,  find  its  mechanical  efficiency,  and  the  friction  horse  power. 

5-  Suppose  the  same  engine,  running  at  the  same  speed  as  in  the  previous 
problem,  has  its  back  pressure  reduced  12  Ibs.  per  sq.  in.  by  means  of  a  con- 
denser thereby  increasing  the  m.e.p.  to  36  Ibs.  per  sq.  in.  Find  its  i.h.p., 
b.h.p.  and  mechanical  efficiency,  assuming  the  same  friction  horse  power  as 
in  the  previous  problem. 

The  addition  of  a  condenser  to  this  engine  increased  its  power  output  by 
what  per  cent? 

6.  A  certain  engine  working  on  the  Rankine  cycle  uses  20  Ibs.  of  steam 
per  i.h.p.  hr.  If  the  steam  has  an  abs.  pressure  of  150  Ibs.  per  sq.  in.  and  a 
temp,  of  458.5°  while  the  exhaust  pressure  is  4  Ibs.  per  sq.  in.  abs.,  find  the 
heat  supplied  per  i.h.p.  min.  and  the  thermal  efficiency  on  i.h.p. 

7-  If  the  engine  of  the  previous  problem  has  a  mechanical  efficiency  of 
90  per  cent,  what  is  the  thermal  efficiency  on  b.h.p.? 

*  The  Ellen  wood  Chart  may  be  used  in  probs. 


PROBLEMS  767 

8.  Suppose  an  engine  in  which  the  mechanical  efficiency  is  85  per  cent  re- 
quires 3000  Ibs.  of  steam  per  hr.  when  delivering  100  h.p.     If  the  steam  has  a 
pressure  of  150  Ibs.  per  sq.  in.  abs.,  and  a  quality  of  98  per  cent,  find  the  heat 
required  per  b.h.p.  min.,  and  the  thermal  efficiency  on  the  i.h.p.  and  on  the 
b.h.p.     The  engine  is  working  on  the  Rankine  cycle,  and  has  a  back  pressure 
of  2  Ibs.  per  sq/in/abs. 

9.  With  th* ••'  same  engine  delivering  the  same  power  as  in  the  ^previous 
problem,  find  {He  same  quantities  if  the  steam  required  is  2400  Ibs.  per  hr., 
the  steam  havirig  a  pressure  of  150  Ibs.  per  sq.  in.  abs.  and  100  degrees  of 
superheat. 

10.  If  a  Diesel  engine  delivers  750  h.p.  hrs.  per  bbl.  of  crude  oil,  find  its 
thermal  efficiency  on  b.h.p.     A  barrel  of  oil  contains  336  Ibs.  and  the  calorific 
value  of  this  oil  is  18,500  B.t.u.  per  Ib. 

11.  An  8"  X  12"  air  compressor,  while  running  200  r.p.m.  gives  an  indi- 
cator card  having  an  area  of  2.7  sq.  in.  for  the  head  end,  and  3  sq.  in.  for  the 
crank  end.     The  length  of  each  card  is  3  in.     Scale  of  the  spring  is  60  Ibs.  per 
in.     The  piston  rod  is  i^  in.  in  diameter.     Find  the  i.h.p. 

12.  A  Diesel  engine  uses  4  bbl.  of  crude  oil  per  day  of  24  hrs.     (i  bbl.  = 
=  336  Ibs.)     The  heating  value  of  the  oil  is  18,000  B.t.u.  per  Ib.     If  the  me- 
chanical efficiency  is  73  per  cent  and  the  thermal  efficiency  on  b.h.p.  is  28.3 
per  cent  find  the  i.h.p.-,  b.h.p.  and  oil  used  per  b.h.p.  hr.  for  this  engine. 

13.  A  I2,ooo-h.p.  steam  turbine  requires  12.3  Ibs.  of  steam  per  h.p.  hr., 
when  receiving  steam  having  100°  of  superheat  and  a  pressure  of  190  Ibs.  per 
sq.  in.  abs.     The  vacuum  is  28  in.,  and  the  barometer  stands  at  30  in. 

(a)  Find  the  cycle  efficiency  for  this  turbine  assuming  it  to  operate  on  the 
Clausius  cycle,  (b)  Find  the  delivered  thermal  efficiency,  (c)  What  portion 
of  the  theoretical  work  of  the  cycle  is  actually  delivered  by  the  turbine? 

14.  With  the  same  data  as  in  the  previous  problem,  find  the  actual  amount 
of  heat  lost  per  min.  in  this  turbine,  in  excess  of  that  rejected  by  the  ideal 
turbine  operating  under  the  same  conditions. 

15.  A  certain  steam  engine  rated  at  500  h.p.  gives  a  total  consumption 
curve  which  is  a  straight  line.     The  total  consumption  at  £  of  rated  load  is 
6250  Ibs.  of  steam  per  hour  while  that  at  rated  load  is  14,000  Ibs.  per  hour. 
Plot  the  total  consumption  and  the  water  rate  curves  for  this  engine  between 
zero  and  rated  curves. 

CHAPTER  XIV. 

1.  Find  the  work  done  (in  B.t.u.),  the  cycle  efficiency  and  the  water  rate 
of  an  ideal  turbine. operating  on  the  Clausius  cycle  with  steam  at  a  pressure 
of  130  Ibs.  per  sq.  in.  abs.  and  100°  of  superheat,  while  the  back  pressure  is 
15  Ibs.  per  sq.  in.  abs. 

2.  Solve  problem  I  using  a  back  pressure  of  i  Ib.  per  sq.  in.  abs.     By  what 
per  cent  was  the  power  of  this  ideal  turbine  increased  by  exhausting  into  a 
condenser? 

3.  Solve  problem  I  using  steam  of  the  same  pressure  but  having  a  quality 
of  unity  at  the  beginning  of  adiabatic  expansion. 

4.  Discuss  the  results  of  the  preceding  problems,  as  to  the  effect  of  super- 
heat and  vacuum  on  the  ideal  water  rates. 

5.  Find  the  net  work  of  the  cycle,  the  cycle  efficiency,  and  the  theoretical 
water  rate  of  an  ideal  engine  working  on  the  Carnot  cycle,  for  which  the 
upper  temperature  is  344.4°  and  the  lower  is  193.22°.     The  pressure  at  the 
beginning  of  the  adiabatic  expansion  is  25  Ibs.  per  sq.  in.  abs. 

6.  Solve  the  previous  problem,  with  all  the  conditions  as  above,  except 
that  the  steam  at  the  beginning  of  adiabatic  expansion  is  dry  and  saturated 
at  344.4°  F. 

7.  Given  admission  pressure  =  130  Ibs.  per  sq.  in.  abs.,  D  ••=  100  ,  release 
press.  =  25  Ibs.  per  sq.  in.  abs.,  and  back  press.  =  15  Ibs.  per  sq.  in.  abs.,  find 
the  theoretical  work  of  the  cycle,  the  cycle  efficiency,  and    the  theoretical 
water  rate,  of  an  engine  operating  on  the  Rankine  cycle. 

8.  Solve  problem  7  when  the  engine  receives  dry  saturated  steam, 


768  HEAT-POWER  ENGINEERING 

9.  Suppose  an  engine  b  working  on  the  feed  pump  cycle,  receiving  steam 
with  an  abs.  press,  of  130  Ibs.  per  sq.  in.  and  100°  of  superheat.     Find  the 
cycle  efficiency,  the  theoretical  water  rate  and  the  actual  water  per  i.h.p.  hr. 
if  the  indicated  thermal  efficiency  is  3  per  cent  and  back  pressure  is  15  Ibs. 

10.  Solve  problem  9,  using  dry  saturated  steam. 

11.  An  engine  is  working  on  the  Rankine  cycle  at  a  pressure  of  130  Ibs. 
per  sq.  in.  abs.  and  superheated  100°;  release  occurs  at  a  pressure  of  25  Ibs. 
per  sq.  in.  abs.;  back  pressure  is  15  Ibs.  per  sq.  in.  abs.     Find  the  theoretical 
water  rate  and  the  cycle  efficiency.     Find  the  actual  steam  used  per  b.h.p.  hr. 
and  the  delivered   thermal  efficiency  if  this  engine  requires  30,000  Ibs.  of 
steam  per  day  of  10  hrs.  when  delivering  100  h.p. 

12.  Given  dry  saturated  steam  having  a  temperature  of  327.8°,  and  an 
exhaust  temperature  of  213°,  find  the  net  work  of  the  cycle,  the  cycle  effi- 
ciency, and  the  theoretical  water  rate  of  an  engine  working  on  the  Carnot 
cycle. 

13.  Solve  problem  12  for  the  Clausius  cycle. 

14.  Solve  problem  12  for  the  Rankine  cycle,  assuming  release  to  occur 
when  a  temperature  of  240.1°  has  been  reached. 

15.  Solve  problem  12  for  the  feed  pump  cycle. 

16.  Starting  with  the  same  A  Qi  and  working  between  the  same  tempera- 
ture limits  as  in  problem  12,  find  the  net  work  of  the  cycle,  the  cycle  efficiency 
and  the  theoretical  water  rate  of  an  engine  working  on  the  Clausius  cycle. 

17.  Solve  problem  16  for  the  Rankine  cycle,  the  release  temperature  being 
240.1°. 

1 8.  Solve  problem  16  for  the  feed  pump  cycle. 

CHAPTER   XV. 

1.  An  engine  has  a  piston  displacement  of  0.2  cu.  ft.     If  its  clearance  is 
10  per  cent,  and  release  takes  place  at  95  per  cent  of  the  stroke,  find  the 
weight  of  steam  in  the  cylinder  at  release,  the  quality  then  being  70  per  cent 
and  the  pressure  25  Ibs.  per  sq.  in.  abs. 

2.  Find  the  quality  of  steam  at  cut  off  in  a  cylinder  in  which  the  piston 
displacement  is  0.1278  cu.  ft.,  clearance  10  per  cent,  cut  off  25  per  cent,  steam 
pressure  at  cut  off  115  Ibs.  per  sq.  in.  abs.,  and  the  weight  of  steam  in  the 
cylinder  at  cut  off  0.012  Ibs.    N\ 

3.  Determine  the  quality  or  decree  of  superheat  of  the  steam  in  an  engine 
cylinder  at  cut  off,  its  pressure  thenlaeing  125  Ibs.  per  sq.  in.  abs.  and  its  weight 
0.013  Ibs.     The  piston  displacement  Xo.  13  cu.  ft.,  clearance  10  per  cent,  and 
the  cut  off  takes  place  at  30  per  cent  ofvthe  stroke. 

4.  Find  the  weight  of  cushion  steam  in  a  6"  X  8"  engine  in  which  clearance 
is  15  per  cent;    compression  begins  at  15  per  cent  of  the  stroke;    the  back 
pressure  is  14.7  Ibs.  per  sq.  in.  abs.,  and  the  quality  of  the  cushion  steam  at 
the  beginning  of  compression  is  95  per  cent.     Find  the  pressure  and  the  qual- 
ity at  the  end  of  this  compression,  assuming  it  to  be  adiabatic. 

5.  Suppose  the  compression  in  the  previous  problem  is  not  adiabatic,  but 
is  such  that  the  compression  pressure  is  30  Ibs.  per  sq.  in.  abs.,  find  the  quality 
of  the  cushion  steam  at  the  end  of  the  stroke. 

6.  An  8"  X  10*  engine  running  300   r.p.m.   double   acting,   with   cut  off 
taking  place  at  15  per  cent  of  the  stroke,  and  at  a  pressure  of  120  Ibs.  per  sq. 
in.  abs.,  requires  35  Ibs.  of  steam  per  i.h.p.  hr.     The  compression  begins  at 
40  per  cent  of  the  stroke  with  a  quality  of  unity  and  a  back  pressure  of  5  Ibs. 
per  sq.  in.  abs.     Clearance  =  10  per  cent. 

If  this  engine  delivers  27  h.p.  and  has  a  mechanical  efficiency  of  90  per  cent, 
(a)  Find  the  quality  of  steam  at  cut  off. 

(6)  If  the  quality  of  the  steam  at  the  throttle  is  unity  and  "wire  drawing" 
amounts  to  5  pounds,  find  the  delivered  thermal  efficiency. 

7.  For  the  previous  problem,  assume  release  to  occur  at  90  per  cent  of  the 
stroke,  with  an  abs.  pressure  of  30  Ibs.  per  sq.  in.     What  is  the  quality  at  this 
point? 


PROBLEMS  769 

8.  Assuming  the  expansion  line  for  problem  6  to  follow  the  law,  PV  = 
const. 

(a)  Find  the  quality  at  15,  20,  30,  40,  50,  65  and  90  per  cent  of  the  stroke. 
(Tabulate  results.) 

(6)  Draw  the  quality  curve  for  this  expansion. 

9.  Suppose  the  engine  in  problem  6  had  received  steam  with  sufficient 
superheat  to  cause  the  quality  at  cut  off  to  be  88  per  cent,  and  that  by  means 
of  a  steam  jacket  the  expansion  line  is  made  to  follow  the  law,  PV-962  =  const. 
Find  the  condition  of  the  steam  at  release,  which  occurs  at  90  per  cent  of  the 
stroke. 

10.  The  thermometer  in  a  throttling  calorimeter  shows  a  temp,  of  223°, 
the  manometer  reads  0.73  in.  of  mercury;   and  the  barometer  stands  at  29.92. 
Find  the  quality  of  the  steam  entering  the  calorimeter  if  its  pressure  is  110.3 
Ibs.  per  sq.  in.  gauge. 

11.  Supposing  that  the  thermometer  in  the  above  calorimeter  had  read 
213°,  all  other  readings  being  the  same,  what  would  be  the  quality?     Discuss. 

12.  If  by  connecting  to  a  condenser  we  may  reduce  the  calorimeter  pressure 
until  the  mercury  manometer  indicates  15.62  in.  below  atmosphere,  find  the 
quality  of  the  steam  below  which  the  instrument  could  not  be  used  with 
steam  pressure  and  atmospheric  pressure  the  same  as  in  problem  10. 

13.  What  pressure  would  you  have  to  maintain  in  the  calorimeter,  in  order 
to  measure  quality  as  low  as  92  per  cent,  the  steam  pressure  being  100  Ibs.  per 
sq.  in.  abs.  and  the  degree  of  superheat  in  the  calorimeter  to  be  not  less  than  5°. 

CHAPTER  XVI. 

Heck's   formula  for  estimating  cylinder  condensation  in  cylinders  which 
are  not  steam  jacketed  is 

0.2 


where  m  =  fraction  of  moisture  in  the  steam  at  any  point  "a"  during  ex- 

pansion. 
N  =  r.p.m. 

_  nominal  cyl.  surface  in  sq.  ft. 

nominal  cyl.  vol.  in  cu.  ft. 
24   ,  48  (  where  d  =  diam.  of  cyl.  in  inches. 
"  ~T       ~d  \  and  /  =  length  of  stroke  in  inches. 
p  =  abs.  press,  in  Ib.  per  sq.  in.  at  point  "a." 
_  total  vol.  up  to  point  "a" 

piston  displ. 

Tf  =  a  special  temperature  function  of  the  pressure  and  is  obtained  from 
the  following  table  by  taking  the  difference  between  the  values  of  K  corre- 
sponding to  the  highest  and  the  lowest  pressures  occurring  in  the  engine. 


P   K 

P    K 

p   K 

p    K 

P   K 

P   K 

I   175 

15   2IO 

50  269  .  5 

90  321-5 

i  60  389 

230  441 

2   179 

3  183 
4  186 
6  191 
8  196 
10  200 

2O   2  2O 
25   229 
30   238 

35  246 

40  254 

45  262 

55  277 
60  284 
65  291 
70  297.5 
75  304 
80  310 

ioo  332.5 
no  343 
120  353 
130  362.5 
140  371-5 
150  380.5 

170  397 
1  80  405 
190  413 

200   420 
2IO   427 

220  434 

240  447-5 
250  454 
260  460  .  5 
270  467 
280  473 
290  479 

770  HEAT-POWER  ENGINEERING 

1.  Find  the  quality  at  cut  off  by  Heck's  formula  for  the  intermediate  cyl- 
inder of  a  triple  expansion  engine  having  a  diam.  of  10  in.  and  a  stroke  of  6  in., 
r.he  speed  being  402  r.p.m.,  cut-off  press.,  112.2;  admission  press.,  130;  and 
back  press.,  51  Ibs.  per  sq.  in.  abs.;  clearance,  10  per  cent;  cut  off,  36.2  per  cent. 
By  test  it  was  found  that  the  actual  quality  at  cut  off  was  85.7  per  cent;   find 
the  per  cent  error  by  computing  with  the  above  formula. 

2.  A  17"  X  24"  engine  running  72  r.p.m.  gives   a  card  which  shows   the 
adm.  press,  to  be  133  Ibs.;  exhaust  press.,  16.2;  cut  off,  98.8  Ibs.  per  sq.  in.  abs. 
Cut  off  occurs  at  18.6  per  cent  stroke  and  clearance  is  9.9  per  cent.     Find  the 
quality  at  cut  off  by  Heck's  formula  and  find  the  per  cent  error  if  test  shows 
the  actual  quality  to  be  72.9  per  cent. 

3.  An  8"  X  10"  engine  running  320  r.p.m.  has  cut  off  at  12  per  cent  with 
a  pressure  of  140;   admission  press,  is  145,  and  back  press.  4  Ibs.  per  sq.  in. 
abs.;    clearance  is  10  per  cent.     If  a  test  shows  the  quality  at  cut  off  to  be 
59  per  cent,  find  the  per  cent  error  in  result  obtained  by  Heck's  formula. 

4.  A  certain  engine  requires  18  Ibs.  of  steam  per  i.h.p.  hour  when  using 
dry  saturated  steam,  but  when  the  steam  is  superheated  340°  it  requires  only 
ii  Ibs.  per  i.h.p.  hour. 

The  admission  pressure  is  150  Ibs.  per  sq.  in.  abs.  and  the  back  pressure  is 
I  Ib.  in  each  case.  Find: 

(a)  The  per  cent  saving  in  steam  required  when  superheat  is  used. 
(6)  The  per  cent  saving  in  heat  required  when  superheat  is  used. 

(c)  The  per  cent  saving  in  steam  required  for  ideal  Clausius  cycle  when 
superheat  is  used. 

(d)  The  per  cent  saving  in  heat  required  for  ideal  Clausius  cycle  when 
superheat  is  used. 

(e)  The  difference  in  the  saving  in  heat  required  for  the  actual   and  the 
ideal  engine.     This  difference  is  due  mainly  to  what? 

5.  An  engine  is  supplied  with  dry  saturated  steam  having  an  abs.  pressure 
of  150  Ibs.  per  sq.  in. 

Back  pressure  is  5  Ibs.  per  sq.  in.  abs.,  the  exhaust  steam  being  liquified  in 
a  surface  condenser. 

When  running  without  a  steam  jacket,  the  engine  requires  20  Ibs.  of  steam 
per  i.h.p.  hr. 

When  running  with  a  jacket,  it  was  found  the  engine  required  18  Ibs.  per 
i.h.p.  hr.  for  the  cylinder,  and  2  Ibs.  per  i.h.p.  for  the  jacket. 

Supposing  there  is  no  loss  of  heat  in  returning  the  condensate  from  the 
jacket,  or  from  the  condenser  to  the  boiler,  and  that  the  jacket  pressure  is 
maintained  at  150  Ibs.  per  sq.  in.  abs., 

(a)  Find  the  heat  required  by  the  engine  per  i.h.p.  hr.  for  each  of  the  above 
cases. 

(b)  Find  the  ind.  thermal  efficiency  for  each  of  the  above  cases. 

(c)  Find  the  per  cent  saving  in  heat  required  per  i.h.p.  due  to  jacketing. 

6.  An  engine  running  without  a  steam  jacket  requires  15.5  Ibs.  of  steam  per 
i.h.p.  hr.,  and  when  running  with  the  steam  jacket  requires  a  total  of  14  Ibs. 
per  i.h.p.  hr.     The  steam  required  by  the  jacket  is  18  per  cent  of  the  total. 

The  admission  press,  and  jacket  press,  are  both  165  Ibs.  per  sq.  in.  abs.; 
the  steam  admitted  to  them  has  a  quality  of  unity. 

In  each  case  the  condensate  from  the  condenser  is  returned  to  the  boiler 
at  a  temp,  of  202°  F.,  but  the  condensate  from  the  steam  jacket  is  delivered 
to  the  boiler  at  a  temp,  of  302°.  Neglecting  all  leakage:  (a)  Find  the  heat 
supplied  by  the  boiler  per  i.h.p.  hr.  for  each  of  the  above  cases.  (6)  Find  the 
per  cent  saving  in  heat  required  due  to  jacketing. 

CHAPTER  XIX. 

I.  (a)  Lay  out  a  symmetrical  valve  seat,  with  width  of  exhaust  cavity 
5  ins.,  of  metal  between  exhaust  cavity  and  port  i£  ins.,  and  of  ports  i|  ins. 
(6)  Draw  in  its  central  position  an  external  valve  having  steam  and  exhaust 
laps  respectively  i£  ins,  and  (negative)  ?  in.  for  the  head  end,  and  is  ins.  and 


PROBLEMS  771 

(positive)  i  in.  for  the  crank  end;  thickness  of  metal  I  in.     Dimension  and 
label  completely. 

2.  Same  as  problem  i,  except  for  an  internal  valve. 

3.  Construct  a  rectangular  diagram  of  valve  displacements  for  a  valve 
having  the  dimensions  given  in  problem  i,  the  angle  of  advance  being  325° 
and  throw  2\  ins.,  (a)  for  the  H.E.;    (ft)  for  the  C.E. 

4.  Same  as  problem  3,  but  for  polar  diagram  of  valve  displacements. 

5.  With  data  of  problems  i  and  3,  construct  the  Sweet  diagram  for  both 
ends  of  valve  and  show:    (a)  the  crank  and  piston  positions  for  all  the  events; 
(ft)  the  angles  of  rotation  of  crank  and  eccentric  for  each  of  the  periods;  (c)  the 
maximum  openings  to  steam  and  exhaust;    (d)  the  lead,     (e)  Construct  an 
elliptical  diagram  from  the  Sweet  diagram. 

6.  Same  as  problem  5,  except  for  Zeuner  diagram. 

7.  Same  as  problem  5,  except  for  Bilgram  diagram. 

8.  Given  cut-off  f  stroke,  the  amount  of  lead  £  in.,  the  maximum  width  of 
opening  of  the  steam  edge  of  the  valve  i  j  ins.,  release  95  per  cent  of  stroke 
for  H.E.  and  90  per  cent  for  C.E.     Determine,  for  both  ends,  the  value  of 
(a)  the  angle  of  advance,  (ft)  throw,  (c)  steam  lap,  (d)  exhaust  lap,  and  (e) 
crank  and  piston  positions  for  each  event. 

9.  In  problems  5  to  8,  find  the  true  positions  of  the  piston  in  its  stroke  for 
each  crank  position  found,  the  length  of  connecting  rod  being  6  times  the 
length  of  crank.     Let  the  eccentric  circle  represent  the  crank  circle. 

10.  A  swinging  eccentric  is  pivoted  diametrically  opposite  the  crank  at  a 
distance  of  8  ins.  from  the  shaft  center;    the  distance  from  pivot  to  eccentric 
center  is  6|  ins.,  the  largest  throw  of  the  eccentric  is  2|  ins.,  the  steam  lap  is 
1 1  ins.  and  the  exhaust  lap  is  i  in.     (a)  Draw  the  path  of  the  swinging  eccen- 
tric as  in  Fig.  160.     Locate  three  eccentric  positions,  and  get  the  throws  and 
angles  of  advance,     (b)  Draw  the  H.E.  Bilgram  diagram  and  show  the  corre- 
sponding positions  of  the  steam  and  exhaust  lap  circles,     (c)  Determine  the 
positions  of  the  crank  for  all  events. 

11.  Same  as  problem  10,  but  using  the  Sweet  diagram. 

12.  Same  as  problem  10,  but  using  the  Zeuner  diagram. 

13.  Independent  cut-off  gear,     (a)  Draw  the  Bilgram  diagram  for  the  main 
valve  to  give  release  90  per  cent  and  compression  85  per  cent  of  stroke,  lead 
-|  in.,  and  maximum  steam  opening  i\  ins.     (b)  With  same  eccentric  throw, 
and  in  position  for  o,  £  and  £  cut-off,  draw  the  lap  circles  for  a  cut-off  valve 
having   i   in.   negative   lap  and  riding  on  an  independent   stationary  seat. 
(c)  Show  the  positions  of  the  eccentrics  with  respect   to  crank  (on  H.E. 
dead  center)   for  each  cut-off,     (d)  Plot  a  diagram  of  openings  similar  to 

14.  Meyer    Valve  Gear,     (a)  Data  same  as  in  problem   13   (a)  for  main 
valve      (ft)  With  throw  of  cut-off  eccentric  3  ins.  and  angle  of  advance  90  , 
construct  the  Bilgram  diagram  and  draw  the  lap  circles  for  the  cut-off  valve 
to  give  cut-off  at  o,  \,  i  and  I  strokes,     (c)  Show  the  positions  of  the  eccen- 
trics with  respect  to  the  crank  (on  H.E.  dead  center). 

CHAPTER  XX. 

NOTE.  —  In  the  following  problems  it  is  assumed  that  the  engine  is  double 
acting  unless  otherwise  stated.  ,     (  ,.      .„ 

1.  It  is  desired  to  build  a  simple  engine  to  give  75  i-h-P-  under  tne  * 
conditions: 

Cut  off  at  20  per  cent. 
Clearance  =  10  per  cent. 
Steam  press.  =  140  Ibs.  per  sq.  in.  abs. 
Back  press.  =  2  Ibs.  per  sq.  m.  abs. 
R.P.M.  =  200. 
If  the  diagram  factor  for  this  type  of  engine  is  0.9  find  size  of  cy lir    er. 

2.  Suppose  it  is  desired  to  build   an  engine  to  give  50  i.h.p.,  "nder  the 
following  conditions:    Cut  off  25  per  cent;  Clearance  12  per  cent.,   Steam 


772  HEAT-POWER  ENGINEERING 

press.  =  150  Ibs.  per  sq.  in.  abs.;  Piston  speed  =  400  ft.  per  min.;  Back  press. 
=  1 6  Ibs.  per  sq.  in  abs.  If  the  diagram  factor  for  this  type  of  engine  is  85 
per  cent,  find  the  diameter  of  the  cylinder  and  select  stroke  and  r.p.m. 

3.  Supposing  that  the  engine  in  problem  I  has  cut  offs  occuring  from  10 
to  50  per  cent  of  stroke,  find  the  i.h.p.  for  these  extremes. 

4.  Given  an  engine  18"  X  24"  running  120  r.p.m.     Back  press.  =  2  Ibs.  per 
sq.  in.  abs;  Clearance  =  10  per  cent;  Cut  off  =  40  per  cent ;  Diagram  factor 
=  85  per  cent.     Supposing  the  cut  off  to  remain  constant,  find  the  i.h.p.'s 
corresponding  to  steam  pressures  of  50,  90  and  130  Ibs.  per  sq.  in.  abs. 

5.  Find  the  weight  of  dry  steam  which  must  be  supplied  per  i.h.p.  hour 
for  each  case  of  problem  4,  assuming  the  quality  at  cut  off  to  be  80  per  cent. 
Assume  compression  pressure  to  be  30  Ibs.  abs.  and  that  the  steam  is  dry  and 
saturated  at  the  end  of  compression. 

6.  A  compound  engine  is  to  give  600  i.h.p.  when  using  steam  having  an 
abs.  press,  of  150  Ibs.  per  sq.  in.  and  having  a  back  press,  of  2  Ibs.  per  sq.  in.  abs. 
If  the  cylinder  ratio  is  to  be  4  and  the  total  ratio  of  expansion  12,  find  the 
size  of  cylinders.     The  piston  speed  is  to  be  750  ft.  per  min.  and  the  engine 
is  to  run  150  r.p.m.     Take  diagram  factor  as  0.8. 

7.  An  8"  X  16"  X  12"  engine  has  cut  off  in  the  high  press,  cylinder  at  £ 
stroke,  the  admission  pressure  is  150  Ibs.  per  sq.  in.  abs.  and  the  back  pressure 
is  2  Ibs.  per  sq.  in.  abs.    Assuming  the  expansion  line  to  be  hyperbolic,  receiver 
drop  and  clearance  to  be  zero,  and  no  initial  superheat,  find:  (a)  The  total 
ratio  of  expansion,     (bj  The  receiver  pressure,     (c)  The  point  of  cut  off  in 
the  low  pressure   cylinder,     (d)  The  temperature   range   in   each   cylinder. 
(e)  The  portion  of  the  work  done  by  each  cylinder.     (/)  The  maximum  force 
exerted  on  each  piston  rod. 

Sketch  the  PV-diagram  for  this  expansion  marking  the  pressure  at  the  end 
of  the  expansion  in  each  cylinder,  and  the  volume  in  terms  of  the  volume  at 
cut  off  in  the  high  pressure  cylinder. 

8.  Assume  the  cut  off  in  the  high  pressure  cylinder  of  the  above  engine 
is  now  made  to  occur  at  5  stroke,  all  other  conditions  remaining  the  same, 
find  the  same  quantities  as  called  for  above. 

9.  Assume  the  above  engine  is  now  made  to  cut  off  at  |   stroke   in   the 
high  pressure  cylinder  and  at  37!  per  cent  stroke  in  the  low,  thus  causing  a 
receiver  drop,  find  this  drop  and  all  the  quantities  called  for  above. 

10.  With  the  data  of  the  previous  problem  find  what  portion  of  the  total 
theoretical  work  was  lost  by  the  receiver  drop. 

11.  With  the  result  of  the  previous  problem  solve  for  the  constant  "K" 
used  in  equation  293  of  the  text.     Then  with  this  value  of  K  find  the  total 
m.e.p.  referred  to  the  low  pressure  cylinder.     Does  this  check  results  already 
obtained  from  problem  9? 

CHAPTER  XXII. 

1.  Determine  the  amount  of  work  theoretically  obtainable  with  a  turbine 
per  pound  of  steam  admitted  at  a  pressure  of  150  Ibs.  per  sq.  in.  and  super- 
heated 100  degrees  and  expanded  to  a  28-inch  vacuum,  (a)  by  calculation, 
(b)  by  means  of  the  T0-chart,  and  (c)  by  means  of  the  Mollier  Chart.* 

2.  Same  as  problem  I  except  that  the  exhaust  pressure  is  atmospheric. 

3.  Determine  the  amount  of  work  theoretically  obtainable  with  a  turbine 
per  pound  of  dry  saturated  steam  at  a  pressure  of  150  Ibs.  per  sq.  in.  and 
exhausting  into  a  28-inch  vacuum. 

4.  Same  as  problem  3,  except  that  the  exhaust  pressure  is  atmospheric. 

5.  Plot  a  curve  showing  the  variation  in  the  amount  of  work  obtainable  per 
pound  of  steam  used  in  a  turbine  with  initial  conditions  varying  from  dry  and 
saturated  at  175  Ibs.  per  sq.  in.  pressure  to  a  superheat  of  150  degrees  above 
the  temperature  of  saturation,  the  turbine  exhausting  into  a  28-inch  vacuum 
in  every  case. 

6.  Plot  a  curve  showing  the  variation  in  the  amount  of  work  obtainable 
per  pound  of  steam  used  in  a  turbine  with  initial  conditions  constant  at  150 

*  (d)  By  the  Ellen  wood  Chart 


PROBLEMS 


773 


degrees  superheat  and  175  Ibs.  per  sq.  in.  pressure  but  with  exhaust  condi- 
tions varying  from  atmospheric  pressure  to  a  vacuum  of  29  inches. 

7.  Determine  the  theoretical  water  rate  of  a  turbine  operating  under  the 
conditions  specified  in  problem  I. 

8.  Determine  the  theoretical  water  rate  of  a  turbine  operating  under  the 
conditions  specified  in  problem  2. 

9.  Determine  the  theoretical  water  rate  of  a  turbine  operating  under  the 
conditions  specified  in  problem  3. 

10.  Determine  the  theoretical  water  rate  of  a  turbine  operating  under  the 
conditions  specified  in  problem  4. 

11.  The  over-all  efficiency  of  a  certain  turbo-generator  unit  is  0.67  when 
receiving  steam  at  a  pressure  of  175  Ibs.  per  sq.  in.  superheated  125  degrees 
and  exhausting  to  a  28.5-inch  vacuum.     What  is  the  water  rate  of  the  unit 
per  k.w.  hour? 

12.  If  the  generator  efficiency  for  the  unit  in  problem  II  be  94  per  cent, 
what  is  the  water  rate  of  the  turbine  per  d.h.p.  hour? 

13.  Find  the  B.t.u.  supplied  per  kw.  minute  for  the  unit  described  in 
problem  n.  (On  basis  of  ideal  feed-water  temperature.) 

14.  Find  the  thermal  efficiency  of  the  unit  described  in  problem  II. 

15.  Assume  a  reciprocating  engine  to  consume  twenty  pounds  of  steam  per 
h.p.  hour  when  exhausting  at  atmospheric  pressure.     How  much  work  could 
theoretically  be  obtained  from  an  exhaust  steam  turbine  receiving  this  steam 
at  a  quality  of  80  per  cent  and  expanding  to  a  27.5-inch  vacuum? 

1 6.  Find  the  theoretical  velocity  of  the  jet  in  an  impulse  turbine  receiving 
steam  at  a  pressure  of  100  Ibs.  per  sq.  in.  with  a  superheat  of  100  degrees  and 
expanding  to  atmospheric  pressure. 

17.  Find  the  theoretical  kinetic  energy  of  the  jet  per  pound  of  steam  dis- 
charged in  problem  16. 

CHAPTER  XXVI. 

1.  Plot  a  curve  showing  the  variation  of  the  theoretical  efficiency  of  the 
Otto  cycle  due  to  changes  in  the  compression  ratio  [(volume  of  piston  dis- 
placement +  clearance)  -i-  clearance  volume]  from  3  to  10  and  with  7  =  1.4. 

2.  Plot  a  similar  curve  for  7  =  1.33. 

3.  A  certain  internal  combustion  engine  operating  on  natural  gas  uses  10.3 
cu.  ft.  of  gas  per  b.h.p.  hour  at  rated  load.     The  calorific  value  of  the  gas  is 
1050  B.t.u.  per  cu.  ft.     (a)  How  many  B.t.u.  are  required  per  b.h.p.  per  hour 
at  rated  load?     (6)  What  is  the  thermal  efficiency  at  rated  load?     (c)  What 
values  of  thermal  efficiency  would  you  expect  at  half  and  quarter  loads? 
Give  method  used  in  arriving  at  answer. 

4.  A  certain  producer-gas  plant  delivers  a  b.h.p.  per  hour  on  one  pound  of 
coal,  the  calorific  value  of  the  coal  being  13,500  B.t.u.  per  pound.     What  is 
the  thermal  efficiency  of  the  plant? 

CHAPTER  XXVII. 

i  The  proximate  analysis  of  coal  as  received  is  moisture,  7  per  cent;  vola- 
tile, 4  per  cent;  fixed  carbon,  81  per  cent;  ash,  8  per  cent  (a)  What  would 
be  the  proximate  analysis  on  a  basis  of  dry  coal?  (b)  What  would  be  the 
proximate  analysis  on  a  basis  of  dry  combustible? 

2.  The  proximate  analysis  of  coal  as  received  is  moisture,  10  per  cent; 
volatile,  30  per  cent;  fixed  carbon,  50  per  cent;  ash,  10  per  cent  (a)  What 
would  be  the  proximate  analysis  on  the  basis  of  dry  coal?  (b)  What  would 
be  the  proximate  analysis  on  the  basis  of  dry  combustible? 

3- 


774  HEAT-POWER  ENGINEERING 

containing  8  per  cent  ash?  (b)  What  would  be  the  proximate  analysis 
of  this  fuel  as  received  when  containing  8  per  cent  ash  and  12  per  cent 
moisture? 

5.  Determine  the  probable  ultimate  analysis  of  an  anthracite  coal  giving 
the  following  proximate  analysis:  volatile,  4  per  cent;  fixed  carbon,  96  per 
cent. 

6.  Determine  the  probable  ultimate  analysis  of  an  anthracite  coal  giving 
the  following  proximate  analysis:    volatile,  3.5  per  cent;   fixed  carbon,  90  per 
cent;  ash,  6.5  per  cent.     (On  basis  ot  dry  coal.) 

7.  Determine  the  probable  ultimate  analysis  of  a  bituminous  coal  giving 
the  following  proximate  analysis:   volatile,  25  per  cent;    fixed  carbon,  75  per 
cent. 

8.  Determine  the  probable  calorific  values  of  the  coal  of  problem  5  by  means 
of  Dulong's  formulas. 

9.    Same  as  8,  but  for  the  coal  of  problem  6. 

10.  Same  as  8,  but  for  the  coal  of  problem  7. 

11.  Determine  the  probable  higher  calorific  value  of  a  petroleum  distillate 
with  a  specific  gravity  indicated  as  95  on  the  Baume  scale. 

12.  Same  as  II,  except  for  a  specific  gravity  of  85  Baume. 

13.  Same  as  n,  except  for  a  specific  gravity  of  75  Baume. 

14.  Plot  a  curve  showing  the  probable  variation  of  higher  calorific  values 
of  petroleum  products  with  specific  gravities  varying  from  50  to  95  Baume. 

CHAPTER  XXVIII. 

1.  What  weight  of  oxygen  will  be  required  to  burn  5  Ibs.  of  carbon  to  car- 
bon dioxide?     What  weight  of  air  will  be  required?     How  much  nitrogen 
will  there  be  in  this  air? 

2.  What  weight  of  oxygen  will  be  required  to  burn  7!  Ibs.  of  carbon  to 
carbon  monoxide?     What  weight  of  air  will  be  required?     What  weight  of 
nitrogen  will  be  contained  in  this  air? 

3.  What  weight  of  carbon  dioxide  will  result  from  the  combustion  of  12 
Ibs  of  carbon?     What  would  be  the  total  weight  of  the  products  of  combus- 
tion (all  material  present  after  combustion)  if  the  carbon  were  burned  with 
the  theoretical  air  supply? 

4.  Seven  pounds  of  carbon  are  burned  with  air  to  carbon  monoxide,     (a) 
What  weight  of  carbon  monoxide  is  formed?     (b)  What  is  the  total  weight 
of  the  products  of  combustion? 

5.  Fifteen   pounds  of  carbon  are  burned  in  oxygen   to  carbon   dioxide, 
(a)  What  weight  of  carbon  dioxide  results?     (b)  How  much  heat  is  liberated? . 
(c)  How  much  heat  would  have  been  liberated  if  the  combustion  had  taken 
place  in  air  instead  of  in  oxygen? 

6.  Seventeen  pounds  of  carbon  are  burned  to  carbon  dioxide  in  an  appa- 
ratus which  makes  it  possible  to  complete  the  combustion  in  one  second,  and  an 
equal  quantity  is  burned  to  the  dioxide  in  an  apparatus  which  requires  one 
hour  to  complete  the  combustion.     Is  there  any  difference  in  the  amount  of 
heat  liberated  in  the  two  cases?     Why? 

7.  Three  pounds  of  carbon  are  burned  in  air  to  carbon  dioxide,     (a)  What 
will  be  the  weight  of  the  products  of  combustion  if  twice  the  theoretical 
quantity  of  air  is  used?     (b)  What  will  be  the  quantity  of  heat  liberated? 

8.  Four  pounds  of  carbon  are  burned  in  air  to  carbon  monoxide,     (a) 
What  will  be  the  weight  of  the  products  of  combustion?     (b)  What  will  be 
the  quantity  of  heat  liberated? 

9.  A  quantity,  of  carbon  monoxide  containing  3  Ibs.  of  carbon  is  burned 
with  theoretical  air  supply  to  carbon  dioxide,     (a)  What  will  be  the  weight 
of  the  products?     (b)  What  quantity  of  heat  will  be  liberated? 

10.  Ten  pounds  of  carbon  monoxide  are  burned  with  i£  times  the  theo- 
retical air  supply,     (a)  What  will  be  the  weight  of  the  products?     (b)  What 
quantity  of  heat  will  be  liberated? 


PROBLEMS 


775 


11.  Twelve  pounds  of  carbon  are  burned  first  to  carbon  monoxide  with  the 
theoretical  quantity  of  air  and  then  the  resultant  carbon  monoxide  is  burned 
with  i^  times  the  theoretical  air.     (a)  What  weight  of  carbon  monoxide  is 
formed  by  the  first  reaction?     (b)  What  is  the  total  weight  of  gas  after  the 
first  reaction?     (c)  What  quantity  of  heat  is  liberated  during  the  first  reac- 
tion?    (d)  What  weight  of  carbon  dioxide  is  formed  by  the  second  reaction? 
0)  What  is  the  total  weight  of  gas  present  after  completion  of^ second  re- 
action if  no  gas  is  lost  during  either  reaction  nor  between  reactions?     (/) 
What  quantity  of  heat  is  liberated  during  the  second  combustion?     (g)  What 
is  the  total  quantity  of  heat  liberated  as  result  of  both  reactions  and  how 
does  this  compare  with  what  would  have  been  obtained  had  the  12  Ibs.  of 
carbon  been  burned  directly  to  carbon  dioxide?     (h)  How  does  the  weight 
of  products  obtained  by  using  two  reactions  compare  with  the  weight  that 
would  have  been  obtained  by  burning  directly  to  the  dioxide  with  i|  times 
theoretical  air? 

12.  Eight  pounds  of  carbon  are  burned  with  air  containing  sufficient  oxy- 
gen to  burn  7  Ibs.  of  carbon  to  carbon  dioxide,     (a)  What  are  the  weights 
of  the  various  products  of  combustion?     (b)  What  is  the  percentage  compo- 
sition of  the  products  of  combustion  on  a  volume  basis?     (c)  What  quantity 
of  heat  is  liberated? 

13.  The  analysis  of  the  gases  obtained  by  burning  carbon  in  air  shows 
15  per  cent  by  volume  of  carbon  dioxide,     (a)  What  is  the  excess  coefficient? 
(b)   How  many  pounds  of  air  were  used  per  pound  of  carbon  burned? 

14.  The  analysis  of  gases  obtained  by  burning  carbon  in  air  gives  79  per 
cent  nitrogen  and  7  per  cent  oxygen.      (a)  What  is  the  excess  coefficient? 
(b)  What  weight  of  air  was  used  per  pound  of  carbon? 

15.  Five  pounds  of  carbon  are  burned  in  air  with  an  excess  of  50  per  cent, 
the  combustion  taking  place  at  constant  pressure,     (a)  What  temperature 
rise  will  result?     (b)  What  will  be  the  final  temperature  if  all  material  is  at 
temperature  of  70°  F.  before  the  start  of  the  combustion? 

1 6.  Sixteen  cubic  feet  of  carbon  monoxide  are  burned  with  the  theoretical 
quantity  of  oxygen  within  a  vessel  of  constant  volume.     What  temperature 
would  be  attained  theoretically  if  the  gases  had  an  initial  temperature  of 
60°  F.? 

17.  What  temperature  would  calculation  lead  one  to  expect  when  account 
is  taken  of  the  variable  specific  heat  of  carbon  dioxide? 

1 8.  Three   pounds  of   hydrogen   are   burned  in  oxygen,     (a)  How  much 
heat  is  liberated?     (b)  What  temperature  should  be  obtained  if  the  specific 
heats  were  constant  and  theoretical  oxygen  were  used,  combustion  occurring 
at  constant  pressure?     (c)  What  value  should  be  attained  with  25  per  cent 
excess  oxygen,  variable  specific  heat  and  constant  pressure? 

19.  What  quantity  of  heat  would  be  lost  by  failure  to  condense  the  water 
vapor  resulting  from  the  combustion  of  3  Ibs.  of  hydrogen  if  the  gases  leave 
at  a  temperature  of  250°  F.  and  room  temperature  is  60°  F.? 

20.  Determine  the  approximate  higher  and  lower  heat  values  by  Dulong  s 
formulas  for  a  fuel  of  the  following  composition  by  weight:    carbon,  70  per 
cent;  hydrogen,  25  per  cent;   oxygen,  2  per  cent;   sulphur,  3  per  cent. 

21.  Determine  the  weight  of  dry  fuel  gases  per  pound  of  carbon  burned 
for  a  case  in  which  the  gases  analyze:  carbon  dioxide,  14  per  cent;   carbon 
monoxide,  2  per  cent;    hydrogen,  I  per  cent;    sulphur  dioxide,  I  per  cent; 
oxygen,  2  per  cent;  nitrogen,  80  per  cent. 

CHAPTER  XXX. 

i  During  the  test  of  a  certain  boiler  it  is  found  that  when  fired  with  coal 
with  a  heat  value  of  14,000  B.t.u.  per  pound  the  ash  contains  0.2  of  a  pound 
of  carbon  per  pound  of  coal  fired,  (a)  What  is  the  heat  value  of  the  ascend- 
ing combustible  per  pound  of  carbon?  (b)  What  is  the  grate  efficiency? 

2.  If  each  pound  of  coal  fired  as  in  problem  I  causes  the  generation  of 
8  Ibs  of  dry  and  saturated  steam  at  a  pressure  of  150  Ibs.  abs.  from  feed 


776  HEAT-POWER  ENGINEERING 

water  at  a  temperature  of  120°  F.,  what  is  the  value  of  the  boiler  efficiency 
according  to  the  A.S.M.E.  definition? 

3.  What  is  the  over-all  efficiency  of  the  boiler  considered  in  problems  I 
and  2  above? 

4.  If  a  boiler  generates  9  Ibs  of  steam  with  a  quality  of  97  per  cent  at  a 
pressure  of  125  Ibs.  abs.  from  feed  at  a  temperature  of  70°  F.,  what  is  the 
equivalent  evaporation? 

5.  A  certain  boiler  generates  steam  at  a  pressure  of   160  Ibs.  abs.,  and 
superheated  100  degrees  from  feed  at  a  temperature  of  200°  F.     What  is  the 
factor  of  evaporation? 

6.  How  many  pounds  of  water  at  a  temperature  of  70°  F.  should  be  con- 
verted into  dry  saturated  steam  at  125  Ibs  gauge  per  hour  by  a  loo-h.p.  boiler 
when  operating  at  normal  load?     What  is  the  factor  of  evaporation  for  this 
case?     How  many  pounds  of  material  would  leave  the  boiler  per  hour  if  it 
gave  steam  with  a  quality  of  97  per  cent? 

CHAPTER  XXXII. 

1.  (a)  Using  Fig.  326  and  Table  XXIV,   how  much  draft   through  the 
boiler  will  probably  be  required  to  burn  20  Ibs.  of  anthracite  pea  coal  per 
square  foot  of  grate  per  hour?     (b)  With  50  ft.  of  flue  and  two  90°  bends,  what 
will  be  the  draft  probably  required  at  the  base  of  the  stack?     (B.  and  W. 
Boiler.) 

2.  (a)  With  flue  temperature  550°  F.  and  air  at  60°.  what  would  be  the 
theoretical  height  of  stack  for  case  given  in  problem  i  ?     (b)  What  would  be 
the  actual  height?     (c)  What  would  be  its  diameter  in  inches  for  a  2000 
boiler  h.p.  plant? 

CHAPTER   XXXV. 

i.  Determine  the  quantity  of  heal  which  will  flow  per  hour  between  two 
planes  I  ft.  apart  and  of  6  sq.  ins.  section  with  a  temperature  difference  of 
100°  F..  the  material  being  commercial  copper  and  no  allowance  being  made 
for  variation  of  specific  conductivity  with  temperature.  Determine  the 
"heat  resistance"  of  the  material  between  the  two  planes. 

"2.  Determine  the  same  quantities  as  called  for  in  problem  i,  but  for  a 
case  in  which  soft  steel  is  the  conducting  material. 

3.  Determine  the  same  quantities  as  called  for  in  problem  i,  but  for  cases 
in  which  water  and  air  are  the  conducting  materials. 

4.  Tabulate  the  values  obtained  for  quantity  of  heat  transmitted  in  above 
cases  and  tabulate  values  as  percentage  by  calling  that  transmitted  by  coppe  • 
loo  per  cent. 

5.  Taking  values  from  Table  XXVI,  determine  the  specific  conductivity  of 
yellow  brass  at  a  temperature  of  200°  F. 

6.  Assuming  values  given  in  the  text  as  correct,  determine  the  amount  of 
heat  lost  by  radiation  in  i  hour  from  the  black  surface  of  a  sphere  of  i  ft. 
radius  and  at  a  temperature  of  1000°  F.     Do  the  same  for  a  temperature  of 
2000° F. 

»  7.  (a)  If  the  temperature  difference  at  end  a  of  the  heating  surface  is 
2000°  and  at  end  b  it  is  200°,  what  is  the  mean  temperature  difference  with 
flow?  (b)  If  K  =  3.7,  how  many  square  feet  of  heating  surface  will  be  re- 
auired  to  transmit  per  hour  33,463  B.t.u.  (=  I  boiler  h.p.)? 
^J  8.  A  surface  condenser  receives  exhaust  steam  at  temperature  H5°F., 
the  initial  temperature  of  the  condensing  water  is  60°  F.  and  its  final  temper- 
ature 105°  F.  (a*  What  is  the  mean  tenperaturc  difference?  (b)  With 
K  =  300,  what  weight  of  dry  steam  will  be  condensed  per  square  foot  of  sur- 
face per  hour?  (c)  What  is  the  efficiency  of  the  surface  (neglecting  losses)? 

9.  In  a  boiler  the  furnace  gases  are  cooled  from  2500°  F.  to  550°  F.  and  the 
temperature  of  the  steam  is  350°  F.  (a)  Neglecting  losses,  what  is  the  mean 
temperature  difference?  (b)  If  3^  Ibs.  of  steam  from  and  at  212°  is  evapo- 
rated per  square  foot  of  heating  surface,  what  is  the  value  of  Kt 


PROBLEMS 


777 


10.  With   parallel  flow  the  initial  and  final  temperature  differences  are 
500     and   203.     (a)  What  is  the   mean   temperature   difference?     (b)  With 
K  =  3  B.t.u.  how  much  heating  surface  is  required  for  heating  10  Ibs  of  water 
per  hour  from  60°  to  192°? 

11.  (a)  With  counter-current  flow,  with  a  temperature  difference  of  322° 
at  one  end  of  the  heating  surface  and  357°  at  the  other  end,  what  is  the  mean 
temperature  difference?     (6)  With  K  =  3  B.t.u.  how  much  heating  surface 
is  required  for  heating  30  Ibs.  of  water  per  hour  from  60°  to  192°  F?? 

12.  In  a  feed  water  heater  90  Ibs.  of  water  per  hour  are  heated  by  I  sq   ft 
of  heating  surface,  K  being  220.     (a)  If  the  initial  temperature  difference  e'a 
is  142°,  what  is  the  final  value  0&,  neglecting  losses?     (6)  What  is  the  effi- 
ciency?    (c)  Compute  the  efficiencies  corresponding  to  different  extents  of 
surface  and  plot  curve  showing  its  variations. 

13.  In  a  boiler  the  initial  temperature  difference  between  gas  and  water  is 
2000°  F.     (a)  If  one  boiler  horse-power  hour  is  equivalent  to  33,479  B.t.u.  and 
K  is  3.7,  what  will  be  the  final  temperature  difference  (neglecting  losses)  if 
100  Ibs.  of  flue  gas  (with  Cp  =  0.24)  are  generated  per  boiler  h.p.  hour.     (6) 
What  is  the  efficiency?     (c)  Compute  the  efficiencies  corresponding  to  differ- 
ent extents  of  surface  and  plot  curves  showing  its  variation. 

14.  In  an   economizer  with   parallel   flow,   K  =  3,    Wc  =  30,    WH  =  100, 
Ch=  0.24,  5=4,  Ta=  600,  ta=  ioo.     Find  06,  Tb  and  /&. 

15.  Same  data  as  problem  14,  but  for  counter  flow,     (a)  Find  00,  06,  Tb 
and  ta. 

CHAPTER  XXXVI. 

1 .  Determine  the  theoretical  percentage  of  saving  effected  by  supplying  feed 
water  at  a  temperature  of  120°  F.  instead  of  60°  F.  to  a  boiler  generating  dry 
saturated  steam  at  a  pressure  of  150  Ibs.  abs. 

2.  Determine  the  theoretical  percentage  of  saving  effected  by  supplying 
feed  water  at  a  temperature  of  200°  F.  instead  of  60°  F.  to  a  boiler  generating 
dry  saturated  steam  at  a  pressure  of  150  Ibs.  abs.     What  is  the  percentage 
saving  if  the  boiler  superheats  the  steam  ioo°?     What  is  the  actual  amount 
of  heat  "saved"  per  pound  of  steam  generated  in  each  case? 

3.  How  many  pounds  of  steam  per  pound  of  water  heated  will  be  required 
to  raise  the  temperature  of  feed  from  60°  F  to  190°  F.  in  an  open  heater  oper- 
ated at  atmospheric  pressure  if  the  steam  enters  the  heater  at  atmospheric 
pressure  and  with  ioo  per  cent  quality?     How  many  will  be  required  if  the 
steam  has  a  quality  of  90  per  cent?     What  weight  of  water  will  leave  the 
heater  in  each  case  for  every  pound  of  water  entering? 

4.  What  is  the  maximum  possible  weight  of  steam  exhausted  from  an 
engine  at  atmospheric  pressure  and  85  per  cent  quality  which  could  be  uti- 
lized in  an  open  feed  heater  if  the  feed  water  is  to  have  its  temperature  raised 
from  50°  F.  to  200°  F.  and  if  the  heater  has  an  efficiency  of  95  per  cent? 

5.  An  economizer  with  counter  flow  receives  flue  gas  at  temperature  of 
600°,  and  water  at  60°.     Thirty  pounds  of  water  are  heated  per  hour  by  ioo 
Ibs.  of  gas  (Cp  =  0.24)  through  4  sq.  ft.  of  surface,  K  being  3.     (a)  Find  the 
increase  in  the  temperature  of  the  feed  water  and  (6)  the  decrease  in  the 
temperature  of  the  flue  gas. 

CHAPTER  XXXVII. 

1.  (a)   In  a  direct-contact  condenser  how  much  condensing  water  per  pound 
of  steam  will  be  required  if  the  vacuum  is  26  ins.  and  the  condensing  water  is 
raised  from  60°  F.  to  within  10°  of  the  temperature  of  the  exhaust  steam 
(£/.  =  0.9)?     (b)  How  much  is  required  with  28-in.  "vacuum"? 

2.  (a)  Same  as  i  except  for  surface  condenser,  the  temperature  of  the  con- 
densate  being  reduced  to  10°  below  that  of  the  exhaust  steam.     (6)  What  is 
the  mean  temperature  difference?     (c)  How  much  cooling  surface  is  required 
per  pound  of  steam  condensed  per  hour  if  K  =  300? 


778  HEAT-POWER  ENGINEERING 

3.  If  400,000  Ibs.  of  condensing  water  are  used  per  hour  in  a  jet  condenser, 
what  would  be  the  probable  plunger  displacement  in  cubic  feet  per  minute  of 
a  single-acting  wet  air  pump? 

4.  (a)  If  a  surface  condenser  used  with  a  turbine  condenses  10,000  Ibs.  of 
steam  per  hour,  what  would  be  the  probable  plunger  displacement  of  a  wet- 
air  pump  in  cubic  feet  per  minute?     (b)  What,  for  a  dry-air  pump,  the  vacuum 
being  28  ins.  Hg.? 

CHAPTER  XL. 

I  to  6.    Same  as  problems  1-6  under  Chap.  XXII,  but  applied  to  nozzles. 

7.  (a)  Neglecting  losses,  find  the  discharge  velocities  per  pound  of  steam 
flowing  in  problems  I  to  4.     (b)  Find  the  area  of  the  nozzle  end  per  pound  of 
steam. 

8.  With  the  initial  conditions  given  in  problems  I  to  4  plot  curves  as  in 
Sec.  331. 

9.  (a)  If  Ef.  =  0.9,  what  heat  remains  per  pound  of  steam  at  the  end  of 
expansion  with  the  same  conditions  as  in  problems  I  to  4?     (6)  What  is  the 
final  quality?     (c)  What  is  the  final  entropy? 

10.  (a)  Compute  the  neck  areas  in  problem  8  by  Napier's  formula.     (6) 
Same,  by  Grashof's  formula. 

11.  (a)  With   uniform   flow  and  allowing  5   Ibs.   drop  in  pressure,  what 
would  be  the  diameter  of  pipe  to  convey  in  i  minute  200  Ibs.  of  dry  steam 
initially  at  150  Ibs.  gauge  pressure,  the  length  of  pipe  being  200  ft.?     (b)  What 
would  be  the  velocity  of  flow? 

12.  (a)  If  a  steam  engine  with  cylinder  18  ins.  diameter  and  stroke  24  ins. 
operates  at  200  r.p.m.,  what  should  be  the  diameter  of  the  steam  pipe?      (b) 
What  should  be  the  diameter  of  the  exhaust  pipe? 

14.  (a)  What  weight  of  air  v.dll  theoretically  flow  per  second  through  a 
nozzle  having  a  neck  area  of  I  sq.  in.,  if  the  initial  pressure  is  80  Ibs.  per  sq. 
in.  abs.  and  temperature  is  60°  F.  and  if  the  discharge  is  into  the  atmosphere? 
(b)  What  will  be  the  velocity  of  flow  at  the  neck? 

15.  (a)  With  initial  pressure  20  Ibs.  per  sq.  in.  abs.  and  temperature  60°  F., 
what  will  be  the  theoretical  velocity  of  discharge  to  the  atmosphere?     (b) 
What  weight  will  flow  per  second  through  an  orifice  having  an  area  of  I  sq.  in.? 

16.  With  I  Ib.  of  air  flowing  through  a  nozzle  per  second  with  initial  pres- 
sure (Pi)  80  Ibs.  per  sq.  in.  abs.  and  temperature  60°  F.,  plot  curves  showing 
how  the  decrease  in  back  pressure  (Px)  affects  (a)  the  velocity  of  flow,  (b)  the 
volume  of  the  air  and  (c)  the  area  of  the  nozzle,  the  abscissas  being  ratios 
Pi/P*. 

CHAPTER  XLI. 

1.  Determine  the  work  which  must  be  done  per  cycle  in  an  air  compressor 
cylinder  without  clearance  which  operates  under  the  following   ideal   condi- 
tions.    At  the  end  of  the  suction  stroke  the  cylinder  contains  one-tenth  of  a 
pound  of  air  at  a  temperature  of  60°  F.  and  a  pressure  of  14.7  Ibs.  per  sq.  in. 
abs. 

2.  Determine  the  work  which  must  be  done  per  cycle  in  an  air  compressor 
cylinder  with  clearance  equal  to  5  per  cent  of  the  piston  displacement  and 
which  operates  under  the  following  conditions.     It  draws  in  one-tenth  of  a 
pound  of  air  during  the  suction  stroke;   this  air  mixed  with  that  caught  in  the 
clearance  has  a  temperature  of  60°  F.  at  the  end  of  the  suction  stroke;    the 
pressure  during  the  suction  stroke  is  constant  and  equal  to  14.7  Ibs.  per  sq.  in. 
abs.;    compression  and  expansion  are  adiabatic;    and  air  is  discharged  at  a 
constant  pressure  of  50  Ibs.  per  sq.  in.  abs. 

3.  Determine  the  capacity  of  such  a  compressor  in  terms  of  free  air  (60°  F. 
and  14.7  Ibs.)  per  min.  if  it  operates  at  a  speed  of  180  r.p.m.  and  is  built 
double  acting. 

4.  Assume  three  compressor  cylinders  without  clearance  and  with  a  piston 
displacement  of  I  cu.  ft.,  one  cylinder  so  arranged  as  to  give  adiabatic  com- 
pression;  one  arranged  to  give  isothermal  compression;   and  one  arranged  to 


PROBLEMS 


779 


give  a  compression  curve  with  exponent  equal  to  1.25.  (a)  Determine  the 
work  done  during  one  compression  in  each  cylinder  and  the  final  temperature 
in  each  case  if  air  with  an  initial  temperature  of  60°  F.  and  at  an  initial  pres- 
sure of  14.7  Ibs.  per  sq.  in.  abs.  is  compressed  to  45  Ibs.  per  sq.  in.  abs.  (b) 
Express  the  saving  in  the  second  and  third  cases  as  a  percentage  of  the  com- 
pression work  in  the  case  of  the  adiabatic  process,  (c)  Determine  the  work 
per  cycle  in  each  case,  assuming  discharge  to  occur  at  the  constant  pressure  of 
45  Ibs.  (d)  Express  savings  as  per  cent,  as  in  (b).  (e)  Make  calculations 
called  for  in  (a),  (b),  (c)  and  (d)  but  with  a  discharge  pressure  of  100  Ibs.  per 
sq.  in.  abs. 

5.  Compare  the  work  done  in  the  air  cylinder  per  cycle  in  the  following 
cases,  express  saving  as  per  cent  of  work  in  least  favorable  case,  and  deter- 
mine discharge  temperature,     (a)  An  air  compressor  cylinder  without  clear- 
ance has  a  diameter  of  16  ins.  and  a  stroke  of  18  ins.     The  air  at  the  end  of 
the  suction  stroke  has  a  temperature  of  60°  F.,  and  a  pressure  of  14.7  Ibs.  per 
sq.  in.  abs.     The  compression  is  adiabatic  and  discharge  occurs  at  a  constant 
pressure  of  ipo  Ibs.  per  sq.  in.  abs.     (b)  The  same  cylinder  with  the  same 
initial  conditions  gives  a  compression  line  with  exponent  equal  to  1.3.     (c) 
Two-stage  compression  is  used  with  an  intercooler.     The  low-pressure  cylin- 
der has  the  same  size  as  before  and  operates  under  the  same  initial  conditions 
but  gives  a  compression  curve  with  exponent  equal  to  1.22  and  discharges  at 
such  a  pressure  that  cooling  at  constant  pressure  to  initial  temperature  will 
give  the  air  a  volume  equal  to  the  piston  displacement  of  the  high-pressure 
cylinder.     The  high-pressure  cylinder  has  a  diameter  of  10  ins.  and  a  stroke 
of  1 8  ins.,  gives  a  compression  curve  with  exponent  equal  to  1.22  and  dis- 
charges at  a  constant  pressure  of  100  Ibs.  per  sq.  in.     There  are  no  transfer 
losses  between  stages. 

6.  Assume  that  I  Ib  of  air  with  initial  conditions  60°  F.  and  14.7  Ibs.  per 
sq.  in.  abs.  has  been  compressed  adiabatically  to  a  pressure  of  80  Ibs.  per  sq. 
in.,  and  then  cooled  at  constant  pressure  to  initial  temperature  after  discharge 
from  the  compressor.     If  this  air  is  used  in  an  air  engine  without  clearance, 
operating  on  a  cycle  of  the  same  shape  as  the  PV-diagram  of  the  Clausius 
cycle,  and  expanding  to  atmospheric  pressure,  determine  (a)  the  work  made 
available  in  the  engine,     (b)  the  efficiency  of  the  process  in  the  ideal  case,  i.e., 
work  made  available  -5-  work  done  in  air  compressor  cylinder,     (c)  The  final 
temperature  attained  in  the  engine  cylinder. 

7.  Assume  the  same  conditions  as  in  problem  6  above,  excepting  that  the 
air  before  entrance  to  the  engine  is  preheated  at  constant  pressure  to  a  tem- 
perature of  300°  F.     Determine  the  values  called  for  under  (a),  (b)  and  (c)  of 
that  problem. 


APPENDIX. 


USE  OF  COMMON  LOGARITHMS  FOR  SPECIAL  CASES. 

CASE  I.    To  DETERMINE  THE  WTH  POWER  OF  A  NUMBER 
LESS  THAN  UNITY. 

Example:  Find  O.51-55  by  logs. 

In  general  logic  Vn  =  w  logio  F;  and  in  this  case  V  —  0.5   and 

n  =  1.55- 

From  the  tables     logio  0.5  =  9.6990  —  10, 

Then,     1.55  logw  0.5  =  1.55  (9.6990  ~  ™)  =  I5-O3345O  -  15-5 
Subtract  5.5  to  reduce  the  negative  part  of 

the  characteristic  to  i  o,  5.5  —    5.5 

Log.  of  answer  =    9.533450  —  10.0 
Corresponding  number  =    0.342  =  0.5*  55. 

(Note  that  a  fraction  raised  to  a  power  greater  than  unity 
gives  a  result  less  than  the  original  fraction.) 

CASE  II.    To  DETERMINE  THE  WTH  ROOT  OF  A  FRACTION. 
Example:  Given  F1-5  =  0.75;  Find  V.     Evidently,— 

logio  F  =  logio  (^0.75)  =  log™  \o-751  V  =  flogioo.75)  •*•  1.5, 
which  is  in  the  general  form  of  logio  V  =  (logio  C)  -r-  n, 
where  C  =  0.75  and  n  =  1.5. 

From  the  tables  logio  0.75  =  9-8751  —  10. 


Then  -75)  =  (9.8751  -  10)  =  6.5g33  _  6.666. 

Add  3.334  to  raise  the  negative  part 

of  the  characteristic  to  10,  3-334°  —    3-334 

Log.  of  V  =  9.9173  —  10.000 

The  corresponding  number  is  0.8266  which  is  ^0.75. 

780 


APPENDIX 


781 


TABLE  A.  —  COMMON  LOGARITHMS  (Loglo). 


JNo. 

01234 

56789 

Diff. 

o 

o   oooo  3010  4771  6021 

6990  7782  8451  9031  9542 

10 

II 

12 
1  13 
14 

oooo  0043  0086  0128  0170 

0414  0453  0492  0531  0569 
0792  0828  0864  0899  0934 
1139  1173  1206  1239  1271 
1461  1492  1523  1553  1584 

0212   0253   0294   0334   0374 
0607   0645   0682   0719   0755 

0969  1004  1038  1072  1106 
J3Q3  1335  1367  1399  1430 
1614  1644  1673  1703  1732 

42 
38 
35 
32 
3° 

IS 

16 

l? 

18 

19 

1761  1790  1818  1847  1875 

2041   2068   2095   2122   2148 

2304  2330  2355  2380  2405 
2553  2577  2601  2625  2648 
2788  2810  2833  2856  2878 

J903  J93*  1959  1987  2014 
2175  2201  2227  2253  2279 
2430  2455  2480  2504  2529 
2672  2695  2718  2742  2765 
2900  2923  2945  2967  2989 

28 
26 
25 
24 

22 

20 

21 
22 
23 
24 

3010  3032  3054  3075  3096 
3222  3243  3263  3284  3304 

3424  3444  3464  3483  3502 
3617  3636  3655  3674  3692 
3802  3820  3838  3856  3874 

3118  3139  3160  3181  3201 
3324  3345  3365  3385  3404 
3522  3541  3560  3579  3598 
3711  3729  3747  3766  3784 
3892  3909  3927  3945  3962 

21 
2O 
19 
19 

18 

25 

26 

27 
28 

29 

3979  3997  4014  4031  4048 
4150  4166  4183  4200  4216 
4314  4330  4346  4362  4378 
4472  4487  4502  4518  4533 
4624  4639  4654  4669  4683 

4065  4082  4099  4116  4133 
4232  4249  4265  4281  4298 
4393  4409  4425  4440  4456 
4548  4564  4579  4594  4609 
4698  4713  4728  4742  4757 

17 

16 
16 
15 
IS 

30 

31 

32 

33 
34 

4771  4786  4800  4814  4829 
4914  4928  4942  4955  4969 
5051  5065  5079  5092  5105 
5185  5198  5211  5224  5237 
53i5  5328  5340  5353  5366 

4843  4857  4871  4886  4900 
4983  4997  5011  5024  5038 
5119  5132  5145  5159  5172 
5250  5263  5276  5289  5302 
5378  5391  5403  54i6  5428 

14 
14 
13 
13 
13 

35 

36 

8 

39 

5441  5453  5465  5478  5490 

5563  5575  5587  5599  5611 
5682  5694  5705  5717  5729 
5798  5809  5821  5832  5843 
5911  5922  5933  5944  5955 

5502  5514  5527  5539  5551 
5623  5635  5647  5658  5670 
5740  5752  5763  5775  5786 
5855  5866  5877  5888  5899 
5966  5977  5988  5999  6010 

12 
12 
12 
II 
II 

40 

4i 
42 
43 
44 

6021  6031  6042  6053  6064 
6128  6138  6149  6160  6170 
6232  6243  6253  6263  6274 
6335  6345  6355  6365  6375 
6435  6444  6454  6464  6474 

6075  6085  6096  6107  6117 
6180  6191  6201  6212  6222 
6284  6294  6304  6314  6325 
6385  6395  6405  6415  6425 
6484  6493  6503  6513  6522 

II 
IO 
10 
10 
10 

45 

46 

47 
48 
49 

6532  6542  6551  6561  6571 
6628  6637  6646  6656  6665 
6721  6730  6739  6749  6758 
6812  6821  6830  6839  6848 
6902  6911  6920  6928  6937 

6580  6590  6599  6609  6618 
6675  6684  6693  6702  6712 
6767  6776  6785  6794  6803 
6857  6866  6875  6884  6893 
6946  6955  6964  6972  6981 

IO 

9 
9 
9 
9 

50 

Si 
52 
53 
54 

6990  6998  7007  7016  7024 
7076  7084  7093  7101  7110 
7160  7168  7177  7185  7i93 
7243  7251  7259  7267  7275 
7324  7332  7340  7348  7356 

7033  7042  7050  7059  7067 
7118  7126  7135  7143  7i52 
7202  7210  7218  7226  7235 
7284  7292  7300  7308  7316 
7364  7372  738o  7388  7396 

9 
9 
8 
8 
8 

e  =  2.71828 


782 


APPENDIX 


TABLE  A.    (Concluded}.  —  COMMON  LOGARITHMS  (Log10). 


No. 

01234 

56789 

Diff. 

1 

57 
58 
59 

7404  7412  7419  7427  7435 
7482  7490  7497  7505  7513 
7559  7566  7574  7582  7589 
7634  7642  7649  7657  7664 
7709  7716  7723  7731  7738 

7443  745i  7459  7466  7474 
7520  7528  7536  7543  7551 
7597  7604  7612  7619  7627 
7672  7679  7686  7694  7701 
7745  7752  776o  7767  7774 

8 
8 
8 

7 
7 

60 

61 
62 

63 
64 

7782  7789  7796  7803  7810 
7853  7860  7868  7875  7882 
7924  7931  7938  7945  7952 
7993  8000  8007  8014  8021 
8062  8069  8075  8082  8089 

7818  7825  7832  7839  7846 
7889  7896  7903  7910  7917 
7959  7966  7973  7980  7987 
8028  8035  8041  8048  8055 
8096  8102  8109  8116  8122 

7 
7 
7 
7 
7 

65 

66 
67 
68 
69 

8129  8136  8142  8149  8156 
8195  8202  8209  8215  8222 
8261  8267  8274  8280  8287 
8325  8331  8338  8344  8351 
8388  8395  8401  8407  8414 

8162  8169  8176  8182  8189 
8228  8235  8241  8248  8254 
8293  8299  8306  8312  8319 
8357  8363  8370  8376  8382 
8420  8426  8432  8439  8445 

7 

6 
6 
6 

70 

7i 
72 

73 
74 

8451  8457  8463  8470  8476 
8513  8519  8525  8531  8537 
8573  8579  8585  8591  8597 
8633  8639  8645  8651  8657 
8692  8698  8704  8710  8716 

8482  8488  8494  8500  8506 
8543  8549  8555  8561  8567 
8603  8609  8615  8621  8627 
8663  8669  8675  8681  8686 
8722  8727  8733  8739  8745 

6 
6 
6 
6 
6 

75 

76 

77 
78 
79 

8751  8756  8762  8768  8774 
8808  8814  8820  8825  8831 
8865  8871  8876  8882  8887 
8921  8927  8932  8938  8943 
8976  8982  8987  8993  8998 

8779  8785  8791  8797  8802 
8837  8842  8848  8854  8859 
8893  8899  8904  8910  8915 
8949  8954  8960  8965  8971 
9004  9009  9015  9020  9025 

6 
6 
6 
6 

5 

80 

81 
82 
83 
84 

85 

86 

87 
88 
89 

9031  9036  9042  9047  9053 
9085  9090  9096  9101  9106 
9138  9143  9149  9154  9159 
9191  9196  9201  9206  9212 
9243  9248  9253  9258  9263 

9058  9063  9069  9074  9079 
9112  9117  9122  9128  9133 
9165  9170  9175  9180  9186 
9217  9222  9227  9232  9238 
9269  9274  9279  9284  9289 

5 
5 
5 
5 
5 

9294  9299  9304  9309  9315 
9345  9350  9355  936o  9365 
9395  9400  9405  9410  9415 
9445  945°  9455  946o  9465 
9494  9499  95°4  95°9  95  13 

9320  9325  9330  9335  9340 
9370  9375  938o  9385  9390 
9420  9425  9430  9435  9440 
9469  9474  9479  9484  9489 
9518  9523  9528  9533  9538 

5 
5 
5 
5 
5 

90 

9i 
92 

93 
94 

95 

06 

97 
98 

99 

9542  9547  9552  9557  9562 
9590  9595  9600  9605  9609 
9638  9643  9647  9652  9657 
9685  9689  9694  9699  9703 
9731  9736  974i  9745  9750 

9566  9571  9576  9581  9586 
9614  9619  9624  9628  9633 
9661  9666  9671  9675  9680 
9708  9713  9717  9722  9727 
9754  9759  9763  9768  9773 

5 
5 
5 
5 
5 

9777  9782  9786  9791  9795 
9823  9827  9832  9836  9841 
9868  9872  9877  9881  9886 
9912  9917  9921  9926  9930 
9956  9961  9965  9969  9974 

9800  9805  9809  9814  9818 
9845  9850  9854  9859  9863 
9890  9894  9899  9903  9908 
9934  9939  9943  9948  9952 
9978  9983  9987  9991  9996 

5 
4 
4 
4 
4 

Naperian  loge  =  2.302  Iogi0. 


APPENDIX  783 

TABLE  B.  —  HYPERBOLIC  OR  NAPERIAN  LOGARITHMS,  (log.). 


N. 

Log. 

N. 

Log. 

N. 

Log. 

N. 

Log. 

N. 

Log. 

.00 

o.oooo 

2.30 

0.8329 

3.60 

.2809 

4.90 

.5892 

6.40 

•8563 

•05 

0.0488 

2-35 

0.8544 

3.65 

.2947 

4-95 

•5994 

6.50 

.8718 

.10 

0.0953 

2.40 

0.8755 

3-70 

-3083 

5.00 

.6094 

6.60 

.8871 

•  15 

0.1398 

2-45 

0.8961 

3-75 

.3218 

5-05 

.6194 

6.70 

.9021 

.20 

0.1823 

2  50 

0.9163 

3.80 

•3350 

.6292 

6.80 

.9169 

•25 

0.2231 

2-55 

0.9361 

3.85 

5-iS 

.6390 

6.90 

9315 

•3° 

o.  2624 

2.60 

0-9555 

3-90 

.3610 

5-20 

.6487 

7.00 

•9459 

•35 

0.3001 

2.65 

0.9746 

3-95 

•3737 

5-25 

.6582 

7.20 

•9741 

.40 

0.3365 

2.70 

0-9933 

4.00 

•3863 

5-30 

.6677 

7.40 

2.0015 

•  45 

0.3716 

2-75 

1.0116 

4-05 

.3987 

5-35 

.6771 

7.60 

2.0281 

•So 

0.4055 

2.80 

i  .  0296 

4.10 

.4110 

5-40 

.6864 

7.80 

2.0541 

•55- 

0.4383 

2.85 

•  0473 

4-15 

•  4231 

5-45 

.6956 

8.00 

2.0794 

.60 

0.4700 

2.90 

•  0647 

4.  20 

•4351 

5-50 

.7047 

8.25 

2.  IIO2 

•65 

0.5008 

2-95 

.0818 

4-25 

.4469 

5-55 

•7138 

8.50 

2  .  I4OI 

.70 

0.5306 

3-oo 

.0986 

4-30 

•  4586 

5-6o 

.7228 

8-75 

2.  1691 

•  75 

0.5596 

3-05 

.1151 

4-35 

.4702 

5.65 

•7317 

9.00 

2.1972 

.80 

0.5878 

3.10 

•  1314 

4.40 

.4816 

5-70 

•7405 

9-25 

2.2246 

•85 

0.6152 

3-15 

•  1474 

4-45 

.4929 

5-75 

.7492 

9-50 

2.2513 

.90 
•95 

0.6419 

0.6678 

3-20 

3-25 

.1632 
.1787 

4-So 
4-55 

•  5041 

5.80 
5.85 

•7579 
.7664 

9-75 

IO.OO 

2.2773 
2  .  3026 

2.00 

0.6931 

3-30 

•1939 

4.60 

.5261 

5-90 

•7750 

II.  OO 

2.3979 

2.05 

2.  IO 

0.7178 

0.7419 

3-35 
3-40 

.2090 
.2238 

4-65 
4-70 

.5369 
.5476 

5-95 
6.00 

.7834 
.7918 

12.  OO 
13.00 

2.4849 
2  -  5649 

2.15 
2.20 
2.25 

0.7655 
0.7885 

0.8109 

3-45 
3-50 
3-55 

•  2384 
.2528 
i  .  2669 

4-75 
4.80 

4-85 

^5686 
•5790 

6.  10 

6.20 

6.30 

.8083 
•  8245 
•  8405 

14.00 
15.00 

16.00 

2.6391 
2.7081 
2.7726 

(1)  To  find  loge  of  a  number  greater  than  10  (for  example  21):  - 
Loge  21  =  loge  (10  X  2.1)  =  loge  io  +  loge  2.1  =  2.3026  +  O-74I9  =  3-O445- 

(2)  Base  e  =  2.71828  and  log,a  =  2.302  X  logioa. 


•/&* 


APPENDIX 


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APPENDIX 


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^  ^o  t^«oo  o 

o  o*  o  o  o 


o  o 
d  d 

00  00 


oooooooooo 


POPOPO<N(N  <NCN<NCSM  MMMMM  MMOOO 

oooooooooo       oooooooooo       oooooooooo       oooooooooo 


to  CO          Cs    M    O    O-OO 


MMWOO         OOOOO         OOOOO        OO  Ooo  oo 
OOOOO\         OOOO\O       OOOOOOOOOO        OOOOOOOOOO 


PO  Tj-  too  vO 

^-OOOO<N          TJ-OOQOM          POtot^OOO 
O  vO  O    t^-  f^*          t^*  f^*  r*»OO  OO          OO  00  OO  OO    Ov 


OOtoMOtO          Mt^  «*500    PO 


*$**'$ 


OOOOO 


. 
fe 


oo^i-ir-po      oo^to*  Tfoo 
fO  to  t^oo  O        M 


. 

WHH 

. 

J  cr 


POPOPOPOPO 

t^.<>HPO»0 

it  ^  10  to  »O 


POPOPOPOPO 

^CJvMPO>0 

\r>  \f)\o 


POPOPOPOfO 


*^  t^OO  00  OO 


788 


APPENDIX 


vOfO         CSMO\M<N  Ortrr)iO(N 

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t^-lO          ^rOMMO  O\OO    r^-^O  *O 


O  O    O 

O      Tt     O 


MWCNMCS  <NCSCSCSCN 


»  ^ 

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APPENDIX 


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C/2 

«  «   * 

7QO 


APPENDIX 


TABLE  D 
PROPERTIES  OF  ONE  POUND  OP 

SUPERHEATED   STEAM. 


[Condensed  from  Marks  and  Davis's  STEAM  TABLES  AND  DIAGRAMS,  1909,  by 
publishers,  Longmans,  Green  &  Co.] 


Sp.  V  =  specific  volume  in  cu.  ft. ;  &Q 
=  total  entropy  above  32°  F. 


permission  of  the 
B.t.u.  total  heat  above  32°  F.; 


Absolute 
Pressure. 
Lbs.  Sq.  In 

Degrees  of  Superheat. 

Sat.  Temp. 

op 

0 

50 

100 

ISO 

200 

250 

300 

15 

(213) 

Sp.V. 
AQ 
A0 

26.27 
1150.7 
1-7549 

28.40 
II74.2 
I  .  7886 

30.46 
1197.6 
1.8199 

32.50 
I22I.O 
1.8492 

34-53 
1244.4 
1.8768 

36.56 
1267.7 
1.9029 

38.58 
1291.  I 
1.9276 

50 

(281) 

Sp.  V. 
AQ 
A4> 

8.51 
1173.6 
1.6581 

9.19 
1198.8 
1.6909 

9.84 
1223.4 
1.7211 

10.48 
1247.7 
I.749I 

ii  .  ii 

1271.8 
1-7755 

11.74 
1295.8 
1.8002 

12.36 

I3I9-7 
1-8237 

100 

(327.8) 

Sp.  V. 
AQ 
A4> 

4-43 
1186.3 
i  .6020 

4-79 
1213.8 

1,6358 

5-14 
1239.7 
1.6658 

5-47 
1264-7 
I-6933 

5-8o 
1289.4 
1.7188 

6.12 

1313-6 

1.7428 

6.44 
1337-8 
1.7656 

1  10 

(334-  8)  1 

Sp.  V. 
AQ 
A<£ 

4-05 
1188.0 
i  •  5942 

4-38 
1215.9 
1.6282 

4.70 
1242.0 
1.6583 

S-oi 
1267.1 
1.6857 

5-31 
1291.9 
1.7110 

5.61 
1316.2 
1-7350 

5-90 
1340.4 
1.7576 

I2O 

(341.3) 

Sp.  V. 
AQ 
A<£ 

3-73 
1189.6 

1.5873 

4.04 
1217.9 
1.6216 

4-33 
1244.1 
1.6517 

4.62 
1269.3 
1.6789 

4.89 
1294.1 
1.7041 

5-17 
1318.4 
1.7280 

5-44 
1342.7 
i  •  7505 

130 

(347-4) 

Sp.  V. 
AQ 
A<t> 

3-45 
1191  .0 
i  .  5807 

3-74 
1219.7 

i.6i53 

4.02 
1246.  i 
1.6453 

4.28 
1271.4 
1.6724 

4-54 
1296.2 
1.6976 

4.80 
1320.6 
1.7213 

5-05 
1344-9 
1-7437 

140 

(353  -1) 

Sp.  V. 
AQ 
A0 

3-22 
II92.2 

1-574-7 

3-49 
1221.4 
1.6096 

3-75 
1248.0 

1-6395 

4.00 

1273-3 
1.6666 

4.24 

1298.  2 
1.6916 

4.48 
1322.6 
1.7152 

4.71 
1346  .  9 
1.7376 

ISO 

(358.5) 

Sp.  V. 
AQ 
A0 

3-oi 
II93-4 
i  .  5692 

3-27 
1223.0 
i  .  6043 

3-5i 
1249.6 

1-6343 

3-75 
1275.1 
1.6612 

3-97 
1300.0 
1.6862 

4.19 

1324-5 
1.7097 

4.41 
1348.8 
1-7320 

160    j 

(363-  6)  1 

Sp.  V. 

'     AC 

A0 

2.83 
II94-5 
i  •  5693 

3-07 
1224.5 

1-5993 

3-30 
1251-3 
1.6292 

3-53 
-1276.8 
1.6561 

3-74 
1301.7 
1.6810 

3-95 
1326.2 

i  •  7043 

4-iS 
1350-6 
i.  7266 

170 

(368.5) 

Sp.  V. 
AQ 
A<f> 

2.68 
II95-4 
1-5590 

2.91 
1225.9 
1-5947 

3-12 

1252.8 
1.6246 

3-34 
1278.4 
1-6513 

3-54 
1303-3 
i  .6762 

3-73 
1327.9 
i  .  6994 

3-92 
1352-3 
1.7217 

180 

(373.i) 

Sp.  V. 
AQ 
A<t> 

2-53 
1196.4 

i  •  5543 

2-75 
1227.2 

i  -  5904 

2.96 

1254-3 
i  .6201 

3.16 
1279.9 
i  .  6468 

3-35 
1304.8 
1.6716 

3-54 
I329-5 
i  .  6948 

3-72 
1353-9 
1.7169 

190    { 

(377-  6)  | 

Sp.  V. 
AQ 
A0 

2.41 
H97.3 
i  •  5498 

2.62 
1228.6 
1.5862 

2.81 

1255.7 
1.6159 

3-00 
1281.3 
1.6425 

3-i9 
1306.3 
1.6627 

3-37 
1330.9 
i  .  6904 

3-55 
1355-5 
1.7124 

200 

(38l.9)| 

Sp.  V. 
AQ 

&4 

2.29 
1198.  i 
i  -  5456 

2.49 
1229.8 
1-5823 

2.68 
1257.1 
i.  6120 

2.86 
1282.6 
1-6385 

3-04 
1307.7 
1.6632 

3.21 

1332-4 
1.6862 

3.38 
1357-0 
i  .  7082 

300 

(417.5) 

Sp.  V. 
AQ 
A0 

i-55 
1204.1 
1.5129 

1.69 
1240.3 
1-5530 

1-83 
1268.2 
1-5824 

1.96 
1294.0 
1.6082 

2.09 

1319-3 
1.6323 

2.21 
1344-3 
I-6550 

2-33 
1369-2 
1-6765 

500 

(467-3) 

Sp.  V. 
AQ 
A0 

0-93 

I2IO.O 
1.470 

1.03 
1256 
1-519 

1.113 
1285 
1-548 

1.22 
I3II 

1-573 

i-3i 
1337 
1-597 

i-39 
1362 
i  .619 

1-47 
1388' 
1.640 

O      10      OI-lflN      O      N     <D    ID  ^     W    "---• 

Vwros  -sai)  3Knss3l'd  simosav 


s. 

^008 


0001 


OOTT 


002T 


008T 


OOH 


(793) 


1500 


ELLEN  WOOD  CHART  (A) 

Reduced  from  six  pages  of  the  Ellenwood 
Cu.  Ft.  per  Pound  Charts  published 

in  book  form  by 
John  Wiley  &  Sons 


12  16  20  24  28  32  36  4O 


5     6     7      8     9    10 
Cu.  Ft.  per  Pound 


12  1C  2O  24  28  32  36  4 


1300 


1200 


1100 


1000 


150 


(794). 


PLATE  IV A.    THE  ELLENWOOD  CHART. 


, 


I,    S     8 1     ELLENWOOD  CHART  (B) 

Reduced  from  six  pages  of  the  Ellenwood 

Charts  published 
Cu.  Ft.  per  Pound 

oo    oo    o    o   oo-      m  book  form  by 

3    §    8    §    §    3   33      John  Wiley  &  Sons 


§§§§§§§ 

»     CO      O     N     3     00     CO 


11OO 


»o   o    ia    o    10    c 

*H     d      N     CO     CO 

Cu.  Ft.  per  Pound 


PLATE  IVB.    THE  ELLENWOOD  CHART  (CONT.) 


(70S) 


796 


APPENDIX 


Heat  Conduction  through  Cylindrical  Walls.  In  the  figure 
assume  the  temperature  inside  the  cylinder  to  be  ti  and  that  at 
the  outer  surface  to  be  /2  (lower),  the  drop  in  temperature  being 
6.  Then  consider  that  there  is  a  temperature  drop  of  dt  through 
the  circular  element  of  thickness  dr  and  of  radius  equal  to  r. 

Then  if  a.  is  the  specific  heat  of  conductivity  (from  page  625) 


dr 


CTl     Ctl    r 
or     A  (2  =  2ira   I        /      -T-. 

«y  r2       »/^2       Q'f 

=  2  TTQ:  (/i  —  4)  lpge 


=  2  ira  6  loge 


where  5  is  the  thickness. 


SYMBOLS. 

(The  numbers  refer  to  the  pages  where  the  symbol  is  first  used  in  a  new  sense.) 
A,  area;  A,  [  j~p  ;  A,  502;  Apu,  107;  ABEf,  537;      (area);  OL,  328. 

B  (Baume);  Bd,  Bdxr,  B/,  Bj  ,  364;  BCEf,  537;  B.P.,  562;  B.t.u.,  i;  b.h.p.,  186. 
C,  257,  326;  C,i4;  Cp,35;  Cv,33;  CEf,  188,  536;  CE/c,64o;  C£/A,64o;  CF,  229; 

C.o.P.,  735;  c  (const.). 
Z?,  in,  579;  DF,  325;  rf  (differential  coefficient);  d,  130,  580;  d.h.p.,  186. 

E,  582;  £/,  82;  Efc,  164,  592,  641;  E/A,  594,  641;  Efn,  372,  e  (base  for  Naperian 

logs.);  e.h.p.,  186. 

F,  36,  575;  FE,  562;  FEf,  536;  /,  575;  f.h-P,  186. 

G,  662;  GEf,  536;  g  (32-2  ft.  sec.). 

H,  338,  580;  #.P.,  234;  A,  257,  578;  h.p.,  180;  h.p.-hr.,  180. 

7,338;  /.P.,  234;  lEf,  189;  i.h.p,  184. 

/, 372. 

K,  335,  572,  639,  698;  Kp,  35;  #r,  34;  KE,  372;  &  (const). 

Z,,  36,  184,  338,  575;  L.P.,  234;  L.H.V.,  488. 

Af,  AT,  502;  MEf,  189;  w,  495;  m.e.p.,  184. 

w,  51,  184,  257,  643,  644,  646. 

OEff,  190;  OEfd,  OEfk,  363. 

/*,  33;   Pm,  324;   PO,  698;    p,  325;  />„»,  l84,    325;    pmff,  pmL:  pmX,  333J    ^,  334- 

Q,  8;  ?,  105;  q/,  q/,  651. 

I?,  32,  258,  315,  328,  372,  626;  REf,  188;  r,  49,  108,  258,  325;  rff,  rL,  rr,  33i- 

S,  572,  626. 

T,  30;    T.,  in;   Tv,  105;   TBEf,  5375   rP£/,  190;   rZ>Jg/jr,  365;  TIEf,  190; 

T.U.E.,  561;  /,  30,  638;  /o4995  <c,  /d,  674;  //,  499,  653;  //,  653;  /»,  /m,  672; 

tv,  105- 

U.E.,  561;  «,  107,  133,  140,  371. 
7,  32,  286,  462;  V,  33,  133;  Vc,  680;  7e8,  719;  Vs,  137;  7»,  680;  7£/,  720; 

»,  286,  371. 
17,  8,  14,  197,  258;  T7C,  239;  Wd,  191,  363;  WW,  363;  Wit  191;  P7/,  T7/A-,  363; 

17,-,  239;  w,  206,  372,  496,  653,  672;  w',  654;  wc,  638;  w/,  205;  w/,  228; 

»«,  205;  WA,  638;  w/r,  496;  w^v,  496. 

X,  481;    *,  1 10,  4795   */•  **»  220. 

y,  108,  476,  481. 
Z,  647;  z>  575; 
",277,625;  /S,  627;  7,38- 

A  (finite  change);  AE,  n;  AEP,  A£,,  158;  A£sx,  I59J  A/,  AQ,  u;  Agfl,  Aft,  m; 
A^ip,  no;  A@a»,  in;  AQVP,  109;  AS,  u;  A0,  66;  A0/>,  A0^,  119;  A0»,  120; 

A0«a,  1 20;   A0V,  119;    A0X,  120. 
0,  259,  626;   00,  06,  639;   dm,  572,  639. 

X,  108;  p,  108;  0,  65;  «,  258. 


797 


INDEX. 


Absolute  temperature,  30. 

velocity,  371. 
Accumulator,  391. 
Adiabatic  changes,  of  gas,  50-53. 

of  sat.  vapor,  153-156. 
of     superheated     vap., 

157-159. 
in  nozzles,  701. 
in  steam  engine,  196. 
reversible,  70. 
Admission,  275,  287. 
After  burning,  409. 

Air,  amt.  for  combustion,  actual,  503-505. 
of  C,  476-482. 
of  H,  486-487. 
deficiency  of,  499. 

excess  coefficient  of,  480,  481,  498,  504. 
properties  of,  477. 
Air  card  (int.  comb,  eng.),  406. 
Air  compressor,  clearance  (effect  of),  719. 
cooling,  724. 
definitions,  716. 
efficiency,  722. 
elementary,  716. 
interceding,  726. 
multistage,  726. 
real,  720. 

volumetric  eff .  of,  722-724. 
work,  717,  718,  720. 
Air  cyles,  air  engines,  730. 

compressors,  716-723. 
Air  engines,  729. 
Air  pumps,  definition,  666. 
size  of,  679. 
types,  677-678. 
Air  required  (see  Air,  amount). 
Air  supply  (see  Air,  amount). 
Air  valve,  auxiliary,  425. 
Alcohol,  469. 

engine  performances,  451. 
Ammonia  compressor,  745. 
refrigerator,  744. 

Analyses  of  coal,  457,  460-462,  509. 
natural  gas,  470. 
producer  gas,  602. 
Analysis  of  flue  gas,  493-502. 
of  coal,  460. 
proximate,  460. 
ultimate,  460. 


Angle  of  advance,  277. 
nozzle,  373. 
range,  301. 
Angularity  of  rod,  connecting,  272,  283-285, 

eccentric,  272,  284. 
Area  (see  Boiler,    Condenser,   Economizer, 

Feed  Heater  and  Grate,  Surface), 
chimney,  581,  583. 
indicator    diagram     (determination), 

184. 
meaning  on  PV-diagr.,  47,  49,  74-79- 

on  T<£-diagr.,  74,  93, 138-140. 
negative,  46,  79. 
nozzles,  703,  705,  710. 
pipe,  711. 

piston,  184,  H.P.  and  L.P.,  328. 
piston  rod  allowance,  323. 
port  opening,  286. 
positive,  46,  78. 
Ash,  459,  464,  510. 

A.S.M.E.  Code,  180,  189,  190,  535,  537,  538. 
Associated  heat,  i,  9,  15. 
Atomizing,  fuel  oil,  530. 
Auxiliaries,  power  plant,  620,  653. 
Auxiliary  air  valve,  425. 

exhaust  ports,  439. 
ports  in  valves,  289. 
Available  hydrogen,  486. 

work  of  cycle,  79. 
Avogadro's  law,  38,  478. 

Back  pressure,  steam  eng.,  214,  354. 

turbines,  367,  394. 
Back  stroke,  271. 
Balance  plate,  290,  291. 

piston  (turbine),  389. 

ring,  292. 

Balanced  valve,  291. 
Barometric  tube  (condenser),  666. 
Bernoulli's  theorem  (flow),  575. 
Bilgram  diagram,  280. 
Blower,  716.    ^;i,;  .' 

producer,  614. 

turbo,  729. 

Blowing  engine,  716,  729. 
Blow-off  valve,  543,  .560. 
Boiler  (see  Boiler  types), 
accessibility,  545. 
accessories,  560. 


799 


8oo 


INDEX 


Boiler  capacity,  563. 

circulation,  542,  546. 
classification,  548. 
cleaning,  545,  547. 
compounds,  687,  688. 
counterflow,  541,  558. 
corrugated  flues,  550,  551. 
energy  stream  for,  534. 
efficiencies,  537,  538,  540. 
explosions,  544. 

feed  water,  547.    (See  Feed  water.) 
header,  554. 
heat  balance,  534. 
heat  transmission,  540. 
heating  surface,  538,  563,  564. 
horse  power,  562. 
losses,  534. 

mud  drum,  543,  554,  556. 
performance,  538,  561. 
plant,  692. 
power,  562. 
rating,  593. 
repairs,  546. 
safety  of,  545. 
selection,  545. 
setting,  549,  551. 
size,  563. 
space,  547,  555. 
steam  space,  547. 
suitability,  545. 
surface,  538-544. 

types,  548-560.    (See  Boiler  types.) 
water  legs,  555. 
Boiler  types,  548-560. 

Babcock  and  Wilcox,  554. 

continental,  550. 

counterflow,  541,  558. 

double  end,  559,  693. 

exposed  tube,  549,  550. 

externally  fired,  548,  551. 

fire  tube,  548,  549. 

full  front,  553. 

half  front,  553. 

Heine,  555. 

horizontal,  548. 

horizontal  return  tubular,  552, 

internally  fired,  548,  549. 

locomotive,  550. 

Niclausse,  559. 

Parker,  558. 

porcupine,  559. 

return  tubular,  552,  553. 

Scotch  marine,  551. 

sectional,  548,  554. 

Stirling,  556. 

submerged  tube,  549,  550. 

tubular,  548,  549. 

tubulous,  548,  554. 

vertical,  548,  549. 

water  tube,  548,  554. 


Boiler  types,  Wickes,  558. 
Boiling,  117. 
Boyle's  law,  29 . 
Brake  horse  power,  iSS. 
Breeching  (see  Flues). 
British  Thermal  Unit,  i,  6. 
B.t.u.  per  h.p.-hr.,  180,  191. 
B.t.u.  (see  Calorific  value). 
Bucket  losses,  370. 

velocity,  360. 
Buckets,  turbine,  359. 
Burner,  oil,  529-532,  gas,  532. 

Calorific  value,  defined  492. 

Dulong's  formula  for,  462, 

463,  492. 

Mahler's  curve  for,  463. 
Calorific  value  of  alcohol,  469. 
carbon,  475. 
carbon  monoxide,  474. 
charcoal,  467. 
coal,  462-466. 
coke,  467. 
hydrogen,  486. 
hydrocarbons,  490—491. 
mixtures,  492. 
natural  gas,  471. 
oils,  468-469. 
producer  gas,  602. 
sulphur,  491. 
wood,  467. 
Calorimeters,  steam,  224-227. 

fuel,  492,  493. 
Cam  shaft,  406. 
Cams,  322,  440. 
Capacity,  boiler,  562. 
furnace,  513. 
hot  air  engine,  398. 
ice  making,  748. 
ice  melting,  748. 
Carbon,  combustion  of,  472-486. 
fixed,  456,  459. 
volatile,  462. 

Carbon  dioxide,  formation,  474,  594. 
and  furnace  eff.,  505. 
refrigeration,  745. 
Carbon  monoxide,  formation,  474,  594. 

method  (of  producer  con- 
trol), 603. 

Carburetors,  423-425. 
Characteristic  curve  (governor),  264. 
Charcoal,  467. 
Charles'  law,  gas,  29-31. 

superheated  vapor,  150. 
Chart,  Mollier,  Ellenwood,  144,  145,  App. 

T<j>,  137,  Appendix. 
Chemical  combination,  heat  from,  3—5* 

equilibrium  (prod.),  594. 
Chimneys,  area  of,  581,  583. 
draft  of,  579- 


INDEX 


801 


Chimneys,  height  of,  580,  581,  583. 
Kent's  formula  for,  582. 
Kingsley's  experiments,  on,  583. 
types  of,  584-585- 
Circulating  pump,  666. 

water  (condenser),  672,  673. 
Circulation,  boiler,  542,  546. 
convection,  629. 
Clapeyron's  equation,  133. 
Clayton's  analysis  of  expansion,  351. 
Clearance,  definition,  203. 

effect  on  compression,  203. 
effect  on  cyl.  condensation,  231. 
in  air  compressors,  719. 
in  internal  comb,  eng.,  404. 
measurement  of,  323,  351. 
radial  (turbine),  386. 
Clinkers  from  coal,  511. 
CO2  recorders,  505. 
COz  (see  Carbon  dioxide). 
Coal,  analysis  of,  460-462,  509. 
anthracite,  457,  458,  465. 
"as  received,"  461. 
bituminous,  456-458,  465. 
briquets,  466,  514. 
caking,  465,  512,  598. 
calorific  value  of  (see  Cal.  value). 
Cannel,  465. 
classification,  456. 
composition,  456,  459. 
Diederich's  formula  for,  462. 
"dry,"  459. 

Dulong's  formula  for,  462. 
dust,  use  of,  466. 
fields  of  U.  S.,  458. 
firing  of,  519,  520. 
formation  of,  455. 
fuel  value  of,  462-466. 
geology  of,  445. 
graphitic,  457. 
Mahler's  curve  for,  463. 
Marks'  curve  for,  461. 
moisture  in,  464. 
noncaking,  465. 

rate  of  combustion  of,  512,  513,  600, 
selection  of,  515-517. 
semianthracite,  457,  458. 
semibituminous,  457,  458,  465. 
sizes  of,  465,  466. 
soft,  456-458. 
sub-bituminous,  457. 
value  as  furnace  fuel,  508-515. 
Coefficient  of  contraction  and  discharge,  715. 
of  excess  air,  480,  481,  498,  504, 

505- 

of  governor  regulation,  257. 
of    performance    (refrigeration), 

735,  739-741,  744, 747- 
Coil,  induction,  434. 
intensifier,  434. 
trembler,  437. 


Coke,  466-467. 

Coking  arch,  524. 

Cold  body,  80. 

Combined  diagram,  multiple-exp.,  349. 

Combustible,  459,  472. 

Combustion,  472-502. 

actual,  503-532. 
air  for,  476-482,  503-505. 
carbon,  472-486. 
complete,  472,  506-508. 
data,  473. 

hydrocarbons,  490-491. 
hydrogen,  486-490. 
line  (int.  comb,  eng.),  411. 
mixtures,  491. 
oxygen  for,  476. 
rate  of,  508,  512-513,  600. 
recorders,  505. 
smokeless,  506-508. 
sulphur,  491. 
surface,  532. 

temperature  of,  482-485. 
Combustion  in  furnaces,  503-532. 
air  for,  503. 

complete,  472,  506-508. 
rate  of,  508,  512-513. 
smokeless,  506-508. 
Commercial  considerations,  622. 

value  of  coal,  508-516. 
value  of  heating  surface,  539. 
Composimeter,  505. 
Composition  of  (see  Analyses  of). 
Compounds,  boiler,  687,  688. 
Compressed  air  (see  Air  compressor). 
Compression,  44,  203. 

adiabatic,  50. 

constant  pressure,  44. 

isothermal,  47. 

pressures  in  int.  comb,  eng., 

table  of,  419. 
quality  during,  214. 
steam  engine,  275,  286,  288, 

293-295- 

Compressors,  turbo,  729.     (See  Air  comp.) 
Condensate,  20. 
Condensation,  cylinder,  229. 
fraction,  229. 
initial,  212. 

reduction  of,  123,  230-243. 
Condenser,  advantages,  673. 
air  in,  665. 

barometric  tube,  666. 
electric  (ignition),  437. 
essentials,  675. 
piping,  667,  677-680. 
pressures,  665. 
pumps,  666,  677. 
steam,  620,  664-677. 
surface  of,  674. 
tail  pipe,  666. 
types,  664-667. 


802  INDEX 

Condensing,  advisability  of,  664.  Cushion  steam,  205. 

gains  from,  235,  367.  Cut-off,  275. 

surface,  675.  changing  in  multi-exp.    eng.,   331, 

water,  20,  672-674.  340-342. 

water  recovery  in,  681.  early,  288,  293,  $95. 

Conduction,  cyl.  losses  by,  214,  223.  governing  int.  comb,  eng.,  429. 

theory  of,  624.  steam  eng.,  256,  352. 

Conductivity  (heat),  625.  influence  on  cyl.  condensation,  232. 

specific  (Table),  628.  in  marine  engines,  338. 

total,  635.  in  simple  engines,  233. 

Conjugate  events,  275.  in  stationary  engines,  337. 

Conservation  of  energy,  6.  limit  of  (Corliss),  312. 

Constant  entropy  changes,  gas,  70.  range,  292. 

vapors,  153-159.  valve,  297,  300,  303. 

Constant  heat  curves  (steam),  142.  Cutting  out  of  nozzles  (turbine),  382. 
Constant   pressure    changes    (see    Isobaric       Cycle,  available  work  of,  79. 

changes.)  Beau  de  Rochas,  94-98. 

Constant  quality  curves  (steam),  140.  Brayton,  98-100. 

Constant  temperature  changes  (see  Isother-  Carnot,  gas,  78-79. 

mal  changes).  reversed,  84,  740. 

Constant  volume  changes  (see  Isovolumic  steam  engine,  194. 

changes.)  vapors,  161. 

Constant  volume  curves,  steam,  140.  Clausius,  167-173,  200-202. 

Constants  for  flue  gas,  479,  481.  closed,  77. 

ideal  gas,  32.  Diesel,  100. 

real  gases,  38-41.  Ericsson,  93-94. 

Consumption  (see  Performance).  four  stroke,  403-414. 

Contact  resistance,  634.  gas,  76-102. 

Continuity  of  state,  121.  Joule,  98-100. 

Convection  (heat),  627.     (See  Boiler  circ.)  losses,  181. 

Conventional  indicator  diagram:  open,  77. 

for  int.  comb,  engine,  406.  Otto,  94-98. 

for  steam  engine,  323-351.  four  stroke,  403-414. 

Cooling  of  condensing  water,  681-684.  two  stroke,  414-417. 

of  internal  comb,  eng.,  407.  Rankine,  173,  189,  190,  201,  202. 

of  producers,  601.  rectangular,  177. 

of  valves  (int.  comb,  eng.),  439.  regenerative,  gas,  90-93- 

ponds,  681.  steam,  199. 

towers,  681-684.  Stirling,  90-93. 

Cost,  depreciation,  622.  two  stroke,  414-417. 

fixed  charges,  623.  vapor,  161-179. 

operating,  623.  Cylinder  arrangement ,  4  2  0-4  2  r . 

St.  Eng.  vs.  Turbine,  393.  condensation,  defined,  229. 

Counterflow,  boiler,  541,  558.  reduction,  230-243. 

defined,  541.  efficiency,  188,  208,  370. 

heat  transmission,  641,  647.  feed,  205,  indicated,  228. 

Cracking  of  oil,  427.  high  pressure,  234. 

in  producers,  608.  lagging,  240. 

Crank  end,  271.  losses,  23,  181. 

Critical  conditions,  122.  low  pressure,  234. 

Critical  pressure,  gas,  122,  714.  ratio,  334~34°- 

steam,  705.  surface  in  clearance,  231. 
Critical  temperature,  gas,  122* 

Critical  velocity  gas,  714.  Dalton's  law,  116;  and  condensers,  665. 

steam,  fol.  Dash  pot,  311. 

Critical  volume,  gas,  122.  Deficiencies  of  air,  losses  from,  499- 

Crosshead,  slotted,  272.  Degree  of  regulation,  257. 

Crude  oil,  467-469.  Degree  of  superheat,  in. 

Culm,  466.  determination  of,  227. 

Cushioning,  286.  Delivered  power,  185. 


INDEX 


803 


Delivered  power,  measurement  of,  186. 
Density,  specific, 
air,  477. 
gases,  40. 

steam,  134,  Appendix. 
Deposits  (scale),  686. 
Depreciation,  622. 
Diagram  (see  also  Valve  diagram). 

adiabatic  changes  of  vapor  on,  157. 

entropy,  119,  Appendix. 

factor,  325-327,  351. 

of  cycle,  PV,  78. 

of    energy    stream    (see    Energy 

stream). 

of  gas  curves,  PV,  43,  T<f>,  73. 
of  gas  cycles,  89-102 . 
of  heat  flow  (see  Energy  steam), 
of  producer  plant,  25,  690. 
of  steam  plant,  18,  691. 
of  T0  changes  of  vapors,  119. 
of  vapor  cycles,  162-179. 
of   vaporization    (heat    changes), 

112. 

steam,  227. 
water  rate,  227,  229. 
Diederich's  equation  (coal),  462. 
Diesel  cycle,  100-102. 

efficiency,  447. 
engine,  417,  427. 
Displacement  of  valve,  273. 
Distillate,  468. 

Double  deck  boiler  plant,  693. 
Draft,  amount  of,  578. 

apparatus,  574-589. 
artificial,  585. 
balanced,  587,  589,  615. 
chimney,  579. 
down,  522,  610. 
forced,  587,  588. 
friction  head,  575,  576. 
furnace,  517-518. 
induced,  587,  589. 
mechanical,  587. 
natural,  579. 

pressure  drop,  517,  574,  578,  581,  582. 
resistance,  574,  577. 
steam  jet,  587,  588. 
Dry  vacuum  pump,  677. 
Dulong's  formula,  462,  463,  492. 
Dutch  oven,  522. 
Dynamics,  of  flow  in  nozzle,  371. 
of  steam  turbine,  371. 

Ebullition,  118. 
Eccentric,  action  of,  274. 

defined,  272. 

for  int.  comb,  eng.,  440. 

relative,  304. 

rod  angularity,  272,  284. 
Econometer,  505. 


Economizer,  boiler  element,  559. 
fuel,  619,  660-663. 
producer,  606. 
surface,  662. 

Economy  (see  Performance). 
Effective  power,  186. 
Efficiency,  air  compressor,  720." 
apparent  (boiler),  537. 
boiler,  535~538. 
boiler  and  grate,  538. 
Bray  ton,  100. 
Carnot,  gas,  82. 

general,  187. 
int.  comb,  eng.,  445. 
steam  engine,  194. 
vapors,  164,  165. 
Clausius,  170,  172. 
cold  gas  (producer),  593. 
combustion  space  (boiler),  536. 
CO-2  and  furnace,  505. 
cycle,  1 88. 

cylinder,  188,  208,  355,  370. 
Diesel,  102,  447. 
Ericsson,  94. 
furnace,  523,  536. 
grate,  523,  536. 
heat  transmission,  639-649. 
hot  air  engine,  400—402. 
indicated,  188,  208,  355,  370. 
internal  comb,  eng.,  445-447. 
mechanical,  189,  224,  413,  446. 
nozzle,  369,  708. 
Otto,  96,  410,  443-447. 
over-all,  190,  211. 
boiler,  538. 

internal  comb,  eng.,  4^7. 
steam  turbines,  363,  366, 

370,  394b. 
producer,  592-594- 
Rankine,  176,  177. 
rectangular  PV,  178,  179. 
refrigeration    (see    Coef.  of  per- 
formance) . 

regeneration,  gas,  92;  steam,  199. 
relative,  188,  445. 
shaft,  370. 

steam  engine,  355-358. 
Stirling,  92. 
thermal,  190,  209,  210,  395,  443, 

446. 

thcrmodynamic  (see  Carnot). 
turbine,  365-370- 
volumetric,  411,  720-724. 
Efficiency  Ratio,  189. 

Electric  energy  (heat),  3;  ignition,  434-438. 
Ellen  wood  Chart,  145,  793,  794,  795. 
Endothermic  reaction,  472 
Energy,  associated  heat,  i,  9,  15. 

change  of  intrinsic,  def.,  n. 

of  gases,  35. 


804 


INDEX 


Energy,  change  of  intrinsic,  of  steam,  156- 

158. 

of  vapors,  108. 
electric  (heat),  3. 
intrinsic,  total,  4. 
kinetic  (flow),  698-702,  708,  709. 
kinetic  (molecular),  10. 
latent  heat,  10-13. 
latent  mechanical,  107. 
potential,  during  vaporization,  13. 

(flow),  698,  699. 
radiant,  630. 
stream,  boiler,  534. 

economizer,  660. 
feed  water  heater,  656,  657. 
general  case,  187. 
internal  comb,  eng.,  445. 
producer,  604. 
producer  power  plant,  25. 
steam  power  plant,  18. 
turbines,  369. 

Engine  economies  (see  Performance). 
Engine  (see  Air   engine,   Blowing  engine, 
Hot  air   engine,   Internal  combustion 
engine,  and  Steam  engine). 
Engine  performance  (see  Performance). 
Engine  room,  694. 
Entropy,  absolute  quantity  of,  72. 
change,  68. 
constant,  70.  , 
of  ideal  gases,  67-72. 
of  liquid,  119. 
of  steam,  132. 
of  superheating,  119. 
of  superheated  vapor,  120. 
of  vaporization,  119. 
total,  of  steam,  137,  Appendix. 
Equalizing  pipe  (turbine),  389 
Equilibrium,  chemical,  594. 
Equilateral  hyperbola,  54,  324. 
Equivalent,  evaporation,  561. 

molecular  weight,  495. 
Ericsson  cycle,  93-94. 

hot-air  engine,  397-401. 
Ether  vapor,  T^-diagram,  154. 
Evaporating  pan,  620,  649. 
Evaporation,  definition,  115. 
equivalent,  561. 
factor  of,  562. 
rates  (boiler),  563. 
unit,  561. 

Events,  valve,  274,  275. 
Excess  air  (combustion),  478-481,  504,  505. 
coefficient,  480,  481,  498,  504. 
percentage,  497. 
Exhaust  lap,  273. 

lap  circle,  282. 

lap  line,  276. 

losses,  int.  comb,  eng.,  448. 

pipe  area,  711. 

ports,  auxiliary,  439. 


Exhaust  valves,  int.  comb,  eng.,  439. 

valve  timing,  441. 
Exhaust  steam,  in  contact  with  walls,  232. 

turbine,  367,  390,  396. 
Exhauster,  induced  draft,  588. 

producer,  614. 
Exothermic  reaction,  472. 
Expansion,  adiabatic,  gas,  50-53. 

in  nozzles,  701. 
in  steam  engines,  196. 
vapors,  153-159- 
constant  pressure   (see  Expan- 
sion, isobaric). 

constant  temperature   (see  Ex- 
pansion, isothermal), 
constant  volume  (see  Expansion, 

isovolumic). 
definition,  44. 
free,  63-64. 

general  curves  of,  54,  55. 
incomplete,  213,  732. 
in  steam  engines,  195,  196. 
isobaric,  of  gas,  44. 

vapors,  146. 
isothermal,  of  gas,  47. 

vapors,  146. 
isovolumic,  of  gas,  46. 

vapors,  159,  160. 
line  (real  hit.  comb,  eng.),  412. 
piping  (of),  696. 
ratio,  48,  330-340. 
valve  (refrigerator),  743. 
Explosions,  boiler,  544. 

producer,  614. 

External  combustion  engine,  397-402.  - 
latent  heat,  10,  13,  107. 
work,  10,  13,  107. 
valve,  273. 
Extractor,  tar,  616. 

Factor  of  evaporation,  562. 

Fan  (draft),  588. 

Feed  water  heaters,  65 1-663  • 

advantages,  651,  655. 

economizer,  660-663. 

heating  surface,  659. 

heat  saving,  651. 

horse  power,  659. 

saving,  651,  655. 

size,  659. 

surface  (extent),  659. 

temperature  increase,  653. 

types,  654-658. 

water  saved,  654. 

Feed  water  impurities  and  treatment,  685. 
Figure  of  merit  (see  Coef.  of  performance). 
Financial  considerations,  622. 
Firing  of  coal,  hand,  519. 

stoker,  520. 

First  law  of  thermodynamics,  6. 
Fixed  carbon,  456,  459. 


INDEX 


805 


Fixed  charges,  623. 
Flame  length,  507,  522. 
Flexible  shaft  (turbine),  376. 
Floor  space,  boiler,  547,  555. 

engine  vs.  turbine,  392. 
Flow,  Bernoulli's  theorem,  575. 
counter  (theory),  641,  647. 
gas  and  vapor,  698-715. 
Grashof's  formula,  710. 
ideal  gas,  712. 
imperfect  gas,  715. 
Napier's  formula,  710. 
parallel,  640,  644. 
pipes  (in),  710. 
saturated  steam,  700. 
unidirectional  (engine),  242. 
velocity  of  gas,  713. 

of  steam,  703. 
Flue  gas  analysis,  477-482,  493-502. 

loss  (see  Stack  losses). 
Flues,  574- 

Fluid  friction  loss,  int.  comb,  eng.,  413. 
Fluttering  of  valve  (air),  721. 
Foaming,  685,  687. 
Foot  pound  (unit),  180. 
Forward  stroke,  271. 
Free  expansion,  63-64. 
Friction,  fluid  (in  int.  comb,  eng.),  413. 
head  (flue  gas),  575. 
horse  power,  186.  f 

losses,  181. 

mechanism,  int.  comb,  eng.,  413. 
steam  engine,  358. 
steam  turbine,  370. 
valve,  291. 
Fuels,  alcohol,  469. 

artificial  gas,  471. 
charcoal,  467. 
coal,  455-467. 
coke,  466—467. 

consumption  of  (see  Performance) 
culm,  466. 
definition  of,  455. 
fuel  oil,  468. 
gasoline,  468. 
graphitic  coal,  457-458. 
industrial  wastes,  467. 
kerosene,  468. 
lignite,  456-458,  465. 
municipal  waste,  467. 
naphtha,  468. 
natural  gas,  470. 
oil,  467-469. 
peat,  456,  464. 
petroleum,  467-469. 
prepared,  455. 
producer  gas,  471,  590,  602. 
wood,  467. 

Fuel  calorimeter,  492. 
Fuel  oil,  468. 


Fuel  oil,  atomizing,  530. 

burning,  529-532. 
Fuel  values  (see  Calorific  values). 
Full  peripheral  discharge,  385. 
Furnace  efficiency,  505. 

capacity,  513. 

fittings,  521. 

grates,  520. 

length,  522. 

losses,  533. 

oil  burning,  529,  gas,  532. 

operation,  517-520. 

rate  of  combustion  in,  513. 

size  for  coal,  513. 
for  oil,  530. 

stokers  (automatic),  523-529. 

types,  521-523. 

volume,  507. 
Fusible  plugs,  560. 

Gain  from  decreasing  back  pressure: 
in  steam  engine,  235.     ^ 
in  steam  turbine,  367,  39^^ 
Gain  from  superheating: 
in  steam  engine,  236,  354. 
in  steam  turbine,  367,  394. 
Gamma,  38. 

value  of,  41 . 
Gas  analyses  (see  Analysis). 

analyses  (flue),  477-483,  493~SO2. 
artificial,  471. 

constants,  ideal,  32;  real,  38-41- 
cycles,  76-102. 
defined,  28,  123. 
expansions,  43—58. 
from  oil,  617. 
furnace  (boiler),  532. 
ideal,  29. 
laws,  28-42. 
natural,  470. 
producer,  471,  590,  602. 
specific  densities  of,  40. 
specific  heats  of,  33-38. 
specific  volumes  of,  41. 
Gas  engines  (see  External  combustion  en- 
gine, Internal  combustion  engine,  and 
Performance). 
Gas  producer,  apparatus  (general),  590. 

carbon    monoxide    method, 

603. 

cooling,  601-607. 
cleaning  apparatus,  615. 
efficiency,  592. 
fuels  for,  607. 
hydrocarbons,      effect      of, 

607. 

limitations,  598. 
mechanical  charging,  615. 
oil,  617. 
size,  600. 


8o6 


INDEX 


Gas  producer,  temperature  control,  603. 
theory,  advanced,  594. 

simple,  590. 
types,  608-615. 

balanced  draft,  615. 
double  zone,  610. 
downdraft,  609-610. 
grate  bottom,  612. 
pressure,  613. 
suction,  614. 
updraft,  608. 
water  bottom,  612. 
Gaseous  state,  region  of,  123. 
Gasoline,  468.     (See  Performance.) 
Gauge  pressure,  182. 
Gay  Lussac's  law,  29. 
Gears,  turbine,  376. 

valve  (see  Valve  gear). 
Governing,  constant  speed,  255. 
cut-off,  256. 
internal     combustion     engine, 

427-431,  441-442. 
isochronous,  260-261. 
methods,  255. 
quality,  429. 
quantity,  429. 
resistance,  255. 
stable,  263. 
steam  engines,  256. 
throttling,  256,  342,  352,  429. 
turbines,  376,  382,  389. 
unstable,  260. 
Governors,  255-270. 

adjustment  of ,  264,  270. 
Armstrong,  269. 
centrifugal,  266. 
characteristics  of ,  264. 
conical,  257. 
flyball,  257-262. 
inertia,  267. 
isochronous,  260,  261. 
loaded,  257. 
pendulum,  257-262. 
Porter,  259. 
Rites,  267. 
shaft,  262-270. 
speed  limitations  of,  258. 
speed  variation  of,  256. 
Sweet,  266. 
theory,  flyball  type,  257. 

shaft  type,  262. 
Watt,  257. 
weighted,  259. 
Grain  alcohol,  469. 
Graphitic  coal,  457~458. 
Grashof's  formula,  710. 
Grates,  area  of,  518. 

boiler,  520-523. 
efficiency  of,  536. 
producer,  612. 


Half  time  shaft,  406. 
Hammering  (of  engine),  287. 
Head  end,  271. 
Header  (boiler),  554. 
Heat,  associated,  i,  15,  19. 
balance,  boiler,  534. 

int.  comb,  engine,  447-449. 
steam  engine  (Hirn's),  219. 
changes  of  intrinsic,  definition,  n. 
gases,  35. 
steam,  156,  158. 
vapors,  108. 
latent,  10,  13,  106-108. 
specific  (see  Specific  heat), 
total,  steam,  130,  137. 

vapor,  1 08. 
Heat  changes  during: 
isobaric  changes  of  gases,  45. 

vapors,  147,  149. 
isothermal  changes  of  gases,  49. 

vapors,  152. 
isovolumic  changes  of  gases,  46. 

vapors,  159, 160. 
Heat  conduction  (theory),  624. 
Heat  conductivity,  625. 
Heat  consumption  (see  Performance). 
Heat  flow  diagram  (see  Energy  stream). 
Heat  from  chemical  combination,  3-5. 
electrical  energy,  3. 
mechanical  energy,  3. 
sun,  2. 

Heat  interchange  with  cylinder,  214-217. 
Heat  of,  combustion,  492. 
liquid,  105,  129. 

area  for,  138. 
meaning  of  term,  108. 
steam,  130. 

area  for,  139. 
superheat,  in,  136,  137. 
vapor,  total,  108. 
vaporization,  latent,  106,  108. 
Heat  resistance,  626. 
Heat  transmission,  actual,  632. 

boiler,  538,  540-544. 
cases  of,  639-650. 
condenser,  675. 
conduction,  624. 
convection,  627. 
economizer,  662. 
feed  water  heater,  659. 
heating  surface,  636. 
radiation,  632. 
superheater,  572. 
(See  Rate.) 
Heat  unit,  i,  6,  561. 
Heat  utilization,  evaporating  pans,  620. 
heating,  621. 
industrial  processes,  620. 
Heat  value,  calorimeters,  492. 

higher,  462,  487-490,  492. 


INDEX 


807 


Heat  value,  lower,  462,  487-49°,  492. 
Heat  value  (see  Calorific  value).    . 
Heater    (see   Feed  water   heaters,    Econo- 
mizers). 
Heating  surface,  boiler,  538,  563. 

commercial  value  of,  539. 

economizer,  662. 

effective,  636. 

extent,  639. 

feed  heater,  659. 

mean    temperature,    637- 

639- 

superheater,  572. 

Heavy  oils  in  internal  comb,  eng.,  426-427. 
Height  of  chimney,  581-583. 
High  pressure  cylinder,  234. 
High  pressure,  effect  on  cylinder  condensa- 
tion, 241,  354. 
on  turbines,  394. 

Higher  heat  value,  462,  487-490,  492. 
Hirn's  analyses,  219-223,  235. 
Horse  power,  boiler,  582. 
brake,  186. 
defined,  180. 
delivered,  186. 
effective,  186. 
friction,  1 86. 

heat  equivalent,  180,  191. 
heater,  659. 
indicated,  183,  184. 
Hot  air  engine,  397-402. 
Hot  body,  80. 

Hot  bulb  (head)  engine,  426. 
Hot  gas  efficiency  (product),  594. 
Hot  well,  20. 

Humidity,  effect  on  stack  losses,  502. 
Hydraulic  inches,  575. 
Hydrocarbons,  490-491. 
Hydrogen,  available,  486. 

combustion  of,  486-490. 
higher  heat  value  of,  487. 
lower  heat  value  of,  487. 
Hyperbola,  equilateral,  54,  324. 

Ice  machine  (see  Refrigeration). 
Ice  making  capacity,  748. 
Ice  melting  capacity,  748. 
Ideal  gas,  29. 

mechanism,  7. 

vs.  real  engine,  180. 

Ignition,  internal  comb,  engine,  433-438. 
Impurities  (feed  water),  685. 
Incomplete  combustion  in  furnace,  472,  481, 

501. 

losses  in  gas  engine,  448. 
Incomplete  expansion,  213,  732. 
Incrustation,  686. 
Indicator,  181. 
Indicator  diagram,  area  of,  184. 

conventional,  323-351,  406. 


Indicator  diagram,  four-stroke  cycle,  406- 

412. 

meaning  of,  182. 
multiple-exp.  eng.,  349. 
scales,  182-187. 
two-stroke  cycle,  415-417. 
Indicated  cylinder  efficiency,  188,  208,  446. 
cylinder  feed,  228. 
horse  power,  183,  184. 
steam  consumption,  227. 
work,  183,  413. 
Induction  coil,  434. 
Initial  condensation  (definition),  212. 
Injection  water  (condenser),  672,  673. 
Injectors,  712. 
Inlet  valve,  internal  comb,  engine,  439. 

timing,  441. 

Insulating  film  (gas),  635. 
Intensifier  coil,  434. 
Intercooling  (air  compressor),  726. 
Interest,  623. 

Interchange  heat  in  engine  cyl.,  214-217. 
Internal  combustion  engine: 

actual,  403-454. 

advantages  and  types  of,  403. 

after  burning,  409. 

air  card,  406. 

cam  shaft,  406. 

cams.  440. 

classification  of,  421-423. 

clearance  space,  404. 

combustion  in,  412. 

combustion  line,  411. 

compression  pressures,  418. 

cooling,  407. 

cylinder  arrangements,  420. 

definition  of,  397. 

diagrams  (indicator),  406-412. 

Diesel,  417,  427,  447. 

double-acting,  420. 

eccentrics,  446.  ^ 

efficiency,  412,  443-454. 

four-stroke  cycle,  403-414. 

fuel  consumption  of  (see  Performance). 

fuels,  418. 

fuels,  modification  for,  418. 

governing,  427-431. 

guarantees,  450-454. 

heat  balance,  447. 

heavy  oil  in,  426,  427. 

hot  bulb  (head),  426. 

ignition  methods,  433-438. 

indicator  diagrams,  406-413. 

indicated  work,  413. 

Koerting,  416. 

losses  in,  410,  447-449. 

mechanical  efficiency  of,  413. 

mechanical  features  of,  420-442. 

oil  engine,  454. 

Otto  efficiency,  413. 


8o8 


INDEX 


Internal  combustion  engine: 
Otto  type,  403. 

performance  (see  Performance), 
power  per  cylinder,  420. 
scavenging,  412. 
size  of,  420. 

single-  and  double-acting,  420. 
suction  line,  409. 
tandem,  422. 
turning  effort  of,  420. 
twin,  422. 

two-stroke  cycle,  403,  414-417. 
valve  gears,  438-442. 
vertical  vs.  horizontal,  421. 
working  substance  of,  403. 
Internal  latent  heat,  10-13,  108  - 
Internal  valve,  273. 
Intrinsic  energy,  4,  n,  35. 

change  of,  n. 
Intrinsic  heat  change,  n. 

gases,  35. 

steam,  145,  156-158. 
vapors,  1 08. 

Irreversible  process,  59^64. 
Isentropic  changes  of  gases,  70. 

vapors,  153-159. 
Isentropics,  70. 

Isobaric  changes  of  gases,  44-45. 
steam,  142. 
vapors,  146-149. 
Isochronous  governing,  260-261. 
Isothermal  changes  of  gases,  44-49. 

vapors,  146-151. 

Isothermal  compression  (steam  engine),  196. 
Isothermal  expansion  (steam  engine),  196. 
Isovolumic  changes  of  gas,  44-47. 
steam,  140. 
vapors,  159-161. 

Jacket  losses,  447. 

Jackets,  air  compressor,  725. 

internal  combustion  engine,  407. 

steam  engine,  238-240. 
Joule's  experiment,  63. 
Junction  box  (boiler),  559. 

Kent's  formula  (chimney),  582. 
Kerosene,  468. 

Kingsley's  experiments  (chimneys),  583. 
Kinetic  energy  of  flow,  general,  698,  700. 
steam,  702. 

Labyrinth  passage,  387. 
Lagged  cylinders,  240. 
Lap,  273,  280,  276,  282. 
Latent  heat,  106-108. 

energy,  10,  13. 

internal,  10,  13. 

Latent  heat  of  vaporization,  external,  107. 
internal,  108. 


Latent  heat  of  vaporization,  total,  108. 
Latent  mechanical  energy,  107. 
Law,  Avogadro's,  38. 
Boyle's,  29. 
Charles',  gas,  29,  31. 

superheated  vapor,  150. 
conservation  of  energy,  6. 
Dalton's,  116. 
gases,  28-33. 
Gay  Lussac's,  29. 
Marriotte's,  29. 
partial  pressures,  117. 
Stefan's,  630. 
thermodynamics,  first,  6. 

second,  8. 
Willans',  352. 
Lead  (valve),  276. 
Leakage,  steam  engine,  214,  230. 

turbines,  369. 
Lignite,  456-458,  465. 
Limitations  of  simple  valve,  288. 

producers,  598. 
Line  of  transference,  329. 
Liquid  and  gaseous  states  (continuity  of), 

121. 

Liquid,  ebullition,  118. 
entropy,  119. 
heat  of,  105,  129. 
pressure  within,  117. 
region  of,  123. 
specific  volume  of,  113. 
Liquid  fuel,  burning,  529-532. 
Load,    distribution    of    (compound    eng.), 

338-341- 

effect  on  water  rate,  233. 
factor,  354. 

range  of  (high-speed  engine),  292. 
Logarithm,  tables,  Appendix, 
use  of,  Appendix. 

Logarithmic  cross-section  paper,  55. 
Loops  (combined  diagrams),  342,  413. 
Losses,  boiler,  534. 
bucket,  370. 

chimney  (see  Losses,  stack), 
cycle,  181. 

cylinder,  23,  181,  214,  223. 
flue  gas,  498. 
friction,  181. 
furnace,  533-536. 
grate,  533~536. 

int.  comb,  eng.,  410,  413,  447-449. 
jacket  (int.  comb,  eng.),  447. 
mechanical,  181. 
nozzle,  369,  708. 
producer,  592-594,  604,  606. 
radiation,  447. 
stack,  498-502. 
steam  engine,  194. 
turbine,  369-370. 
unpreventable  (boiler),  534. 


INDEX 


809 


Low-pressure  cylinder,  234. 
Low-pressure  turbine,  390,  396. 
Lower  heat  value,  462,  487-492. 

MacFarlane-Gray's  formula,  315. 
Mahler's  curve  (coal),  463. 
Marine  propulsion  by  turbines,  391. 
Marks'  curve  (coal),  461. 
Marriotte's  law,  29. 

Maximum  thrust  (compound  engine),  331. 
Maximum  valve  opening,  286,  295. 
Mean  effective  pressure,  184. 

referred,  328. 

Mean  hydraulic  radius,  576. 
Mean  specific  heats  of  gas,  484-485. 

of  superheated  steam,  136. 
Mean  temperature  head,  heat  transmission, 

Cases  I-IV,  639-649. 
Mechanical  energy,  heat  from,  3. 

latent,  107. 

Method  of  ordinates  (area),  185. 
Mixture  of  elements  (combustion  of),  491- 

492. 
Moisture  in  coal,  459,  464,  509. 

loss  in  flue  gas,  502. 
Mollier  chart,  144,  Appendix. 
Motion,  perpetual,  ist  type,  7,  88. 

2d  type,  7,  9,  87,  88. 
3d  type,  7,  85,  88. 
Mud  drum,  543,  555,  556. 
Multipass,  boiler,  554.- 

condenser,  673. 
Multiple  effect,  650. 
Multiple-expansion  engine,  234. 
changing  cut-off  in,  340-342. 
comb  hied  diagrams,  349. 
conventional  diagrams,  327. 
cylinder  ratios,  336-340. 
distribution  of  work,  338. 
expansion  ratios,  336-340. 
indicator  diagram,  340. 
PV-diagram,  348. 
Municipal  waste  (fuel),  467. 

n,  51,  184,  257. 

n,  value  for  air  compressors,  721,  725. 
gas  adiabatics,  52. 
steam  adiabatics,  156. 
Napier's  formula  (flow),  710. 
Naphtha,  468. 
Natural  fuels,  455. 
gas,  470. 
oil,  467-469. 
Neck  of  nozzle,  704,  714. 

Grashof's  rule,  710. 
Napier's  rule,  710. 
Negative  work,  area,  46. 

definition,  79. 
Network,  79. 
Noncaking  coal,  465. 


Nonconducting  materials,  240,  241. 
Normal  power,  353. 
Nozzle,  applications,  712. 

area,  703. 

gas,  712-715. 

Grashof's  formula,  710. 

loss,  369,  708. 

Napier's  formula,  710. 

neck,  704,  714. 

steam,  703,  709. 

Oil,  burning  of,  529-532. 
distillates,  467. 
feeding  systems,  250. 
kinds,  467. 
petroleum,  467. 
producer  gas  from,  617. 
Opening,  diagram,  278. 
early,  287. 
valve,  273. 
Operating  costs,  623. 
Overload  capacity  of  boiler,  563. 
Overload,  effect  on  water  rate,  233- 

valve,  366,  389,  394. 
Oxygen  for  combustion,  476-482. 

Parallel  flow,  640,  644. 
Parr's  classification,  458. 
Partial  pressures,  117. 

in  condensers,  665. 
Passes,  boiler,  554. 

condenser,  673. 
Peat,  456,  464. 
Performance,  boiler,  538,  561. 

coefficient  of,   735-736,    739, 

741,  744,  747. 

comparison  of  (true),  191,354. 
defined,  191. 
heat  basis,  191. 
ice  machines  (see  Refrigera- 
tion). 

int.  comb.eng.,  449-454. 
refrigeration,    735~736,    739, 

741,  744,  747- 

steam  engine,  223,  352-358. 
steam  turbine,  393-396. 
Periods  of  valve  operation,  274. 
Perpetual  motion,  ist  type,  7,  88. 

2d  type,  7,  9,  87,  88. 
3d  type,  7,  85,  88. 
Petroleum,  467-469. 

burning,  529. 
Pipes,  steam  flow  m,  710. 
Piping,  boiler,  697. 

condenser,  667,  677. 
expansion  of,  696. 
feed  water  heater,  659. 
power  plants,  694. 
steam,  694. 
Piston,  balance  (turbine),  389. 


8io 


INDEX 


Piston  speed,  245,  246. 
Pitch  in  producer,  607. 
Planimeter,  184. 
Plant  (see  Power  plant). 
Pond,  cooling,  68 1. 
Port,  areas,  285. 

auxiliary,  in  valves,  289. 
auxiliary  exhaust,  439. 
openings,  285. 
Positive  work  area,  46. 

definition,  78. 
Potential  energy  (flow),  698,  699. 

of  vaporization  (see  Latent  heat). 
Potential  heat,  537. 
Power,  1 80. 

air  refrigeration,  739. 
boiler,  562. 
brake,  186. 
delivered,  186. 
effective,  186. 

external  comb,  eng.,  397,  399. 
friction,  186. 
horse,  180. 
indicated,  184. 

internal  comb,  eng.,  413,  414. 
normal,  353. 
per  cycle,  420. 
producer  gas,  24. 
rated,  353. 

Power  plant,  16,  24,  690-697. 
choice,  690. 

heat  flow  diagram,  18,  25. 
internal  comb,  eng.,  25,  690. 
piping  (see  Piping), 
steam,  16,  690-697. 
Preheater,  compressed  air  engine,  732. 

producer,  606. 
Preignition,  412,  418. 
Prepared  fuels,  455. 
Pressure,  back,  steam  engine,  214. 

turbine,  367. 
compression,  int.  comb,  eng.,  418, 

419. 

constant  (see  Isobaric). 
critical,  gas,  714. 

steam,  705. 
drop  in  flue,  574,  578. 
effect  on  economy,  241,  354,  394. 
gauge,  182. 
heating  system,  621. 
mean  effective,  184. 
m.e.p.,  184. 
of  mixture,  117. 
referred  m.e.p.,  328. 
stages  (turbine),  381. 
usual  steam,  241. 
within  a  liquid,  117. 

Pressure-volume  diagram  (area),  47,  74,  79. 
Price  of  coal,  basis  of,  509. 
Prime  mover,  16, 


Process,  irreversible,  59-64. 

reversible,  59. 
Producer  gas,  500-618. 

analyses,  602. 
oil,  617. 
plant,  24. 

Producers  (see  Gas  producers). 
Progressive  distillation  of  vol.  matter,  525. 

oil,  468. 

Progressive  specific  heat  (steam),  130. 
Properties  of  air,  477. 

gases  (see  Gas  constants), 
steam,  126-145,  Appendix. 

sources,  127. 

Propulsion  by  turbine,  391. 
Proximate  analysis  of  coal,  460-462. 
Pumps,  air,  667,  677-680. 
circulating,  666. 
dry  vacuum,  677. 
feed,  697. 
tail,  667,  669. 
vacuum,  666,  677-680. 
wet  vacuum,  678. 
PV-quantity,  345-347- 

Q,  8;  q,  105. 

Quadruple  expansion  engine,  234,  339. 

Quality,  no. 

curves,  139,  154,  206,  351. 

during  compression,  214. 

factor,  no. 

Quality  governing,  429. 
Quantity  governing,  429. 
Quintuple  expansion  engine,  234. 


r,  49,  131,  334- 

R,  32,  38,  40,  41,  334. 

Racing,  427. 

Radial  clearance  (turbine),  386. 

Radiant  energy,  630. 

Radiation  (heat),  629. 

losses,  in  int.  comb,  engine,  447. 
in  steam  engine,  214,  223. 
in  turbine,  370. 
misuse  of  term,  632. 
Range,  angle,  301. 

of  cut-off,  292. 

Rankine  Cycle  Ratio,  189,  190. 
Rate  of  combustion  of  coal,  512-513. 
combustion  and  smoke,  508. 
consumption  of  working  substance, 

191. 

fuel  consumption,  191. 
See    Performance,     Heat    Trans- 
mission. 
Rated  power,  353. 

boiler,  563. 
Rating  of  boiler,  563. 

refrigeration  mach.,  748. 


INDEX 


811 


Ratio  of  expansion,  48. 

in  multiple  exp.  eng.,  334,  340. 
in  simple  eng.,  234. 
Reaction,  endothermic,  472. 
exothermic,  472. 
reversing,  476. 
Real  and  ideal  engines,  180. 
Receiver,  air,  732. 

infinite,  330. 
line,  329. 
reheating,  240. 
steam  engine,  240,  251. 
Receiver  pressure,  formula  for,  335. 
selection  of,  331. 
with  no  clearance,  332. 
Reciprocating  parts,  244. 

cushioning  of,  286. 
Rectangular  PV-diagram,  177-179. 
Referred  m.e.p.,  328. 
Refrigeration,  air  machine,  738. 

absorption  process,  746. 

ammonia,  746. 

coefficient    of    performance, 

735,  739,  74i,  744,  747- 
materials  for,  744. 
mechanical,  734. 
rating,  748. 

thermodynamics  of,  734. 
vapor  compr.  machine,  741. 
vapors,  kinds,  744. 
Regenerator,  90. 

turbine,  391. 

Region  of  gaseous  and  liquid  state,  123. 
saturation,  114. 
superheat,  114-123. 
Regulation  coefficient,  257. 
Reheating  receiver,  240. 
Relative  eccentric,  304. 
velocity,  371. 
Release,  275.  &\ 

early,  288,  293,  295,  347. 
Resistance,  contact,  634. 

governing,  255. 
heat,  626. 
surface,  634. 

Resistance  to  flow  (flue  gas),  574. 
Reversed  Carnot  cycle,  84. 

refrigeration,  740. 
Reversed  chemical  reaction,  476. 
Reversible  adiabatics,  70. 
isentropics,  70. 
processes,  59. 
Reversibility,  59-64- 
Revolutions  per  minute,  246. 

effect  on  cyl.  cond.,  241. 
Rider  hot-air  engine,  398,  400. 
Ripper's  experiment  (sup.  steam),  237. 
Rites'  inertia  governor,  267. 
Rotary  air  pump,  678. 
engines,  248. 


Rotating  parts  of  st.  eng.,  244. 
Rotative  speed,  effect  on  cyl.  cond.,  241. 

of  Corliss  engines,  246. 
Rotor,  359. 
Running  over  and  under,  250. 

Safety  cam,  313. 

valve,  560. 
Saturated     steam,     properties,      126-135, 

Appendix. 
Saturated  vapors,  109,  in. 

defining  condition  of,  115 
properties  of,  103-110. 
Saturation  curve,  113. 

for  mult.  exp.  eng.,  351. 
steam,  139,  206. 
Scale,  boiler,  686. 

of  indicator  diagram,  182-183. 
Scavenging  engine,  412. 
Scotch  yoke,  272. 
Scrubber,  dry,  wet,  616. 
Second  law  of  thermodynamics,  8,  9. 
Sensible  heat,  1 1 . 

change  of,  36. 
flue  gas,  501. 
producer  gas,  593,  601. 
Sentinel  whistle,  560. 
Separator,  steam,  697. 
Shaft  for  high-speed  turbine,  376. 

half  time,  406. 
Shroud  ring,  376. 
Simple  engine  vs.  compound,  233. 
Single  effect  vacuum  pan,  649. 
Sleeve  motors,  438. 
Slide  valve  (see  Valves). 
Slotted  crosshead,  272. 
Smoke,  composition  of,  508. 

prevention  of,  506-508. 
Soft  coal,  456-458. 
Solar  heat,  2. 
Spark  plug,  436. 
Specific  density  of  gases,  38-41. 

steam,  134,  Appendix. 
Specific  heat,  14. 

conductivity,  625,  628. 
gases,  484-485. 
ideal  gas,  33-35- 
mean,  14. 
progressive,  130. 
steam,  130. 
superheat,  135-136. 
true,  15-34. 
variable,  15. 
Specific  volume  of  gases,  38-41. 

steam,  133,  Appendix, 
super,  steam,  137. 
vapors,  113. 
Speed,  piston,  245,  246,  286. 

rotative,  effect  on  cyl.  cond.,  241. 

of  low-speed  engines,  246. 


8l2 


INDEX 


Spontaneous  ignition,  418,  434. 
Stack  (see  Chimney),  losses,  498-502. 
Stagnant  film,  635. 
State,  continuity  of,  121. 
Steam  data,  127. 

properties  of,  126-145,  Appendix, 
saturated  (table),  Appendix, 
specific  heat  of,  130-136. 
superheated,  135-137,  Appendix. 
Steam,  behavior  of,  in  cylinder,  208-229. 
Steam  calorimeter,  224-227. 
Steam  consumption  (see  Performance). 
Steam  distribution  chart,  344. 
Steam  engine  (see  Steam  engine  types): 
action  of  steam  in,  208-229. 
Carnot  cycle  and,  194. 
classification  of,  245-254. 
compared  with  turbine,  360. 
comp.  and  exp.  lines,  195-196. 
consumption,  197-202,  352-358. 
cycles,  161-179,  194-207. 
cylinder  condensation,  230-243. 
diagrams  (indicator),  323-351. 
efficiencies,  186-191. 
data,  356-358. 
governors,  255-270. 
jackets,  238-240. 
losses,  194. 
parts,  244. 
performance,  353-358. 

data,  354-358. 
determination,  223. 
steam  consumption,  actual,  205,  352-358. 

indicated,  227. 
theoretical,  194-207. 

types,  245-254  (see  Steam  engine  types), 
valves  and  gears,  271-322. 
water  rate,  actual  curves,  232. 
data,  354-358. 
defined,  224. 
diagram,  229. 
Steam  engine  types: 

angle  compound,  252. 

center  crank,  250. 

compound,  233,  234. 

Corliss,  247. 

cross  compound,  251. 

double  acting,  248. 

duplex  compound,  252. 

high  speed,  245,  292,  293,  308. 

inclosed,  250. 

lokomobile,  240. 

left  hand,  249. 

low  speed,  246. 

marine,  253,  338. 

medium  speed,  246. 

multiple  expansion,  335. 

oscillating,  249. 

quadruple  expansion,  234,  339. 

quintuple  expansion,  234. 


Steam  engine  types: 

reciprocating,  248. 
reversing,  254. 
right  hand,  249. 
self  oiling,  250. 
side  crank,  249. 
single  acting,  248. 
steeple  compound,  251. 
straight  flow,  242. 
tandem,  250. 

triple  expansion,  234,  336,  338. 
unidirectional  flow,  242. 
Woolf,  328. 
Steam  heating,  621. 
Steam  injector,  712. 
Steam  jacketing,  238-240. 
Steam  jets,  587,  588. 

blowers  (producer),  613. 
Steam  nozzle  (see  Nozzle),  703. 
Steam  pipes  (see  Pipes),  711. 

piping,  694. 

Steam  power  plants,  16,  690-697. 
Steam  properties  (see  Steam). 
Steam  turbine,  359-396. 
accumulator,  391. 
advantages,  392. 
Allis-Chalmers,  389. 
applications,  390. 
back  pressure  (effect),  367. 
Bliss,  384. 
Branca's,  359. 
classification, 
clearance,  386. 
Curtis,  375,  380. 
defined,  359. 
De  Laval,  373. 
dynamics,  371. 
double  flow,  386. 
efficiency,  363-365. 
Electra,  382. 
energy  stream,  369. 
exhaust  steam,  367,  390,  396 
flexible  shaft,  376. 
gears,  376. 

governing,  368,  382,  389. 
heat  supplied,  364. 
Hero's,  359. 
impulse,  359,  360. 
Kerr,  379. 
labyrinth,  387. 
leakage,  367. 
losses,  369-370. 
low  pressure,  367,  390,  396. 
marine  propulsion,  391. 
multi-stage,  361,  379,  390. 
nozzle,  359-361. 
losses,  369. 
theory,  697-715. 
overload,  capacity,  366. 
valve,  366,  394. 


INDEX 


813 


Steam  turbine,  Pelton,  379- 

performance  of  (see  Performance). 

Parsons,  375,  387- 

pilot  valve,  382. 

pressure  stage,  381. 

Rateau,  374,  379,  394- 

reaction,  360,  384,  387. 

Riedler-Stumpf,  383. 

rotor,  359. 

shroud  ring,  376. 

single-stage,  379. 

small  vs.  large,  395. 

Sturtevant,  384. 

superheated  steam  with,  367. 

Terry,  383. 

tests,  395. 

thermodynamics  of,  362,  369. 

velocity  compounding,  380,  382. 

water  rate,  363,  365. 

water  seal,  379. 

Westinghouse-Parsons,  389. 

windage,  365. 

Zoelly,  374,  380. 
Stefan's  law  (radiation),  630. 
Stokers,  520,  523-529. 
Stoking  (see  Firing). 
Stratification,  furnace  gases,  507 
Stroke,  back,  271. 

forward,  271. 
Suction  line,  409. 

producer,  614. 
Sulphur,  combustion  of,  491. 

dioxide  refrigeration,  745. 

in  coal,  464,  511. 
Superheat,  degree  of,  in. 

determination  of,  227. 
Superheated  steam  (see  Steam),  effect  on, 
cylinder  cond.,  236-238,  354. 

steam  turbine,  367,  394. 
Superheated  vapor,  in. 

Charles'  law  for,  150. 
properties  of,  111-115. 
region,  123. 
Superheater,  127,  565-573. 

advantages,  236-238,  367,  565. 
arrangements,  567. 
protection  of,  571. 
surface,  572. 
types,  566. 
Surface,  boiler,  538,  563. 

combustion,  532. 

condenser,  675. 

economizer,  662. 

effect  of  clearance,  231. 

feed  water  heater,  659. 

resistance,  634. 

superheater,  572. 

water  in  boiler,  546. 
t,30. 
T.30. 


T^-diagram,  chart,  Appendix. 

derived  from  PV,  217,  218. 
Table  I,  40;  II,  58;  III,  102;  IV,  241;  V,  325; 
VI/325J  VII,  355;  VIII,  358;  IX,  358; 
X,  395;  XI,  419;  XII,  443;  XIII,  457; 
XIV,  458;  XV,  460;  XVI,  465;  XVII, 
466;  XVIII,  470;  XIX,  473;  XX,  477; 
XXI,  479;  XXII,  481;  XXIII,  491; 
XXIV,  578;  XXV,  602;  XXVI,  628. 
Tables,  air,  properties  of ,  477. 

coal  classification,  old,  457. 

Parr's,  458. 
sizes,  465,  466. 
coal,  ultimate  analyses,  460. 
combustion  data,  473. 
compression  pressures,  419. 
conductivities,  628. 
diagram  factors,  325. 
draft  through  boilers,  578. 
efficiencies,  steam  engine,  358. 

Otto  engine,  443. 
flue  gas  constants,  479,  481. 
formulas,  volume  changes  of  gases, 

58. 

gas  constants,  40. 
cycles,  102. 
expansions,  58. 
hydrocarbons,  491. 
logarithms,  Appendix, 
natural  gas,  470. 
Parr's  classification  (coal),  458. 
performance,  steam  eng.,  355,  358. 

turbines,  395. 

pressure  drops,  flue  gas  in  boiler,  578. 
producer  gas,  602. 
steam,  saturated,  Appendix. 

superheated,  Appendix, 
steam  pressures,  usual,  241. 
symbols,  Appendix, 
volume  changes  (gas),  58. 
(i  +  loge  r)  -H  r,  325. 
Tail  pipe,  666. 

pump,  669. 
Tar  extractor,  616. 

in  producer,  607. 
Temperature,  absolute,  30. 

control  (producer),  603-605. 
from  combustion,  482-485. 
head,  mean,  639-649. 
range  (comp.  eng.),  331. 
vaporization,  105. 

Temperature-entropy,  changes  of,  gases,  72. 
vapors,  1 1 8. 
chart,  138,  143,  Ap- 
pendix. 

Tests  (see  Performance). 
Thermal  equilibrium,  vapor  and  liquid,  109. 
Thermal  value  (see  Calorific  value). 
Thermodynamics,  defined,  xvi. 
Throttled  steam,  211,  212. 


8 14  INDEX 


Thrust  bearing  (turbine),  389. 

maximum  (comp.  eng.),  332« 
Time  element  (cyl.  condensation),  231. 
Timer  (ignition),  436. 
Timing  opening,  441. 

valves,  434. 

Transmission  of  heat  (see  Heat  trans.) 
Traps,  697. 
Travel,  valve,  273. 
Trip  cut-off,  309. 
Triple  effect  (vacuum  pan.),  650. 
True  comparison  of  performance,  354. 
Try  cocks,  560. 
Tubes  (boiler)  exposed,  549. 

replacing,  547,  548. 

submerged,  549. 
Tumlirz's  equation,  137. 
Turbines  (see  Steam  Turbine). 
Turbo-compressors,  729. 
Turf,  456. 
Turning  effort,  int.  comb,  eng.,  420. 

uniformity  of,  332. 


u,  107,  133,  140. 
Ultimate  analysis  (coal),  460. 
Uncombined  hydrogen,  486. 
Underload,  effect  on  water  rate,  233. 
Unit  of  evaporation,  561. 

heat,  i,  6. 

work,  1 80. 
Uptakes  (see  Flues). 
Upton's  Curves  (sp.  ht.),  484,  485. 
U.  S.  coal  fields,  458. 

v,  286,  V,  32,  V,  33,  133,  286. 
Vacuum,  effect  on  steam  eng.,  235,  354. 

on  turbine,  367,  394. 
Valve  (see  Valve  types), 
action,  274. 
balancing,  291. 
definition,  272-273. 
diagrams,  274-288.    (See  Valve  gear 

diagrams.) 
events,  274. 
fluttering,  721. 
friction,  291. 

gears,  271-322.     (See  Valve  gears.) 
lead,  276. 
limitations,  288. 
opening,  273,  285-287,  295. 
steam  velocity  through,  286. 
travel,  273. 

types  (see  Valve  types). 
Valve  gears,  Allan  link  gear,  316. 
Buckeye,  302. 
cam,  322. 

Corliss,  H.  S.,  293,  308. 
L.  S.,  307-314* 
rod,  315. 


Valve  gears,  diagrams  (see  Valve  gear  dig 

grams). 

double  eccentric  Corliss,  313. 
floating  lever,  322. 
Gooch,  316. 
high  speed,  292,  293. 
independent  cut-off,  297. 
int.  comb,  eng.,  438-442. 
Joy,  319- 
link,  314-317. 
low  speed,  307-314. 
Mclntosh-Seymour,  306. 
Marshall,  318. 
Meyer,  304. 
open  rod,  315. 
oscillating,  307. 
poppett,  321. 
Porter- Allen,  317. 
radial,  317-321. 
riding  cut-off,  297,  302-307. 
Russell,  304. 

single  eccentric  Corliss,  309. 
Stephenson,  314. 
trip  cut-off,  309. 
Walschaert,  320. 
Valve  gear  diagrams,  Bilgram,  280,  299. 

elliptical,  277,  299. 

oval,  285. 

polar,  275. 

rectilinear,  275. 

Sweet,  278,  299. 

valve  openings,  278. 

Zeuner,  279,  285. 
Valve  types,  Allen,  289. 

auxiliary  air,  425. 

auxiliary  ported,  289. 

balanced,  291. 

blow  off,  560. 

carburetting,  424. 

cooled  (gas),  439. 

Corliss,  308,  309. 

cut-off  (riding),  297,  302-30^ 

double  ported,  289. 

D-valve,  271. 

exhaust,  439,  441. 

external,  273. 

gas,  431. 

gridiron,  306. 

inlet,  439,  44i- 

automatic,  439. 
main,  297. 
marine,  289. 
mixing,  423,  431,  432. 
multiport,  289. 
mushroom,  438. 
oscillating,  307. 
overload,  turbine,  366. 
pilot,  382. 
piston,  288. 
poppet,  321,  322,  438. 


INDEX 


8*5 


Valve  types,  proportioning  (gas),  431. 
relief,  292. 

riding  cut-off,  297,  302-307. 
safety,  560. 
sleeve,  438. 
slide,  gas,  438. 
stop,  560. 
Sweet,  290. 
Trick,  289. 
trip  cut-off,  309. 
Woodbury,  291. 
Van  der  Waal's  equation,  123. 
Vapor,  cycles,  161-179. 
defined,  103,  123. 
dry,  109. 
ether,  154. 
expansion,  114. 
formation,  103. 
heat,  108. 

properties,  111-115. 
region,  123. 
saturated,  109,  in. 
superheated,  in. 
table  (discussion),  113. 
^  wet,  109. 

Vaporization,  heat  of,  106-108. 
Vaporizer  (producer),  606. 
Velocity,  absolute,  371. 
bucket,  360. 
chimney  gases,  582. 
compounding,  380,  382. 
critical  (nozzle),  gas,  714. 

steam,  705. 

diagram  (turbine),  360. 
flow,  flue  gas,  576. 
gas,  713. 
steam,  702. 
jet,  360,  373. 
piston,  246,  286. 
relative,  371. 
steam  through  ports,  286. 
Volatile  matter  (coal),  456,  459,  506-510. 
Volume  changes,  gas,  53,  58. 

vapors,  146-160. 
Volumes,  gases  (see  Gas  constants). 

gas  (from  comb,  of  C),  477-482. 
steam,  saturated,  133,  Appendix, 
superheated,  137,  Appen- 
dix, 
water,  113. 

Water,  condensing,  20,  672-674. 
column,  560. 
curve,  138. 
gauge,  560. 

injection  (air  comp.),  725. 
jacket,  405,  407,  725. 


Water,  legs,  555. 

purification,  685-689. 
rate  (see  Water  rate), 
seal,  turbine,  379. 

producer,  612. 
specific  heat,  130. 
treatment,  685-689. 
volume,  113. 
Water  rate,  224. 

steam  eng.,  198,  201,  355,  358. 
steam  turbine,  363,  391,  393- 

395- 
Water  rate  curves,  steam  engine,  232. 

turbine,  363,  365,  392. 
Weight,  air,  477. 

flue  gas,  495,  497~499>  SOL 
gases  (see  Gas  constants). 
See  Air  for  combustion. 
See  Oxygen  for  combustion. 
Wet  vacuum  air  pump,  678. 
Wet  vapor  method  (producer),  605. 
Wetness  factor,  206. 
Whistle,  sentinel,  560. 
Willans'  law,  352. 
Windage,  365. 

loss,  370. 

Wiredrawing,  211. 
Wood  (fuel),  467. 

Work,  areas  (positive  and  neg.),  46. 
positive  and  negative,  78-79. 
Work  done  on  and  by  piston,  23. 

area  for,  47,  49,  74-79. 
Work,  equalization  (multi.  exp.  eng.),  332, 

335,  341,  342. 
Work  during  changes,  adiabatics,  gas,  51. 

vapor,  156. 
isobarics,  gas,  45. 

vapor,  149,  151. 
isothermals,  gas,  48. 

vapor,  151. 
isovolumics,  gas,  47. 
Work  of  cycles,  Brayton  (Joule),  99. 
Carnot,  gas,  79-82. 

vapor,  162,  165. 
Clausius,  169,  172. 
Diesel,  101. 
Ericsson,  93. 

Otto  (Beau  de  Rochas),  95. 
Rankine,  175,  176. 
rectangular  PV,  178, 179. 
Stirling,  92. 
Working  substance,  76,  397,  403. 


Zero,  absolute,  30, 


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